Chakradhar Guntuboina, Adrita Das, Parisa Mollaei et al.
Recent advances in Language Models have enabled the protein modeling community with a powerful tool since protein sequences can be represented as text. Specifically, by taking advantage of Transformers, sequence-to-property prediction will be amenable without the need for explicit structural data. In this work, inspired by recent progress in Large Language Models (LLMs), we introduce PeptideBERT, a protein language model for predicting three key properties of peptides (hemolysis, solubility, and non-fouling). The PeptideBert utilizes the ProtBERT pretrained transformer model with 12 attention heads and 12 hidden layers. We then finetuned the pretrained model for the three downstream tasks. Our model has achieved state of the art (SOTA) for predicting Hemolysis, which is a task for determining peptide's potential to induce red blood cell lysis. Our PeptideBert non-fouling model also achieved remarkable accuracy in predicting peptide's capacity to resist non-specific interactions. This model, trained predominantly on shorter sequences, benefits from the dataset where negative examples are largely associated with insoluble peptides. Codes, models, and data used in this study are freely available at: https://github.com/ChakradharG/PeptideBERT
Kazem Meidani, Parshin Shojaee, Chandan K. Reddy et al.
In an era where symbolic mathematical equations are indispensable for modeling complex natural phenomena, scientific inquiry often involves collecting observations and translating them into mathematical expressions. Recently, deep learning has emerged as a powerful tool for extracting insights from data. However, existing models typically specialize in either numeric or symbolic domains, and are usually trained in a supervised manner tailored to specific tasks. This approach neglects the substantial benefits that could arise from a task-agnostic multi-modal understanding between symbolic equations and their numeric counterparts. To bridge the gap, we introduce SNIP, a Symbolic-Numeric Integrated Pre-training model, which employs contrastive learning between symbolic and numeric domains, enhancing their mutual similarities in the embeddings. By performing latent space analysis, we observe that SNIP provides cross-domain insights into the representations, revealing that symbolic supervision enhances the embeddings of numeric data and vice versa. We evaluate SNIP across diverse tasks, including symbolic-to-numeric mathematical property prediction and numeric-to-symbolic equation discovery, commonly known as symbolic regression. Results show that SNIP effectively transfers to various tasks, consistently outperforming fully supervised baselines and competing strongly with established task-specific methods, especially in the low data regime scenarios where available data is limited. Code and model are available at: https://github.com/deep-symbolic-mathematics/Multimodal-Math-Pretraining
Data-driven learning of partial differential equations' solution operators has recently emerged as a promising paradigm for approximating the underlying solutions. The solution operators are usually parameterized by deep learning models that are built upon problem-specific inductive biases. An example is a convolutional or a graph neural network that exploits the local grid structure where functions' values are sampled. The attention mechanism, on the other hand, provides a flexible way to implicitly exploit the patterns within inputs, and furthermore, relationship between arbitrary query locations and inputs. In this work, we present an attention-based framework for data-driven operator learning, which we term Operator Transformer (OFormer). Our framework is built upon self-attention, cross-attention, and a set of point-wise multilayer perceptrons (MLPs), and thus it makes few assumptions on the sampling pattern of the input function or query locations. We show that the proposed framework is competitive on standard benchmark problems and can flexibly be adapted to randomly sampled input.
Machine learning models are gaining increasing popularity in the domain of fluid dynamics for their potential to accelerate the production of high-fidelity computational fluid dynamics data. However, many recently proposed machine learning models for high-fidelity data reconstruction require low-fidelity data for model training. Such requirement restrains the application performance of these models, since their data reconstruction accuracy would drop significantly if the low-fidelity input data used in model test has a large deviation from the training data. To overcome this restraint, we propose a diffusion model which only uses high-fidelity data at training. With different configurations, our model is able to reconstruct high-fidelity data from either a regular low-fidelity sample or a sparsely measured sample, and is also able to gain an accuracy increase by using physics-informed conditioning information from a known partial differential equation when that is available. Experimental results demonstrate that our model can produce accurate reconstruction results for 2d turbulent flows based on different input sources without retraining.
Accurate and efficient prediction of polymer properties is of great significance in polymer design. Conventionally, expensive and time-consuming experiments or simulations are required to evaluate polymer functions. Recently, Transformer models, equipped with self-attention mechanisms, have exhibited superior performance in natural language processing. However, such methods have not been investigated in polymer sciences. Herein, we report TransPolymer, a Transformer-based language model for polymer property prediction. Our proposed polymer tokenizer with chemical awareness enables learning representations from polymer sequences. Rigorous experiments on ten polymer property prediction benchmarks demonstrate the superior performance of TransPolymer. Moreover, we show that TransPolymer benefits from pretraining on large unlabeled dataset via Masked Language Modeling. Experimental results further manifest the important role of self-attention in modeling polymer sequences. We highlight this model as a promising computational tool for promoting rational polymer design and understanding structure-property relationships from a data science view.
Numerically solving partial differential equations typically requires fine discretization to resolve necessary spatiotemporal scales, which can be computationally expensive. Recent advances in deep learning have provided a new approach to solving partial differential equations that involves the use of neural operators. Neural operators are neural network architectures that learn mappings between function spaces and have the capability to solve partial differential equations based on data. This study utilizes a novel neural operator called Hyena, which employs a long convolutional filter that is parameterized by a multilayer perceptron. The Hyena operator is an operation that enjoys sub-quadratic complexity and state space model to parameterize long convolution that enjoys a global receptive field. This mechanism enhances the model's comprehension of the input's context and enables data-dependent weight for different partial differential equations instances. To measure how effective the layers are in solving partial differential equations, we conduct experiments on Diffusion-Reaction equation and Navier Stokes equation. Our findings indicate Hyena Neural operator can serve as an efficient and accurate model for learning partial differential equations solution operator. The data and code used can be found at: https://github.com/Saupatil07/Hyena-Neural-Operator
Metal-Organic Frameworks (MOFs) are materials with a high degree of porosity that can be used for applications in energy storage, water desalination, gas storage, and gas separation. However, the chemical space of MOFs is close to an infinite size due to the large variety of possible combinations of building blocks and topology. Discovering the optimal MOFs for specific applications requires an efficient and accurate search over an enormous number of potential candidates. Previous high-throughput screening methods using computational simulations like DFT can be time-consuming. Such methods also require optimizing 3D atomic structure of MOFs, which adds one extra step when evaluating hypothetical MOFs. In this work, we propose a structure-agnostic deep learning method based on the Transformer model, named as MOFormer, for property predictions of MOFs. The MOFormer takes a text string representation of MOF (MOFid) as input, thus circumventing the need of obtaining the 3D structure of hypothetical MOF and accelerating the screening process. Furthermore, we introduce a self-supervised learning framework that pretrains the MOFormer via maximizing the cross-correlation between its structure-agnostic representations and structure-based representations of crystal graph convolutional neural network (CGCNN) on >400k publicly available MOF data. Using self-supervised learning allows the MOFormer to intrinsically learn 3D structural information though it is not included in the input. Experiments show that pretraining improved the prediction accuracy of both models on various downstream prediction tasks. Furthermore, we revealed that MOFormer can be more data-efficient on quantum-chemical property prediction than structure-based CGCNN when training data is limited. Overall, MOFormer provides a novel perspective on efficient MOF design using deep learning.
