Aditi S. Krishnapriyan

Geoffrey Négiar, Michael W. Mahoney, Aditi S. Krishnapriyan · berkeley

We introduce a practical method to enforce partial differential equation (PDE) constraints for functions defined by neural networks (NNs), with a high degree of accuracy and up to a desired tolerance. We develop a differentiable PDE-constrained layer that can be incorporated into any NN architecture. Our method leverages differentiable optimization and the implicit function theorem to effectively enforce physical constraints. Inspired by dictionary learning, our model learns a family of functions, each of which defines a mapping from PDE parameters to PDE solutions. At inference time, the model finds an optimal linear combination of the functions in the learned family by solving a PDE-constrained optimization problem. Our method provides continuous solutions over the domain of interest that accurately satisfy desired physical constraints. Our results show that incorporating hard constraints directly into the NN architecture achieves much lower test error when compared to training on an unconstrained objective.

Da Long, Wei W. Xing, Aditi S. Krishnapriyan et al.

Discovering governing equations from data is important to many scientific and engineering applications. Despite promising successes, existing methods are still challenged by data sparsity and noise issues, both of which are ubiquitous in practice. Moreover, state-of-the-art methods lack uncertainty quantification and/or are costly in training. To overcome these limitations, we propose a novel equation discovery method based on Kernel learning and BAyesian Spike-and-Slab priors (KBASS). We use kernel regression to estimate the target function, which is flexible, expressive, and more robust to data sparsity and noises. We combine it with a Bayesian spike-and-slab prior -- an ideal Bayesian sparse distribution -- for effective operator selection and uncertainty quantification. We develop an expectation-propagation expectation-maximization (EP-EM) algorithm for efficient posterior inference and function estimation. To overcome the computational challenge of kernel regression, we place the function values on a mesh and induce a Kronecker product construction, and we use tensor algebra to enable efficient computation and optimization. We show the advantages of KBASS on a list of benchmark ODE and PDE discovery tasks.

Divyam Goel, Nithin Chalapathi, Sanjeev Raja et al.

Inverse problems in partial differential equations (PDEs) involve estimating the physical parameters of a system from observed spatiotemporal solution fields.Neural networks are well-suited for PDE parameter estimation due to their capability to model function-to-function space transformations. While existing benchmarks of machine learning methods for PDEs primarily focus on the forward problem, there are no similar comprehensive studies and benchmark datasets on PDE inverse problems, i.e., mapping solution fields to underlying physical parameters. We fill this gap by introducing PDEInvBench, a comprehensive benchmark dataset consisting of numerical simulations for both time-dependent and time-independent PDEs across a wide range of physical behaviors and parameters. Our dataset includes evaluation splits that assess performance in both in-distribution and various out-of-distribution settings. Using our benchmark dataset, we comprehensively explore the design space of neural networks for PDE inverse problems along three key dimensions: (1) optimization procedures, analyzing the role of supervised, self-supervised, and test-time training objectives on performance, (2) problem representations, where we study the value of architectural choices with different inductive biases and various conditioning strategies, and (3) scaling, which we perform with respect to both model and data size. Our experiments reveal several practical insights: 1) neural networks perform best with a two-stage training procedure: initial supervision with PDE parameters followed by test-time fine-tuning using the PDE residual, 2) incorporating PDE derivatives as input features consistently improves accuracy, and 3) increasing the diversity of initial conditions in the training data yields greater performance gains than expanding the range of PDE parameters. We make our dataset and codebase publicly available.

