Nicholas Lubbers

Satish Karra, Mohamed Mehana, Nicholas Lubbers et al.

Throughout computational science, there is a growing need to utilize the continual improvements in raw computational horsepower to achieve greater physical fidelity through scale-bridging over brute-force increases in the number of mesh elements. For instance, quantitative predictions of transport in nanoporous media, critical to hydrocarbon extraction from tight shale formations, are impossible without accounting for molecular-level interactions. Similarly, inertial confinement fusion simulations rely on numerical diffusion to simulate molecular effects such as non-local transport and mixing without truly accounting for molecular interactions. With these two disparate applications in mind, we develop a novel capability which uses an active learning approach to optimize the use of local fine-scale simulations for informing coarse-scale hydrodynamics. Our approach addresses three challenges: forecasting continuum coarse-scale trajectory to speculatively execute new fine-scale molecular dynamics calculations, dynamically updating coarse-scale from fine-scale calculations, and quantifying uncertainty in neural network models.

Bharat Srikishan, Daniel O'Malley, Mohamed Mehana et al.

Modeling the evolution of physical systems is critical to many applications in science and engineering. As the evolution of these systems is governed by partial differential equations (PDEs), there are a number of computational simulations which resolve these systems with high accuracy. However, as these simulations incur high computational costs, they are infeasible to be employed for large-scale analysis. A popular alternative to simulators are neural network surrogates which are trained in a data-driven manner and are much more computationally efficient. However, these surrogate models suffer from high rollout error when used autoregressively, especially when confronted with training data paucity. Existing work proposes to improve surrogate rollout error by either including physical loss terms directly in the optimization of the model or incorporating computational simulators as `differentiable layers' in the neural network. Both of these approaches have their challenges, with physical loss functions suffering from slow convergence for stiff PDEs and simulator layers requiring gradients which are not always available, especially in legacy simulators. We propose the Hybrid PDE Predictor with Reinforcement Learning (HyPER) model: a model-agnostic, RL based, cost-aware model which combines a neural surrogate, RL decision model, and a physics simulator (with or without gradients) to reduce surrogate rollout error significantly. In addition to reducing in-distribution rollout error by 47%-78%, HyPER learns an intelligent policy that is adaptable to changing physical conditions and resistant to noise corruption. Code available at https://github.com/scailab/HyPER.

Austin Rodriguez, Justin S. Smith, Sakib Matin et al.

The Hessian matrix (second derivatives) encodes far richer local curvature of the potential energy surface than energies and forces alone. However, training machine-learning interatomic potentials (MLIPs) with full Hessians is often impractical because explicitly forming and storing Hessian matrices scales quadratically in cost and memory. We introduce Projected Hessian Learning (PHL), a scalable second-order training framework that injects curvature information using only Hessian-vector products (HVPs). Rather than constructing the Hessian, PHL projects curvature along stochastic probe directions and uses an unbiased stochastic trace-based loss with favorable system-size scaling, enabling curvature-informed training without quadratic memory growth. We benchmark PHL on a chemically diverse dataset of reactants, products, transition states, intrinsic reaction coordinates, and normal-mode sampled geometries computed at omegaB97XD/6-31G(d). We compare energy-force training (E-F), two HVP-based schemes (E-F-HVP with one-hot or randomized probes), and full energy-force-Hessian training (E-F-H). With randomized probes per minibatch, both HVP schemes match full-Hessian training in energy, force, and Hessian accuracy while delivering >24x epoch speedups for the small molecular systems studied. In a fixed-probe regime with one HVP per molecule, randomized projections consistently outperform one-column probing, especially for far-from-equilibrium geometries. Overall, PHL replaces explicit Hessian supervision with force-complexity curvature training, retaining most second-order accuracy gains while scaling to larger, more complex molecular systems.

Sakib Matin, Emily Shinkle, Yulia Pimonova et al.

The quality of machine learning interatomic potentials (MLIPs) strongly depends on the quantity of training data as well as the quantum chemistry (QC) level of theory used. Datasets generated with high-fidelity QC methods are typically restricted to small molecules and may be missing energy gradients, which make it difficult to train accurate MLIPs. We present an ensemble knowledge distillation (EKD) method to improve MLIP accuracy when trained to energy-only datasets. First, multiple teacher models are trained to QC energies and then generate atomic forces for all configurations in the dataset. Next, the student MLIP is trained to both QC energies and to ensemble-averaged forces generated by the teacher models. We apply this workflow on the ANI-1ccx dataset where the configuration energies computed at the coupled cluster level of theory. The resulting student MLIPs achieve new state-of-the-art accuracy on the COMP6 benchmark and show improved stability for molecular dynamics simulations.

Javier E. Santos, Agnese Marcato, Roman Colman et al.

Generative diffusion models have achieved remarkable success in producing high-quality images. However, these models typically operate in continuous intensity spaces, diffusing independently across pixels and color channels. As a result, they are fundamentally ill-suited for applications involving inherently discrete quantities-such as particle counts or material units-that are constrained by strict conservation laws like mass conservation, limiting their applicability in scientific workflows. To address this limitation, we propose Discrete Spatial Diffusion (DSD), a framework based on a continuous-time, discrete-state jump stochastic process that operates directly in discrete spatial domains while strictly preserving particle counts in both forward and reverse diffusion processes. By using spatial diffusion to achieve particle conservation, we introduce stochasticity naturally through a discrete formulation. We demonstrate the expressive flexibility of DSD by performing image synthesis, class conditioning, and image inpainting across standard image benchmarks, while exactly conditioning total image intensity. We validate DSD on two challenging scientific applications: porous rock microstructures and lithium-ion battery electrodes, demonstrating its ability to generate structurally realistic samples under strict mass conservation constraints, with quantitative evaluation using state-of-the-art metrics for transport and electrochemical performance.