Parshin Shojaee, Kazem Meidani, Amir Barati Farimani et al.
Symbolic regression (SR) is a challenging task in machine learning that involves finding a mathematical expression for a function based on its values. Recent advancements in SR have demonstrated the effectiveness of pre-trained transformer-based models in generating equations as sequences, leveraging large-scale pre-training on synthetic datasets and offering notable advantages in terms of inference time over classical Genetic Programming (GP) methods. However, these models primarily rely on supervised pre-training goals borrowed from text generation and overlook equation discovery objectives like accuracy and complexity. To address this, we propose TPSR, a Transformer-based Planning strategy for Symbolic Regression that incorporates Monte Carlo Tree Search into the transformer decoding process. Unlike conventional decoding strategies, TPSR enables the integration of non-differentiable feedback, such as fitting accuracy and complexity, as external sources of knowledge into the transformer-based equation generation process. Extensive experiments on various datasets show that our approach outperforms state-of-the-art methods, enhancing the model's fitting-complexity trade-off, extrapolation abilities, and robustness to noise.
Graph neural networks (GNNs), which are capable of learning representations from graphical data, are naturally suitable for modeling molecular systems. This review introduces GNNs and their various applications for small organic molecules. GNNs rely on message-passing operations, a generic yet powerful framework, to update node features iteratively. Many researches design GNN architectures to effectively learn topological information of 2D molecule graphs as well as geometric information of 3D molecular systems. GNNs have been implemented in a wide variety of molecular applications, including molecular property prediction, molecular scoring and docking, molecular optimization and de novo generation, molecular dynamics simulation, etc. Besides, the review also summarizes the recent development of self-supervised learning for molecules with GNNs.
AmirPouya Hemmasian, Francis Ogoke, Parand Akbari et al.
Powder-based additive manufacturing has transformed the manufacturing industry over the last decade. In Laser Powder Bed Fusion, a specific part is built in an iterative manner in which two-dimensional cross-sections are formed on top of each other by melting and fusing the proper areas of the powder bed. In this process, the behavior of the melt pool and its thermal field has a very important role in predicting the quality of the manufactured part and its possible defects. However, the simulation of such a complex phenomenon is usually very time-consuming and requires huge computational resources. Flow-3D is one of the software packages capable of executing such simulations using iterative numerical solvers. In this work, we create three datasets of single-trail processes using Flow-3D and use them to train a convolutional neural network capable of predicting the behavior of the three-dimensional thermal field of the melt pool solely by taking three parameters as input: laser power, laser velocity, and time step. The CNN achieves a relative Root Mean Squared Error of 2% to 3% for the temperature field and an average Intersection over Union score of 80% to 90% in predicting the melt pool area. Moreover, since time is included as one of the inputs of the model, the thermal field can be instantly obtained for any arbitrary time step without the need to iterate and compute all the steps
Recent advances in equivariant graph neural networks (GNNs) have made deep learning amenable to developing fast surrogate models to expensive ab initio quantum mechanics (QM) approaches for molecular potential predictions. However, building accurate and transferable potential models using GNNs remains challenging, as the data is greatly limited by the expensive computational costs and level of theory of QM methods, especially for large and complex molecular systems. In this work, we propose denoise pretraining on nonequilibrium molecular conformations to achieve more accurate and transferable GNN potential predictions. Specifically, atomic coordinates of sampled nonequilibrium conformations are perturbed by random noises and GNNs are pretrained to denoise the perturbed molecular conformations which recovers the original coordinates. Rigorous experiments on multiple benchmarks reveal that pretraining significantly improves the accuracy of neural potentials. Furthermore, we show that the proposed pretraining approach is model-agnostic, as it improves the performance of different invariant and equivariant GNNs. Notably, our models pretrained on small molecules demonstrate remarkable transferability, improving performance when fine-tuned on diverse molecular systems, including different elements, charged molecules, biomolecules, and larger systems. These results highlight the potential for leveraging denoise pretraining approaches to build more generalizable neural potentials for complex molecular systems.
Learning from human demonstrations (behavior cloning) is a cornerstone of robot learning. However, most behavior cloning algorithms require a large number of demonstrations to learn a task, especially for general tasks that have a large variety of initial conditions. Humans, however, can learn to complete tasks, even complex ones, after only seeing one or two demonstrations. Our work seeks to emulate this ability, using behavior cloning to learn a task given only a single human demonstration. We achieve this goal by using linear transforms to augment the single demonstration, generating a set of trajectories for a wide range of initial conditions. With these demonstrations, we are able to train a behavior cloning agent to successfully complete three block manipulation tasks. Additionally, we developed a novel addition to the temporal ensembling method used by action chunking agents during inference. By incorporating the standard deviation of the action predictions into the ensembling method, our approach is more robust to unforeseen changes in the environment, resulting in significant performance improvements.
Francis Ogoke, Kyle Johnson, Michael Glinsky et al.
Laser Powder Bed Fusion has become a widely adopted method for metal Additive Manufacturing (AM) due to its ability to mass produce complex parts with increased local control. However, AM produced parts can be subject to undesirable porosity, negatively influencing the properties of printed components. Thus, controlling porosity is integral for creating effective parts. A precise understanding of the porosity distribution is crucial for accurately simulating potential fatigue and failure zones. Previous research on generating synthetic porous microstructures have succeeded in generating parts with high density, isotropic porosity distributions but are often inapplicable to cases with sparser, boundary-dependent pore distributions. Our work bridges this gap by providing a method that considers these constraints by deconstructing the generation problem into its constitutive parts. A framework is introduced that combines Generative Adversarial Networks with Mallat Scattering Transform-based autocorrelation methods to construct novel realizations of the individual pore geometries and surface roughness, then stochastically reconstruct them to form realizations of a porous printed part. The generated parts are compared to the existing experimental porosity distributions based on statistical and dimensional metrics, such as nearest neighbor distances, pore volumes, pore anisotropies and scattering transform based auto-correlations.