Danny Reidenbach, Aditi S. Krishnapriyan

Molecular conformer generation (MCG) is an important task in cheminformatics and drug discovery. The ability to efficiently generate low-energy 3D structures can avoid expensive quantum mechanical simulations, leading to accelerated virtual screenings and enhanced structural exploration. Several generative models have been developed for MCG, but many struggle to consistently produce high-quality conformers. To address these issues, we introduce CoarsenConf, which coarse-grains molecular graphs based on torsional angles and integrates them into an SE(3)-equivariant hierarchical variational autoencoder. Through equivariant coarse-graining, we aggregate the fine-grained atomic coordinates of subgraphs connected via rotatable bonds, creating a variable-length coarse-grained latent representation. Our model uses a novel aggregated attention mechanism to restore fine-grained coordinates from the coarse-grained latent representation, enabling efficient generation of accurate conformers. Furthermore, we evaluate the chemical and biochemical quality of our generated conformers on multiple downstream applications, including property prediction and oracle-based protein docking. Overall, CoarsenConf generates more accurate conformer ensembles compared to prior generative models.

Sanjeev Raja, Martin Šípka, Michael Psenka et al.

Transition path sampling (TPS), which involves finding probable paths connecting two points on an energy landscape, remains a challenge due to the complexity of real-world atomistic systems. Current machine learning approaches use expensive, task-specific, and data-free training procedures, limiting their ability to benefit from high-quality datasets and large-scale pre-trained models. In this work, we address TPS by interpreting candidate paths as trajectories sampled from stochastic dynamics induced by the learned score function of pre-trained generative models, specifically denoising diffusion and flow matching. Under these dynamics, finding high-likelihood transition paths becomes equivalent to minimizing the Onsager-Machlup (OM) action functional. This enables us to repurpose pre-trained generative models for TPS in a zero-shot manner, in contrast with bespoke, task-specific approaches in previous work. We demonstrate our approach on varied molecular systems, obtaining diverse, physically realistic transition pathways and generalizing beyond the pre-trained model's original training dataset. Our method can be easily incorporated into new generative models, making it practically relevant as models continue to scale and improve with increased data availability. Code is available at github.com/ASK-Berkeley/OM-TPS.

Daniel Rothchild, Andrew S. Rosen, Eric Taw et al.

We present an investigation into diffusion models for molecular generation, with the aim of better understanding how their predictions compare to the results of physics-based calculations. The investigation into these models is driven by their potential to significantly accelerate electronic structure calculations using machine learning, without requiring expensive first-principles datasets for training interatomic potentials. We find that the inference process of a popular diffusion model for de novo molecular generation is divided into an exploration phase, where the model chooses the atomic species, and a relaxation phase, where it adjusts the atomic coordinates to find a low-energy geometry. As training proceeds, we show that the model initially learns about the first-order structure of the potential energy surface, and then later learns about higher-order structure. We also find that the relaxation phase of the diffusion model can be re-purposed to sample the Boltzmann distribution over conformations and to carry out structure relaxations. For structure relaxations, the model finds geometries with ~10x lower energy than those produced by a classical force field for small organic molecules. Initializing a density functional theory (DFT) relaxation at the diffusion-produced structures yields a >2x speedup to the DFT relaxation when compared to initializing at structures relaxed with a classical force field.

Sanjeev Raja, Ishan Amin, Fabian Pedregosa et al.

Machine learning force fields (MLFFs) are an attractive alternative to ab-initio methods for molecular dynamics (MD) simulations. However, they can produce unstable simulations, limiting their ability to model phenomena occurring over longer timescales and compromising the quality of estimated observables. To address these challenges, we present Stability-Aware Boltzmann Estimator (StABlE) Training, a multi-modal training procedure which leverages joint supervision from reference quantum-mechanical calculations and system observables. StABlE Training iteratively runs many MD simulations in parallel to seek out unstable regions, and corrects the instabilities via supervision with a reference observable. We achieve efficient end-to-end automatic differentiation through MD simulations using our Boltzmann Estimator, a generalization of implicit differentiation techniques to a broader class of stochastic algorithms. Unlike existing techniques based on active learning, our approach requires no additional ab-initio energy and forces calculations to correct instabilities. We demonstrate our methodology across organic molecules, tetrapeptides, and condensed phase systems, using three modern MLFF architectures. StABlE-trained models achieve significant improvements in simulation stability, data efficiency, and agreement with reference observables. The stability improvements cannot be matched by reducing the simulation timestep; thus, StABlE Training effectively allows for larger timesteps. By incorporating observables into the training process alongside first-principles calculations, StABlE Training can be viewed as a general semi-empirical framework applicable across MLFF architectures and systems. This makes it a powerful tool for training stable and accurate MLFFs, particularly in the absence of large reference datasets. Our code is available at https://github.com/ASK-Berkeley/StABlE-Training.