Francis Ogoke, Quanliang Liu, Olabode Ajenifujah et al.
Defects in laser powder bed fusion (L-PBF) parts often result from the meso-scale dynamics of the molten alloy near the laser, known as the melt pool. For instance, the melt pool can directly contribute to the formation of undesirable porosity, residual stress, and surface roughness in the final part. Experimental in-situ monitoring of the three-dimensional melt pool physical fields is challenging, due to the short length and time scales involved in the process. Multi-physics simulation methods can describe the three-dimensional dynamics of the melt pool, but are computationally expensive at the mesh refinement required for accurate predictions of complex effects, such as the formation of keyhole porosity. Therefore, in this work, we develop a generative deep learning model based on the probabilistic diffusion framework to map low-fidelity, coarse-grained simulation information to the high-fidelity counterpart. By doing so, we bypass the computational expense of conducting multiple high-fidelity simulations for analysis by instead upscaling lightweight coarse mesh simulations. Specifically, we implement a 2-D diffusion model to spatially upscale cross-sections of the coarsely simulated melt pool to their high-fidelity equivalent. We demonstrate the preservation of key metrics of the melting process between the ground truth simulation data and the diffusion model output, such as the temperature field, the melt pool dimensions and the variability of the keyhole vapor cavity. Specifically, we predict the melt pool depth within 3 $μm$ based on low-fidelity input data 4$\times$ coarser than the high-fidelity simulations, reducing analysis time by two orders of magnitude.
Industry 4.0 has revolutionized manufacturing by driving digitalization and shifting the paradigm toward additive manufacturing (AM). Fused Deposition Modeling (FDM), a key AM technology, enables the creation of highly customized, cost-effective products with minimal material waste through layer-by-layer extrusion, posing a significant challenge to traditional subtractive methods. However, the susceptibility of material extrusion techniques to errors often requires expert intervention to detect and mitigate defects that can severely compromise product quality. While automated error detection and machine learning models exist, their generalizability across diverse 3D printer setups, firmware, and sensors is limited, and deep learning methods require extensive labeled datasets, hindering scalability and adaptability. To address these challenges, we present a process monitoring and control framework that leverages pre-trained Large Language Models (LLMs) alongside 3D printers to detect and address printing defects. The LLM evaluates print quality by analyzing images captured after each layer or print segment, identifying failure modes and querying the printer for relevant parameters. It then generates and executes a corrective action plan. We validated the effectiveness of the proposed framework in identifying defects by comparing it against a control group of engineers with diverse AM expertise. Our evaluation demonstrated that LLM-based agents not only accurately identify common 3D printing errors, such as inconsistent extrusion, stringing, warping, and layer adhesion, but also effectively determine the parameters causing these failures and autonomously correct them without any need for human intervention.
Rishikesh Magar, Yuyang Wang, Amir Barati Farimani
Machine learning (ML) models have been widely successful in the prediction of material properties. However, large labeled datasets required for training accurate ML models are elusive and computationally expensive to generate. Recent advances in Self-Supervised Learning (SSL) frameworks capable of training ML models on unlabeled data have mitigated this problem and demonstrated superior performance in computer vision and natural language processing tasks. Drawing inspiration from the developments in SSL, we introduce Crystal Twins (CT): an SSL method for crystalline materials property prediction. Using a large unlabeled dataset, we pre-train a Graph Neural Network (GNN) by applying the redundancy reduction principle to the graph latent embeddings of augmented instances obtained from the same crystalline system. By sharing the pre-trained weights when fine-tuning the GNN for regression tasks, we significantly improve the performance for 7 challenging material property prediction benchmarks
The success of diffusion probabilistic models in generative tasks, such as text-to-image generation, has motivated the exploration of their application to regression problems commonly encountered in scientific computing and various other domains. In this context, the use of diffusion regression models for ensemble prediction is becoming a practice with increasing popularity. Under such background, we conducted a study to quantitatively evaluate the effectiveness of ensemble methods on solving different regression problems using diffusion models. We consider the ensemble prediction of a diffusion model as a means for zero-shot uncertainty quantification, since the diffusion models in our study are not trained with a loss function containing any uncertainty estimation. Through extensive experiments on 1D and 2D data, we demonstrate that ensemble methods consistently improve model prediction accuracy across various regression tasks. Notably, we observed a larger accuracy gain in auto-regressive prediction compared with point-wise prediction, and that enhancements take place in both the mean-square error and the physics-informed loss. Additionally, we reveal a statistical correlation between ensemble prediction error and ensemble variance, offering insights into balancing computational complexity with prediction accuracy and monitoring prediction confidence in practical applications where the ground truth is unknown. Our study provides a comprehensive view of the utility of diffusion ensembles, serving as a useful reference for practitioners employing diffusion models in regression problem-solving.
Developing fast surrogates for Partial Differential Equations (PDEs) will accelerate design and optimization in almost all scientific and engineering applications. Neural networks have been receiving ever-increasing attention and demonstrated remarkable success in computational modeling of PDEs, however; their prediction accuracy is not at the level of full deployment. In this work, we utilize the transformer architecture, the backbone of numerous state-of-the-art AI models, to learn the dynamics of physical systems as the mixing of spatial patterns learned by a convolutional autoencoder. Moreover, we incorporate the idea of multi-scale hierarchical time-stepping to increase the prediction speed and decrease accumulated error over time. Our model achieves similar or better results in predicting the time-evolution of Navier-Stokes equations compared to the powerful Fourier Neural Operator (FNO) and two transformer-based neural operators OFormer and Galerkin Transformer.
Seongwon Kim, Parisa Mollaei, Akshay Antony et al.
With the rise of Transformers and Large Language Models (LLMs) in Chemistry and Biology, new avenues for the design and understanding of therapeutics have opened up to the scientific community. Protein sequences can be modeled as language and can take advantage of recent advances in LLMs, specifically with the abundance of our access to the protein sequence datasets. In this paper, we developed the GPCR-BERT model for understanding the sequential design of G Protein-Coupled Receptors (GPCRs). GPCRs are the target of over one-third of FDA-approved pharmaceuticals. However, there is a lack of comprehensive understanding regarding the relationship between amino acid sequence, ligand selectivity, and conformational motifs (such as NPxxY, CWxP, E/DRY). By utilizing the pre-trained protein model (Prot-Bert) and fine-tuning with prediction tasks of variations in the motifs, we were able to shed light on several relationships between residues in the binding pocket and some of the conserved motifs. To achieve this, we took advantage of attention weights, and hidden states of the model that are interpreted to extract the extent of contributions of amino acids in dictating the type of masked ones. The fine-tuned models demonstrated high accuracy in predicting hidden residues within the motifs. In addition, the analysis of embedding was performed over 3D structures to elucidate the higher-order interactions within the conformations of the receptors.