Tobias Kreiman, Aditi S. Krishnapriyan

Machine Learning Force Fields (MLFFs) are a promising alternative to expensive ab initio quantum mechanical molecular simulations. Given the diversity of chemical spaces that are of interest and the cost of generating new data, it is important to understand how MLFFs generalize beyond their training distributions. In order to characterize and better understand distribution shifts in MLFFs, we conduct diagnostic experiments on chemical datasets, revealing common shifts that pose significant challenges, even for large foundation models trained on extensive data. Based on these observations, we hypothesize that current supervised training methods inadequately regularize MLFFs, resulting in overfitting and learning poor representations of out-of-distribution systems. We then propose two new methods as initial steps for mitigating distribution shifts for MLFFs. Our methods focus on test-time refinement strategies that incur minimal computational cost and do not use expensive ab initio reference labels. The first strategy, based on spectral graph theory, modifies the edges of test graphs to align with graph structures seen during training. Our second strategy improves representations for out-of-distribution systems at test-time by taking gradient steps using an auxiliary objective, such as a cheap physical prior. Our test-time refinement strategies significantly reduce errors on out-of-distribution systems, suggesting that MLFFs are capable of and can move towards modeling diverse chemical spaces, but are not being effectively trained to do so. Our experiments establish clear benchmarks for evaluating the generalization capabilities of the next generation of MLFFs. Our code is available at https://tkreiman.github.io/projects/mlff_distribution_shifts/.

Ryan Liu, Eric Qu, Tobias Kreiman et al.

Machine Learning Interatomic Potentials (MLIPs) sometimes fail to reproduce the physical smoothness of the quantum potential energy surface (PES), leading to erroneous behavior in downstream simulations that standard energy and force regression evaluations can miss. Existing evaluations, such as microcanonical molecular dynamics (MD), are computationally expensive and primarily probe near-equilibrium states. To improve evaluation metrics for MLIPs, we introduce the Bond Smoothness Characterization Test (BSCT). This efficient benchmark probes the PES via controlled bond deformations and detects non-smoothness, including discontinuities, artificial minima, and spurious forces, both near and far from equilibrium. We show that BSCT correlates strongly with MD stability while requiring a fraction of the cost of MD. To demonstrate how BSCT can guide iterative model design, we utilize an unconstrained Transformer backbone as a testbed, illustrating how refinements such as a new differentiable $k$-nearest neighbors algorithm and temperature-controlled attention reduce artifacts identified by our metric. By optimizing model design systematically based on BSCT, the resulting MLIP simultaneously achieves a low conventional E/F regression error, stable MD simulations, and robust atomistic property predictions. Our results establish BSCT as both a validation metric and as an "in-the-loop" model design proxy that alerts MLIP developers to physical challenges that cannot be efficiently evaluated by current MLIP benchmarks.

Kai Nelson, Tobias Kreiman, Sergey Levine et al.

A fundamental challenge in science and engineering is the simulation-to-experiment gap. While we often possess prior knowledge of physical laws, these physical laws can be too difficult to solve exactly for complex systems. Such systems are commonly modeled using simulators, which impose computational approximations. Meanwhile, experimental measurements more faithfully represent the real world, but experimental data typically consists of observations that only partially reflect the system's full underlying state. We propose a data-driven distribution alignment framework that bridges this simulation-to-experiment gap by pre-training a generative model on fully observed (but imperfect) simulation data, then aligning it with partial (but real) observations of experimental data. While our method is domain-agnostic, we ground our approach in the physical sciences by introducing Adversarial Distribution Alignment (ADA). This method aligns a generative model of atomic positions -- initially trained on a simulated Boltzmann distribution -- with the distribution of experimental observations. We prove that our method recovers the target observable distribution, even with multiple, potentially correlated observables. We also empirically validate our framework on synthetic, molecular, and experimental protein data, demonstrating that it can align generative models with diverse observables. Our code is available at https://kaityrusnelson.com/ada/.

Eric Qu, Aditi S. Krishnapriyan

Scaling has been critical in improving model performance and generalization in machine learning. It involves how a model's performance changes with increases in model size or input data, as well as how efficiently computational resources are utilized to support this growth. Despite successes in other areas, the study of scaling in Neural Network Interatomic Potentials (NNIPs) remains limited. NNIPs act as surrogate models for ab initio quantum mechanical calculations. The dominant paradigm here is to incorporate many physical domain constraints into the model, such as rotational equivariance. We contend that these complex constraints inhibit the scaling ability of NNIPs, and are likely to lead to performance plateaus in the long run. In this work, we take an alternative approach and start by systematically studying NNIP scaling strategies. Our findings indicate that scaling the model through attention mechanisms is efficient and improves model expressivity. These insights motivate us to develop an NNIP architecture designed for scalability: the Efficiently Scaled Attention Interatomic Potential (EScAIP). EScAIP leverages a multi-head self-attention formulation within graph neural networks, applying attention at the neighbor-level representations. Implemented with highly-optimized attention GPU kernels, EScAIP achieves substantial gains in efficiency--at least 10x faster inference, 5x less memory usage--compared to existing NNIPs. EScAIP also achieves state-of-the-art performance on a wide range of datasets including catalysts (OC20 and OC22), molecules (SPICE), and materials (MPTrj). We emphasize that our approach should be thought of as a philosophy rather than a specific model, representing a proof-of-concept for developing general-purpose NNIPs that achieve better expressivity through scaling, and continue to scale efficiently with increased computational resources and training data.

Hongwei Jin, Prasanna Balaprakash, Allen Zou et al.

The threat of geomagnetic disturbances (GMDs) to the reliable operation of the bulk energy system has spurred the development of effective strategies for mitigating their impacts. One such approach involves placing transformer neutral blocking devices, which interrupt the path of geomagnetically induced currents (GICs) to limit their impact. The high cost of these devices and the sparsity of transformers that experience high GICs during GMD events, however, calls for a sparse placement strategy that involves high computational cost. To address this challenge, we developed a physics-informed heterogeneous graph neural network (PIHGNN) for solving the graph-based dc-blocker placement problem. Our approach combines a heterogeneous graph neural network (HGNN) with a physics-informed neural network (PINN) to capture the diverse types of nodes and edges in ac/dc networks and incorporates the physical laws of the power grid. We train the PIHGNN model using a surrogate power flow model and validate it using case studies. Results demonstrate that PIHGNN can effectively and efficiently support the deployment of GIC dc-current blockers, ensuring the continued supply of electricity to meet societal demands. Our approach has the potential to contribute to the development of more reliable and resilient power grids capable of withstanding the growing threat that GMDs pose.

Eric Qu, Brandon M. Wood, Aditi S. Krishnapriyan et al.

Machine-learning interatomic potentials (MLIPs) have advanced rapidly, with many top models relying on strong physics-based inductive biases. However, as models scale to larger systems like biomolecules and electrolytes, they struggle to accurately capture long-range (LR) interactions, leading current approaches to rely on explicit physics-based terms or components. In this work, we propose AllScAIP, a straightforward, attention-based, and energy-conserving MLIP model that scales to O(100 million) training samples. It addresses the long-range challenge using an all-to-all node attention component that is data-driven. Extensive ablations reveal that in low-data/small-model regimes, inductive biases improve sample efficiency. However, as data and model size scale, these benefits diminish or even reverse, while all-to-all attention remains critical for capturing LR interactions. Our model achieves state-of-the-art energy/force accuracy on molecular systems, as well as a number of physics-based evaluations (OMol25), while being competitive on materials (OMat24) and catalysts (OC20). Furthermore, it enables stable, long-timescale MD simulations that accurately recover experimental observables, including density and heat of vaporization predictions.