Alison Bartsch, Charlotte Avra, Amir Barati Farimani
Deformable object manipulation presents a unique set of challenges in robotic manipulation by exhibiting high degrees of freedom and severe self-occlusion. State representation for materials that exhibit plastic behavior, like modeling clay or bread dough, is also difficult because they permanently deform under stress and are constantly changing shape. In this work, we investigate each of these challenges using the task of robotic sculpting with a parallel gripper. We propose a system that uses point clouds as the state representation and leverages pre-trained point cloud reconstruction Transformer to learn a latent dynamics model to predict material deformations given a grasp action. We design a novel action sampling algorithm that reasons about geometrical differences between point clouds to further improve the efficiency of model-based planners. All data and experiments are conducted entirely in the real world. Our experiments show the proposed system is able to successfully capture the dynamics of clay, and is able to create a variety of simple shapes.
Srivathsan Badrinarayanan, Chakradhar Guntuboina, Parisa Mollaei et al.
Peptides are essential in biological processes and therapeutics. In this study, we introduce Multi-Peptide, an innovative approach that combines transformer-based language models with Graph Neural Networks (GNNs) to predict peptide properties. We combine PeptideBERT, a transformer model tailored for peptide property prediction, with a GNN encoder to capture both sequence-based and structural features. By employing Contrastive Language-Image Pre-training (CLIP), Multi-Peptide aligns embeddings from both modalities into a shared latent space, thereby enhancing the model's predictive accuracy. Evaluations on hemolysis and nonfouling datasets demonstrate Multi-Peptide's robustness, achieving state-of-the-art 86.185% accuracy in hemolysis prediction. This study highlights the potential of multimodal learning in bioinformatics, paving the way for accurate and reliable predictions in peptide-based research and applications.
Ionic Liquids (ILs) provide a promising solution for CO$_2$ capture and storage to mitigate global warming. However, identifying and designing the high-capacity IL from the giant chemical space requires expensive, and exhaustive simulations and experiments. Machine learning (ML) can accelerate the process of searching for desirable ionic molecules through accurate and efficient property predictions in a data-driven manner. But existing descriptors and ML models for the ionic molecule suffer from the inefficient adaptation of molecular graph structure. Besides, few works have investigated the explainability of ML models to help understand the learned features that can guide the design of efficient ionic molecules. In this work, we develop both fingerprint-based ML models and Graph Neural Networks (GNNs) to predict the CO$_2$ absorption in ILs. Fingerprint works on graph structure at the feature extraction stage, while GNNs directly handle molecule structure in both the feature extraction and model prediction stage. We show that our method outperforms previous ML models by reaching a high accuracy (MAE of 0.0137, $R^2$ of 0.9884). Furthermore, we take the advantage of GNNs feature representation and develop a substructure-based explanation method that provides insight into how each chemical fragments within IL molecules contribute to the CO$_2$ absorption prediction of ML models. We also show that our explanation result agrees with some ground truth from the theoretical reaction mechanism of CO$_2$ absorption in ILs, which can advise on the design of novel and efficient functional ILs in the future.
Abraham George, Alison Bartsch, Amir Barati Farimani
The use of human demonstrations in reinforcement learning has proven to significantly improve agent performance. However, any requirement for a human to manually 'teach' the model is somewhat antithetical to the goals of reinforcement learning. This paper attempts to minimize human involvement in the learning process while retaining the performance advantages by using a single human example collected through a simple-to-use virtual reality simulation to assist with RL training. Our method augments a single demonstration to generate numerous human-like demonstrations that, when combined with Deep Deterministic Policy Gradients and Hindsight Experience Replay (DDPG + HER) significantly improve training time on simple tasks and allows the agent to solve a complex task (block stacking) that DDPG + HER alone cannot solve. The model achieves this significant training advantage using a single human example, requiring less than a minute of human input. Moreover, despite learning from a human example, the agent is not constrained to human-level performance, often learning a policy that is significantly different from the human demonstration.
The design of aerodynamic shapes, such as airfoils, has traditionally required significant computational resources and relied on predefined design parameters, which limit the potential for novel shape synthesis. In this work, we introduce a data-driven methodology for airfoil generation using a diffusion model. Trained on a dataset of preexisting airfoils, our model can generate an arbitrary number of new airfoils from random vectors, which can be conditioned on specific aerodynamic performance metrics such as lift and drag, or geometric criteria. Our results demonstrate that the diffusion model effectively produces airfoil shapes with realistic aerodynamic properties, offering substantial improvements in efficiency, flexibility, and the potential for discovering innovative airfoil designs. This approach significantly expands the design space, facilitating the synthesis of high-performance aerodynamic shapes that transcend the limitations of traditional methods.
Francis Ogoke, Sumesh Kalambettu Suresh, Jesse Adamczyk et al.
The stochastic formation of defects during Laser Powder Bed Fusion (L-PBF) negatively impacts its adoption for high-precision use cases. Optical monitoring techniques can be used to identify defects based on layer-wise imaging, but these methods are difficult to scale to high resolutions due to cost and memory constraints. Therefore, we implement generative deep learning models to link low-cost, low-resolution images of the build plate to detailed high-resolution optical images of the build plate, enabling cost-efficient process monitoring. To do so, a conditional latent probabilistic diffusion model is trained to produce realistic high-resolution images of the build plate from low-resolution webcam images, recovering the distribution of small-scale features and surface roughness. We first evaluate the performance of the model by analyzing the reconstruction quality of the generated images using peak-signal-to-noise-ratio (PSNR), structural similarity index measure (SSIM) and wavelet covariance metrics that describe the preservation of high-frequency information. Additionally, we design a framework based upon the Segment Anything foundation model to recreate the 3D morphology of the printed part and analyze the surface roughness of the reconstructed samples. Finally, we explore the zero-shot generalization capabilities of the implemented framework to other part geometries by creating synthetic low-resolution data.