Yiheng Du, Aditi S. Krishnapriyan

Computationally resolving turbulence remains a central challenge in fluid dynamics due to its multi-scale interactions. Fully resolving large-scale turbulence through direct numerical simulation (DNS) is computationally prohibitive, motivating data-driven machine learning alternatives. In this work, we propose EddyFormer, a Transformer-based spectral-element (SEM) architecture for large-scale turbulence simulation that combines the accuracy of spectral methods with the scalability of the attention mechanism. We introduce an SEM tokenization that decomposes the flow into grid-scale and subgrid-scale components, enabling capture of both local and global features. We create a new three-dimensional isotropic turbulence dataset and train EddyFormer to achieves DNS-level accuracy at 256^3 resolution, providing a 30x speedup over DNS. When applied to unseen domains up to 4x larger than in training, EddyFormer preserves accuracy on physics-invariant metrics-energy spectra, correlation functions, and structure functions-showing domain generalization. On The Well benchmark suite of diverse turbulent flows, EddyFormer resolves cases where prior ML models fail to converge, accurately reproducing complex dynamics across a wide range of physical conditions.

Tobias Kreiman, Yutong Bai, Fadi Atieh et al.

Graph Neural Networks (GNNs) are the dominant architecture for molecular machine learning, particularly for molecular property prediction and machine learning interatomic potentials (MLIPs). GNNs perform message passing on predefined graphs often induced by a fixed radius cutoff or k-nearest neighbor scheme. While this design aligns with the locality present in many molecular tasks, a hard-coded graph can limit expressivity due to the fixed receptive field and slows down inference with sparse graph operations. In this work, we investigate whether pure, unmodified Transformers trained directly on Cartesian coordinates$\unicode{x2013}$without predefined graphs or physical priors$\unicode{x2013}$can approximate molecular energies and forces. As a starting point for our analysis, we demonstrate how to train a Transformer to competitive energy and force mean absolute errors under a matched training compute budget, relative to a state-of-the-art equivariant GNN on the OMol25 dataset. We discover that the Transformer learns physically consistent patterns$\unicode{x2013}$such as attention weights that decay inversely with interatomic distance$\unicode{x2013}$and flexibly adapts them across different molecular environments due to the absence of hard-coded biases. The use of a standard Transformer also unlocks predictable improvements with respect to scaling training resources, consistent with empirical scaling laws observed in other domains. Our results demonstrate that many favorable properties of GNNs can emerge adaptively in Transformers, challenging the necessity of hard-coded graph inductive biases and pointing toward standardized, scalable architectures for molecular modeling.

Yue Jian, Curtis Wu, Danny Reidenbach et al.

Structure-based drug design (SBDD) aims to generate ligands that bind strongly and specifically to target protein pockets. Recent diffusion models have advanced SBDD by capturing the distributions of atomic positions and types, yet they often underemphasize binding affinity control during generation. To address this limitation, we introduce \textbf{\textnormal{\textbf{BADGER}}}, a general \textbf{binding-affinity guidance framework for diffusion models in SBDD}. \textnormal{\textbf{BADGER} }incorporates binding affinity awareness through two complementary strategies: (1) \textit{classifier guidance}, which applies gradient-based affinity signals during sampling in a plug-and-play fashion, and (2) \textit{classifier-free guidance}, which integrates affinity conditioning directly into diffusion model training. Together, these approaches enable controllable ligand generation guided by binding affinity. \textnormal{\textbf{BADGER} } can be added to any diffusion model and achieves up to a \textbf{60\% improvement in ligand--protein binding affinity} of sampled molecules over prior methods. Furthermore, we extend the framework to \textbf{multi-constraint diffusion guidance}, jointly optimizing for binding affinity, drug-likeness (QED), and synthetic accessibility (SA) to design realistic and synthesizable drug candidates.