Learning control policies with large discrete action spaces is a challenging problem in the field of reinforcement learning due to present inefficiencies in exploration. With high dimensional action spaces, there are a large number of potential actions in each individual dimension over which policies would be learned. In this work, we introduce a Deep Reinforcement Learning (DRL) algorithm call Multi-Action Networks (MAN) Learning that addresses the challenge of high-dimensional large discrete action spaces. We propose factorizing the N-dimension action space into N 1-dimensional components, known as sub-actions, creating a Value Neural Network for each sub-action. Then, MAN uses temporal-difference learning to train the networks synchronously, which is simpler than training a single network with a large action output directly. To evaluate the proposed method, we test MAN on three scenarios: an n-dimension maze task, a block stacking task, and then extend MAN to handle 12 games from the Atari Arcade Learning environment with 18 action spaces. Our results indicate that MAN learns faster than both Deep Q-Learning and Double Deep Q-Learning, implying our method is a better performing synchronous temporal difference algorithm than those currently available for large discrete action spaces.
Jong Hoon Park, Gauri Pramod Dalwankar, Alison Bartsch et al.
Accurately determining fluid viscosity is crucial for various industrial and scientific applications. Traditional methods of viscosity measurement, though reliable, often require manual intervention and cannot easily adapt to real-time monitoring. With advancements in machine learning and computer vision, this work explores the feasibility of predicting fluid viscosity by analyzing fluid oscillations captured in video data. The pipeline employs a 3D convolutional autoencoder pretrained in a self-supervised manner to extract and learn features from semantic segmentation masks of oscillating fluids. Then, the latent representations of the input data, produced from the pretrained autoencoder, is processed with a distinct inference head to infer either the fluid category (classification) or the fluid viscosity (regression) in a time-resolved manner. When the latent representations generated by the pretrained autoencoder are used for classification, the system achieves a 97.1% accuracy across a total of 4,140 test datapoints. Similarly, for regression tasks, employing an additional fully-connected network as a regression head allows the pipeline to achieve a mean absolute error of 0.258 over 4,416 test datapoints. This study represents an innovative contribution to both fluid characterization and the evolving landscape of Artificial Intelligence, demonstrating the potential of deep learning in achieving near real-time viscosity estimation and addressing practical challenges in fluid dynamics through the analysis of video data capturing oscillating fluid dynamics.
Meshing is a critical, but user-intensive process necessary for stable and accurate simulations in computational fluid dynamics (CFD). Mesh generation is often a bottleneck in CFD pipelines. Adaptive meshing techniques allow the mesh to be updated automatically to produce an accurate solution for the problem at hand. Existing classical techniques for adaptive meshing require either additional functionality out of solvers, many training simulations, or both. Current machine learning techniques often require substantial computational cost for training data generation, and are restricted in scope to the training data flow regime. MeshDQN is developed as a general purpose deep reinforcement learning framework to iteratively coarsen meshes while preserving target property calculation. A graph neural network based deep Q network is used to select mesh vertices for removal and solution interpolation is used to bypass expensive simulations at each step in the improvement process. MeshDQN requires a single simulation prior to mesh coarsening, while making no assumptions about flow regime, mesh type, or solver, only requiring the ability to modify meshes directly in a CFD pipeline. MeshDQN successfully improves meshes for two 2D airfoils.
Modeling the ion concentration profile in nanochannel plays an important role in understanding the electrical double layer and electroosmotic flow. Due to the non-negligible surface interaction and the effect of discrete solvent molecules, molecular dynamics (MD) simulation is often used as an essential tool to study the behavior of ions under nanoconfinement. Despite the accuracy of MD simulation in modeling nanoconfinement systems, it is computationally expensive. In this work, we propose neural network to predict ion concentration profiles in nanochannels with different configurations, including channel widths, ion molarity, and ion types. By modeling the ion concentration profile as a probability distribution, our neural network can serve as a much faster surrogate model for MD simulation with high accuracy. We further demonstrate the superior prediction accuracy of neural network over XGBoost. Lastly, we demonstrated that neural network is flexible in predicting ion concentration profiles with different bin sizes. Overall, our deep learning model is a fast, flexible, and accurate surrogate model to predict ion concentration profiles in nanoconfinement.
Designing mechanical linkages to achieve target end-effector trajectories presents a fundamental challenge due to the intricate coupling between continuous node placements, discrete topological configurations, and nonlinear kinematic constraints. The highly nonlinear motion-to-configuration relationship means small perturbations in joint positions drastically alter trajectories, while the combinatorially expanding design space renders conventional optimization and heuristic methods computationally intractable. We introduce an autoregressive diffusion framework that exploits the dyadic nature of linkage assembly by representing mechanisms as sequentially constructed graphs, where nodes correspond to joints and edges to rigid links. Our approach combines a causal transformer with a Denoising Diffusion Probabilistic Model (DDPM), both conditioned on target trajectories encoded via a transformer encoder. The causal transformer autoregressively predicts discrete topology node-by-node, while the DDPM refines each node's spatial coordinates and edge connectivity to previously generated nodes. This sequential generation enables adaptive trial-and-error synthesis where problematic nodes exhibiting kinematic locking or collisions can be selectively regenerated, allowing autonomous correction of degenerate configurations during design. Our graph-based, data-driven methodology surpasses traditional optimization approaches, enabling scalable inverse design that generalizes to mechanisms with arbitrary node counts. We demonstrate successful synthesis of linkage systems containing up to 20 nodes with extensibility to N-node architectures. This work advances autoregressive graph generation methodologies and computational kinematic synthesis, establishing new paradigms for scalable inverse design of complex mechanical systems.
Parshin Shojaee, Kazem Meidani, Shashank Gupta et al.
Mathematical equations have been unreasonably effective in describing complex natural phenomena across various scientific disciplines. However, discovering such insightful equations from data presents significant challenges due to the necessity of navigating extremely large combinatorial hypothesis spaces. Current methods of equation discovery, commonly known as symbolic regression techniques, largely focus on extracting equations from data alone, often neglecting the domain-specific prior knowledge that scientists typically depend on. They also employ limited representations such as expression trees, constraining the search space and expressiveness of equations. To bridge this gap, we introduce LLM-SR, a novel approach that leverages the extensive scientific knowledge and robust code generation capabilities of Large Language Models (LLMs) to discover scientific equations from data. Specifically, LLM-SR treats equations as programs with mathematical operators and combines LLMs' scientific priors with evolutionary search over equation programs. The LLM iteratively proposes new equation skeleton hypotheses, drawing from its domain knowledge, which are then optimized against data to estimate parameters. We evaluate LLM-SR on four benchmark problems across diverse scientific domains (e.g., physics, biology), which we carefully designed to simulate the discovery process and prevent LLM recitation. Our results demonstrate that LLM-SR discovers physically accurate equations that significantly outperform state-of-the-art symbolic regression baselines, particularly in out-of-domain test settings. We also show that LLM-SR's incorporation of scientific priors enables more efficient equation space exploration than the baselines. Code and data are available: https://github.com/deep-symbolic-mathematics/LLM-SR
Abraham George, Selam Gano, Pranav Katragadda et al.
Tactile information is a critical tool for dexterous manipulation. As humans, we rely heavily on tactile information to understand objects in our environments and how to interact with them. We use touch not only to perform manipulation tasks but also to learn how to perform these tasks. Therefore, to create robotic agents that can learn to complete manipulation tasks at a human or super-human level of performance, we need to properly incorporate tactile information into both skill execution and skill learning. In this paper, we investigate how we can incorporate tactile information into imitation learning platforms to improve performance on manipulation tasks. We show that incorporating visuo-tactile pretraining improves imitation learning performance, not only for tactile agents (policies that use tactile information at inference), but also for non-tactile agents (policies that do not use tactile information at inference). For these non-tactile agents, pretraining with tactile information significantly improved performance (for example, improving the accuracy on USB plugging from 20% to 85%), reaching a level on par with visuo-tactile agents, and even surpassing them in some cases. For demonstration videos and access to our codebase, see the project website: https://sites.google.com/andrew.cmu.edu/visuo-tactile-pretraining
Aayush Shah, Chakradhar Guntuboina, Amir Barati Farimani
In recent years, natural language processing (NLP) models have demonstrated remarkable capabilities in various domains beyond traditional text generation. In this work, we introduce PeptideGPT, a protein language model tailored to generate protein sequences with distinct properties: hemolytic activity, solubility, and non-fouling characteristics. To facilitate a rigorous evaluation of these generated sequences, we established a comprehensive evaluation pipeline consisting of ideas from bioinformatics to retain valid proteins with ordered structures. First, we rank the generated sequences based on their perplexity scores, then we filter out those lying outside the permissible convex hull of proteins. Finally, we predict the structure using ESMFold and select the proteins with pLDDT values greater than 70 to ensure ordered structure. The properties of generated sequences are evaluated using task-specific classifiers - PeptideBERT and HAPPENN. We achieved an accuracy of 76.26% in hemolytic, 72.46% in non-hemolytic, 78.84% in non-fouling, and 68.06% in solubility protein generation. Our experimental results demonstrate the effectiveness of PeptideGPT in de novo protein design and underscore the potential of leveraging NLP-based approaches for paving the way for future innovations and breakthroughs in synthetic biology and bioinformatics. Codes, models, and data used in this study are freely available at: https://github.com/aayush-shah14/PeptideGPT.
Abraham George, Alison Bartsch, Amir Barati Farimani
Across the robotics field, quality demonstrations are an integral part of many control pipelines. However, collecting high-quality demonstration trajectories remains time-consuming and difficult, often resulting in the number of demonstrations being the performance bottleneck. To address this issue, we present a method of Virtual Reality (VR) Teleoperation that uses an Oculus VR headset to teleoperate a Franka Emika Panda robot. Although other VR teleoperation methods exist, our code is open source, designed for readily available consumer hardware, easy to modify, agnostic to experimental setup, and simple to use.
Rishikesh Magar, Yuyang Wang, Cooper Lorsung et al.
Machine learning (ML) has demonstrated the promise for accurate and efficient property prediction of molecules and crystalline materials. To develop highly accurate ML models for chemical structure property prediction, datasets with sufficient samples are required. However, obtaining clean and sufficient data of chemical properties can be expensive and time-consuming, which greatly limits the performance of ML models. Inspired by the success of data augmentations in computer vision and natural language processing, we developed AugLiChem: the data augmentation library for chemical structures. Augmentation methods for both crystalline systems and molecules are introduced, which can be utilized for fingerprint-based ML models and Graph Neural Networks(GNNs). We show that using our augmentation strategies significantly improves the performance of ML models, especially when using GNNs. In addition, the augmentations that we developed can be used as a direct plug-in module during training and have demonstrated the effectiveness when implemented with different GNN models through the AugliChem library. The Python-based package for our implementation of Auglichem: Data augmentation library for chemical structures, is publicly available at: https://github.com/BaratiLab/AugLiChem.
Diffusion models have gained tremendous success in text-to-image generation, yet still lag behind with visual understanding tasks, an area dominated by autoregressive vision-language models. We propose a large-scale and fully end-to-end diffusion model for multi-modal understanding and generation that significantly improves on existing diffusion-based multimodal models, and is the first of its kind to support the full suite of vision-language modeling capabilities. Inspired by the multimodal diffusion transformer (MM-DiT) and recent advances in discrete diffusion language modeling, we leverage a cross-modal maximum likelihood estimation framework that simultaneously trains the conditional likelihoods of both images and text jointly under a single loss function, which is back-propagated through both branches of the diffusion transformer. The resulting model is highly flexible and capable of a wide range of tasks including image generation, captioning, and visual question answering. Our model attained competitive performance compared to recent unified image understanding and generation models, demonstrating the potential of multimodal diffusion modeling as a promising alternative to autoregressive next-token prediction models.
Achuth Chandrasekhar, Jonathan Chan, Francis Ogoke et al.
Generalized large language models (LLMs) such as GPT-4 may not provide specific answers to queries formulated by materials science researchers. These models may produce a high-level outline but lack the capacity to return detailed instructions on manufacturing and material properties of novel alloys. Enhancing a smaller model with specialized domain knowledge may provide an advantage over large language models which cannot be retrained quickly enough to keep up with the rapid pace of research in metal additive manufacturing (AM). We introduce "AMGPT," a specialized LLM text generator designed for metal AM queries. The goal of AMGPT is to assist researchers and users in navigating the extensive corpus of literature in AM. Instead of training from scratch, we employ a pre-trained Llama2-7B model from Hugging Face in a Retrieval-Augmented Generation (RAG) setup, utilizing it to dynamically incorporate information from $\sim$50 AM papers and textbooks in PDF format. Mathpix is used to convert these PDF documents into TeX format, facilitating their integration into the RAG pipeline managed by LlamaIndex. Expert evaluations of this project highlight that specific embeddings from the RAG setup accelerate response times and maintain coherence in the generated text.
Parshin Shojaee, Ngoc-Hieu Nguyen, Kazem Meidani et al.