Shengjie Luo, Tianlang Chen, Aditi S. Krishnapriyan

Developing equivariant neural networks for the E(3) group plays an important role in modeling 3D data across real-world applications. Enforcing this equivariance primarily involves the tensor products of irreducible representations (irreps). However, the computational complexity of such operations increases significantly as higher-order tensors are used. In this work, we propose a systematic approach to substantially accelerate the computation of the tensor products of irreps. We mathematically connect the commonly used Clebsch-Gordan coefficients to the Gaunt coefficients, which are integrals of products of three spherical harmonics. Through Gaunt coefficients, the tensor product of irreps becomes equivalent to the multiplication between spherical functions represented by spherical harmonics. This perspective further allows us to change the basis for the equivariant operations from spherical harmonics to a 2D Fourier basis. Consequently, the multiplication between spherical functions represented by a 2D Fourier basis can be efficiently computed via the convolution theorem and Fast Fourier Transforms. This transformation reduces the complexity of full tensor products of irreps from $\mathcal{O}(L^6)$ to $\mathcal{O}(L^3)$, where $L$ is the max degree of irreps. Leveraging this approach, we introduce the Gaunt Tensor Product, which serves as a new method to construct efficient equivariant operations across different model architectures. Our experiments on the Open Catalyst Project and 3BPA datasets demonstrate both the increased efficiency and improved performance of our approach.

Aditi S. Krishnapriyan, Alejandro F. Queiruga, N. Benjamin Erichson et al.

Dynamical systems that evolve continuously over time are ubiquitous throughout science and engineering. Machine learning (ML) provides data-driven approaches to model and predict the dynamics of such systems. A core issue with this approach is that ML models are typically trained on discrete data, using ML methodologies that are not aware of underlying continuity properties. This results in models that often do not capture any underlying continuous dynamics -- either of the system of interest, or indeed of any related system. To address this challenge, we develop a convergence test based on numerical analysis theory. Our test verifies whether a model has learned a function that accurately approximates an underlying continuous dynamics. Models that fail this test fail to capture relevant dynamics, rendering them of limited utility for many scientific prediction tasks; while models that pass this test enable both better interpolation and better extrapolation in multiple ways. Our results illustrate how principled numerical analysis methods can be coupled with existing ML training/testing methodologies to validate models for science and engineering applications.

Aditi S. Krishnapriyan, Amir Gholami, Shandian Zhe et al.

Recent work in scientific machine learning has developed so-called physics-informed neural network (PINN) models. The typical approach is to incorporate physical domain knowledge as soft constraints on an empirical loss function and use existing machine learning methodologies to train the model. We demonstrate that, while existing PINN methodologies can learn good models for relatively trivial problems, they can easily fail to learn relevant physical phenomena for even slightly more complex problems. In particular, we analyze several distinct situations of widespread physical interest, including learning differential equations with convection, reaction, and diffusion operators. We provide evidence that the soft regularization in PINNs, which involves PDE-based differential operators, can introduce a number of subtle problems, including making the problem more ill-conditioned. Importantly, we show that these possible failure modes are not due to the lack of expressivity in the NN architecture, but that the PINN's setup makes the loss landscape very hard to optimize. We then describe two promising solutions to address these failure modes. The first approach is to use curriculum regularization, where the PINN's loss term starts from a simple PDE regularization, and becomes progressively more complex as the NN gets trained. The second approach is to pose the problem as a sequence-to-sequence learning task, rather than learning to predict the entire space-time at once. Extensive testing shows that we can achieve up to 1-2 orders of magnitude lower error with these methods as compared to regular PINN training.

Arnur Nigmetov, Aditi S. Krishnapriyan, Nicole Sanderson et al.