Scientific equation discovery is a fundamental task in the history of scientific progress, enabling the derivation of laws governing natural phenomena. Recently, Large Language Models (LLMs) have gained interest for this task due to their potential to leverage embedded scientific knowledge for hypothesis generation. However, evaluating the true discovery capabilities of these methods remains challenging, as existing benchmarks often rely on common equations that are susceptible to memorization by LLMs, leading to inflated performance metrics that do not reflect discovery. In this paper, we introduce LLM-SRBench, a comprehensive benchmark with 239 challenging problems across four scientific domains specifically designed to evaluate LLM-based scientific equation discovery methods while preventing trivial memorization. Our benchmark comprises two main categories: LSR-Transform, which transforms common physical models into less common mathematical representations to test reasoning beyond memorized forms, and LSR-Synth, which introduces synthetic, discovery-driven problems requiring data-driven reasoning. Through extensive evaluation of several state-of-the-art methods, using both open and closed LLMs, we find that the best-performing system so far achieves only 31.5% symbolic accuracy. These findings highlight the challenges of scientific equation discovery, positioning LLM-SRBench as a valuable resource for future research.
Conventional mechanical design follows an iterative process in which initial concepts are refined through cycles of expert assessment and resource-intensive Finite Element Method (FEM) analysis to meet performance goals. While machine learning models have been developed to assist in parts of this process, they typically require large datasets, extensive training, and are often tailored to specific tasks, limiting their generalizability. To address these limitations, we propose a framework that leverages a pretrained Large Language Model (LLM) in conjunction with an FEM module to autonomously generate, evaluate, and refine structural designs based on performance specifications and numerical feedback. The LLM operates without domain-specific fine-tuning, using general reasoning to propose design candidates, interpret FEM-derived performance metrics, and apply structurally sound modifications. Using 2D truss structures as a testbed, we show that the LLM can effectively navigate highly discrete and multi-faceted design spaces, balance competing objectives, and identify convergence when further optimization yields diminishing returns. Compared to Non-dominated Sorting Genetic Algorithm II (NSGA-II), our method achieves faster convergence and fewer FEM evaluations. Experiments with varying temperature settings (0.5, 1.0, 1.2) and model sizes (GPT-4.1 and GPT-4.1-mini) indicate that smaller models yield higher constraint satisfaction with fewer steps, while lower temperatures enhance design consistency. These results establish LLMs as a promising new class of reasoning-based, natural language-driven optimizers for autonomous design and iterative structural refinement.
The growth of global consumption has motivated important applications of deep learning to smart manufacturing and machine health monitoring. In particular, analyzing vibration data offers great potential to extract meaningful insights into predictive maintenance by the detection of bearing faults. Deep learning can be a powerful method to predict these mechanical failures; however, they lack generalizability to new tasks or datasets and require expensive, labeled mechanical data. We address this by presenting a novel self-supervised pretraining and fine-tuning framework based on transformer models. In particular, we investigate different tokenization and data augmentation strategies to reach state-of-the-art accuracies using transformer models. Furthermore, we demonstrate self-supervised masked pretraining for vibration signals and its application to low-data regimes, task adaptation, and dataset adaptation. Pretraining is able to improve performance on scarce, unseen training samples, as well as when fine-tuning on fault classes outside of the pretraining distribution. Furthermore, pretrained transformers are shown to be able to generalize to a different dataset in a few-shot manner. This introduces a new paradigm where models can be pretrained on unlabeled data from different bearings, faults, and machinery and quickly deployed to new, data-scarce applications to suit specific manufacturing needs.
Zijie Li, Anthony Zhou, Amir Barati Farimani · cmu
Autoregressive next-step prediction models have become the de-facto standard for building data-driven neural solvers to forecast time-dependent partial differential equations (PDEs). Denoise training that is closely related to diffusion probabilistic model has been shown to enhance the temporal stability of neural solvers, while its stochastic inference mechanism enables ensemble predictions and uncertainty quantification. In principle, such training involves sampling a series of discretized diffusion timesteps during both training and inference, inevitably increasing computational overhead. In addition, most diffusion models apply isotropic Gaussian noise on structured, uniform grids, limiting their adaptability to irregular domains. We propose a latent diffusion model for PDE simulation that embeds the PDE state in a lower-dimensional latent space, which significantly reduces computational costs. Our framework uses an autoencoder to map different types of meshes onto a unified structured latent grid, capturing complex geometries. By analyzing common diffusion paths, we propose to use a coarsely sampled noise schedule from flow matching for both training and testing. Numerical experiments show that the proposed model outperforms several deterministic baselines in both accuracy and long-term stability, highlighting the potential of diffusion-based approaches for robust data-driven PDE learning.
Peter Myung-Won Pak, Francis Ogoke, Andrew Polonsky et al.
We present a deep learning approach for quantifying and localizing ex-situ porosity within Laser Powder Bed Fusion fabricated samples utilizing in-situ thermal image monitoring data. Our goal is to build the real time porosity map of parts based on thermal images acquired during the build. The quantification task builds upon the established Convolutional Neural Network model architecture to predict pore count and the localization task leverages the spatial and temporal attention mechanisms of the novel Video Vision Transformer model to indicate areas of expected porosity. Our model for porosity quantification achieved a $R^2$ score of 0.57 and our model for porosity localization produced an average IoU score of 0.32 and a maximum of 1.0. This work is setting the foundations of part porosity "Digital Twins" based on additive manufacturing monitoring data and can be applied downstream to reduce time-intensive post-inspection and testing activities during part qualification and certification. In addition, we seek to accelerate the acquisition of crucial insights normally only available through ex-situ part evaluation by means of machine learning analysis of in-situ process monitoring data.
Neural solvers for partial differential equations (PDEs) have great potential to generate fast and accurate physics solutions, yet their practicality is currently limited by their generalizability. PDEs evolve over broad scales and exhibit diverse behaviors; predicting these phenomena will require learning representations across a wide variety of inputs which may encompass different coefficients, boundary conditions, resolutions, or even equations. As a step towards generalizable PDE modeling, we adapt masked pretraining for physics problems. Through self-supervised learning across PDEs, masked autoencoders can consolidate heterogeneous physics to learn rich latent representations. We show that learned representations can generalize to a limited set of unseen equations or parameters and are meaningful enough to regress PDE coefficients or the classify PDE features. Furthermore, conditioning neural solvers on learned latent representations can improve time-stepping and super-resolution performance across a variety of coefficients, discretizations, or boundary conditions, as well as on certain unseen PDEs. We hope that masked pretraining can emerge as a unifying method across large, unlabeled, and heterogeneous datasets to learn latent physics at scale.
Manipulating deformable objects remains a challenge within robotics due to the difficulties of state estimation, long-horizon planning, and predicting how the object will deform given an interaction. These challenges are the most pronounced with 3D deformable objects. We propose SculptDiff, a goal-conditioned diffusion-based imitation learning framework that works with point cloud state observations to directly learn clay sculpting policies for a variety of target shapes. To the best of our knowledge this is the first real-world method that successfully learns manipulation policies for 3D deformable objects. For sculpting videos and access to our dataset and hardware CAD models, see the project website: https://sites.google.com/andrew.cmu.edu/imitation-sculpting/home
Akshat Chaudhari, Chakradhar Guntuboina, Hongshuo Huang et al.
The pursuit of novel alloys tailored to specific requirements poses significant challenges for researchers in the field. This underscores the importance of developing predictive techniques for essential physical properties of alloys based on their chemical composition and processing parameters. This study introduces AlloyBERT, a transformer encoder-based model designed to predict properties such as elastic modulus and yield strength of alloys using textual inputs. Leveraging the pre-trained RoBERTa encoder model as its foundation, AlloyBERT employs self-attention mechanisms to establish meaningful relationships between words, enabling it to interpret human-readable input and predict target alloy properties. By combining a tokenizer trained on our textual data and a RoBERTa encoder pre-trained and fine-tuned for this specific task, we achieved a mean squared error (MSE) of 0.00015 on the Multi Principal Elemental Alloys (MPEA) data set and 0.00611 on the Refractory Alloy Yield Strength (RAYS) dataset. This surpasses the performance of shallow models, which achieved a best-case MSE of 0.00025 and 0.0076 on the MPEA and RAYS datasets respectively. Our results highlight the potential of language models in material science and establish a foundational framework for text-based prediction of alloy properties that does not rely on complex underlying representations, calculations, or simulations.
Francis Ogoke, Peter Myung-Won Pak, Alexander Myers et al.
Insufficient overlap between the melt pools produced during Laser Powder Bed Fusion (L-PBF) can lead to lack-of-fusion defects and deteriorated mechanical and fatigue performance. In-situ monitoring of the melt pool subsurface morphology requires specialized equipment that may not be readily accessible or scalable. Therefore, we introduce a machine learning framework to correlate in-situ two-color thermal images observed via high-speed color imaging to the two-dimensional profile of the melt pool cross-section. Specifically, we employ a hybrid CNN-Transformer architecture to establish a correlation between single bead off-axis thermal image sequences and melt pool cross-section contours measured via optical microscopy. In this architecture, a ResNet model embeds the spatial information contained within the thermal images to a latent vector, while a Transformer model correlates the sequence of embedded vectors to extract temporal information. Our framework is able to model the curvature of the subsurface melt pool structure, with improved performance in high energy density regimes compared to analytical melt pool models. The performance of this model is evaluated through dimensional and geometric comparisons to the corresponding experimental melt pool observations.
Neural networks have shown promising potential in accelerating the numerical simulation of systems governed by partial differential equations (PDEs). Different from many existing neural network surrogates operating on high-dimensional discretized fields, we propose to learn the dynamics of the system in the latent space with much coarser discretizations. In our proposed framework - Latent Neural PDE Solver (LNS), a non-linear autoencoder is first trained to project the full-order representation of the system onto the mesh-reduced space, then a temporal model is trained to predict the future state in this mesh-reduced space. This reduction process simplifies the training of the temporal model by greatly reducing the computational cost accompanying a fine discretization. We study the capability of the proposed framework and several other popular neural PDE solvers on various types of systems including single-phase and multi-phase flows along with varying system parameters. We showcase that it has competitive accuracy and efficiency compared to the neural PDE solver that operates on full-order space.
Zijie Li, Anthony Zhou, Saurabh Patil et al. · cmu
Accurate weather forecasting is crucial in various sectors, impacting decision-making processes and societal events. Data-driven approaches based on machine learning models have recently emerged as a promising alternative to numerical weather prediction models given their potential to capture physics of different scales from historical data and the significantly lower computational cost during the prediction stage. Renowned for its state-of-the-art performance across diverse domains, the Transformer model has also gained popularity in machine learning weather prediction. Yet applying Transformer architectures to weather forecasting, particularly on a global scale is computationally challenging due to the quadratic complexity of attention and the quadratic increase in spatial points as resolution increases. In this work, we propose a factorized-attention-based model tailored for spherical geometries to mitigate this issue. More specifically, it utilizes multi-dimensional factorized kernels that convolve over different axes where the computational complexity of the kernel is only quadratic to the axial resolution instead of overall resolution. The deterministic forecasting accuracy of the proposed model on $1.5^\circ$ and 0-7 days' lead time is on par with state-of-the-art purely data-driven machine learning weather prediction models. We also showcase the proposed model holds great potential to push forward the Pareto front of accuracy-efficiency for Transformer weather models, where it can achieve better accuracy with less computational cost compared to Transformer based models with standard attention.
Neural surrogates for partial differential equations (PDEs) have become popular due to their potential to quickly simulate physics. With a few exceptions, neural surrogates generally treat the forward evolution of time-dependent PDEs as a black box by directly predicting the next state. While this is a natural and easy framework for applying neural surrogates, it can be an over-simplified and rigid framework for predicting physics. In this work, we evaluate an alternate framework in which neural solvers predict the temporal derivative and an ODE integrator forwards the solution in time, which has little overhead and is broadly applicable across model architectures and PDEs. We find that by simply changing the training target and introducing numerical integration during inference, neural surrogates can gain accuracy and stability in finely-discretized regimes. Predicting temporal derivatives also allows models to not be constrained to a specific temporal discretization, allowing for flexible time-stepping during inference or training on higher-resolution PDE data. Lastly, we investigate why this framework can be beneficial and in what situations does it work well.
Neural operators have recently grown in popularity as Partial Differential Equation (PDE) surrogate models. Learning solution functionals, rather than functions, has proven to be a powerful approach to calculate fast, accurate solutions to complex PDEs. While much work has been done evaluating neural operator performance on a wide variety of surrogate modeling tasks, these works normally evaluate performance on a single equation at a time. In this work, we develop a novel contrastive pretraining framework utilizing Generalized Contrastive Loss that improves neural operator generalization across multiple governing equations simultaneously. Governing equation coefficients are used to measure ground-truth similarity between systems. A combination of physics-informed system evolution and latent-space model output are anchored to input data and used in our distance function. We find that physics-informed contrastive pretraining improves accuracy for the Fourier Neural Operator in fixed-future and autoregressive rollout tasks for the 1D and 2D Heat, Burgers', and linear advection equations.