Optimization, a key tool in machine learning and statistics, relies on regularization to reduce overfitting. Traditional regularization methods control a norm of the solution to ensure its smoothness. Recently, topological methods have emerged as a way to provide a more precise and expressive control over the solution, relying on persistent homology to quantify and reduce its roughness. All such existing techniques back-propagate gradients through the persistence diagram, which is a summary of the topological features of a function. Their downside is that they provide information only at the critical points of the function. We propose a method that instead builds on persistence-sensitive simplification and translates the required changes to the persistence diagram into changes on large subsets of the domain, including both critical and regular points. This approach enables a faster and more precise topological regularization, the benefits of which we illustrate with experimental evidence.

Nicolas Swenson, Aditi S. Krishnapriyan, Aydin Buluc et al.

Understanding protein structure-function relationships is a key challenge in computational biology, with applications across the biotechnology and pharmaceutical industries. While it is known that protein structure directly impacts protein function, many functional prediction tasks use only protein sequence. In this work, we isolate protein structure to make functional annotations for proteins in the Protein Data Bank in order to study the expressiveness of different structure-based prediction schemes. We present PersGNN - an end-to-end trainable deep learning model that combines graph representation learning with topological data analysis to capture a complex set of both local and global structural features. While variations of these techniques have been successfully applied to proteins before, we demonstrate that our hybridized approach, PersGNN, outperforms either method on its own as well as a baseline neural network that learns from the same information. PersGNN achieves a 9.3% boost in area under the precision recall curve (AUPR) compared to the best individual model, as well as high F1 scores across different gene ontology categories, indicating the transferability of this approach.

Aditi S. Krishnapriyan, Joseph Montoya, Maciej Haranczyk et al.

Machine learning has emerged as a powerful approach in materials discovery. Its major challenge is selecting features that create interpretable representations of materials, useful across multiple prediction tasks. We introduce an end-to-end machine learning model that automatically generates descriptors that capture a complex representation of a material's structure and chemistry. This approach builds on computational topology techniques (namely, persistent homology) and word embeddings from natural language processing. It automatically encapsulates geometric and chemical information directly from the material system. We demonstrate our approach on multiple nanoporous metal-organic framework datasets by predicting methane and carbon dioxide adsorption across different conditions. Our results show considerable improvement in both accuracy and transferability across targets compared to models constructed from the commonly-used, manually-curated features, consistently achieving an average 25-30% decrease in root-mean-squared-deviation and an average increase of 40-50% in R2 scores. A key advantage of our approach is interpretability: Our model identifies the pores that correlate best to adsorption at different pressures, which contributes to understanding atomic-level structure--property relationships for materials design.

Aditi S. Krishnapriyan, Maciej Haranczyk, Dmitriy Morozov

Machine learning has emerged as an attractive alternative to experiments and simulations for predicting material properties. Usually, such an approach relies on specific domain knowledge for feature design: each learning target requires careful selection of features that an expert recognizes as important for the specific task. The major drawback of this approach is that computation of only a few structural features has been implemented so far, and it is difficult to tell a priori which features are important for a particular application. The latter problem has been empirically observed for predictors of guest uptake in nanoporous materials: local and global porosity features become dominant descriptors at low and high pressures, respectively. We investigate a feature representation of materials using tools from topological data analysis. Specifically, we use persistent homology to describe the geometry of nanoporous materials at various scales. We combine our topological descriptor with traditional structural features and investigate the relative importance of each to the prediction tasks. We demonstrate an application of this feature representation by predicting methane adsorption in zeolites, for pressures in the range of 1-200 bar. Our results not only show a considerable improvement compared to the baseline, but they also highlight that topological features capture information complementary to the structural features: this is especially important for the adsorption at low pressure, a task particularly difficult for the traditional features. Furthermore, by investigation of the importance of individual topological features in the adsorption model, we are able to pinpoint the location of the pores that correlate best to adsorption at different pressure, contributing to our atom-level understanding of structure-property relationships.