Alice E. A. Allen, Emily Shinkle, Roxana Bujack et al.

The representation of atomic configurations for machine learning models has led to the development of numerous descriptors, often to describe the local environment of atoms. However, many of these representations are incomplete and/or functionally dependent. Incomplete descriptor sets are unable to represent all meaningful changes in the atomic environment. Complete constructions of atomic environment descriptors, on the other hand, often suffer from a high degree of functional dependence, where some descriptors can be written as functions of the others. These redundant descriptors do not provide additional power to discriminate between different atomic environments and increase the computational burden. By employing techniques from the pattern recognition literature to existing atomistic representations, we remove descriptors that are functions of other descriptors to produce the smallest possible set that satisfies completeness. We apply this in two ways: first we refine an existing description, the Atomistic Cluster Expansion. We show that this yields a more efficient subset of descriptors. Second, we augment an incomplete construction based on a scalar neural network, yielding a new message-passing network architecture that can recognize up to 5-body patterns in each neuron by taking advantage of an optimal set of Cartesian tensor invariants. This architecture shows strong accuracy on state-of-the-art benchmarks while retaining low computational cost. Our results not only yield improved models, but point the way to classes of invariant bases that minimize cost while maximizing expressivity for a host of applications.

Roxana Bujack, Emily Shinkle, Alice Allen et al.

Moment invariants are a powerful tool for the generation of rotation-invariant descriptors needed for many applications in pattern detection, classification, and machine learning. A set of invariants is optimal if it is complete, independent, and robust against degeneracy in the input. In this paper, we show that the current state of the art for the generation of these bases of moment invariants, despite being robust against moment tensors being identically zero, is vulnerable to a degeneracy that is common in real-world applications, namely spherical functions. We show how to overcome this vulnerability by combining two popular moment invariant approaches: one based on spherical harmonics and one based on Cartesian tensor algebra.

Saptati Datta, Nicolas W. Hengartner, Yulia Pimonova et al.

Meta-learning has emerged as a powerful paradigm for leveraging information across related tasks to improve predictive performance on new tasks. In this paper, we propose a statistical framework for analyzing meta-learning through the lens of predictor subspace characterization and quantification of task diversity. Specifically, we model the shared structure across tasks using a latent subspace and introduce a measure of diversity that captures heterogeneity across task-specific predictors. We provide both simulation-based and theoretical evidence indicating that achieving the desired prediction accuracy in meta-learning depends on the proportion of predictor variance aligned with the shared subspace, as well as on the accuracy of subspace estimation.

Yulia Pimonova, Michael G. Taylor, Alice Allen et al.

Chemists in search of structure-property relationships face great challenges due to limited high quality, concordant datasets. Machine learning (ML) has significantly advanced predictive capabilities in chemical sciences, but these modern data-driven approaches have increased the demand for data. In response to the growing demand for explainable AI (XAI) and to bridge the gap between predictive accuracy and human comprehensibility, we introduce LAMeL - a Linear Algorithm for Meta-Learning that preserves interpretability while improving the prediction accuracy across multiple properties. While most approaches treat each chemical prediction task in isolation, LAMeL leverages a meta-learning framework to identify shared model parameters across related tasks, even if those tasks do not share data, allowing it to learn a common functional manifold that serves as a more informed starting point for new unseen tasks. Our method delivers performance improvements ranging from 1.1- to 25-fold over standard ridge regression, depending on the domain of the dataset. While the degree of performance enhancement varies across tasks, LAMeL consistently outperforms or matches traditional linear methods, making it a reliable tool for chemical property prediction where both accuracy and interpretability are critical.

Emily Shinkle, Aleksandra Pachalieva, Riti Bahl et al.

Coarse-graining is a molecular modeling technique in which an atomistic system is represented in a simplified fashion that retains the most significant system features that contribute to a target output, while removing the degrees of freedom that are less relevant. This reduction in model complexity allows coarse-grained molecular simulations to reach increased spatial and temporal scales compared to corresponding all-atom models. A core challenge in coarse-graining is to construct a force field that represents the interactions in the new representation in a way that preserves the atomistic-level properties. Many approaches to building coarse-grained force fields have limited transferability between different thermodynamic conditions as a result of averaging over internal fluctuations at a specific thermodynamic state point. Here, we use a graph-convolutional neural network architecture, the Hierarchically Interacting Particle Neural Network with Tensor Sensitivity (HIP-NN-TS), to develop a highly automated training pipeline for coarse grained force fields which allows for studying the transferability of coarse-grained models based on the force-matching approach. We show that this approach not only yields highly accurate force fields, but also that these force fields are more transferable through a variety of thermodynamic conditions. These results illustrate the potential of machine learning techniques such as graph neural networks to improve the construction of transferable coarse-grained force fields.

Javier E Santos, Zachary R. Fox, Nicholas Lubbers et al.

Typical generative diffusion models rely on a Gaussian diffusion process for training the backward transformations, which can then be used to generate samples from Gaussian noise. However, real world data often takes place in discrete-state spaces, including many scientific applications. Here, we develop a theoretical formulation for arbitrary discrete-state Markov processes in the forward diffusion process using exact (as opposed to variational) analysis. We relate the theory to the existing continuous-state Gaussian diffusion as well as other approaches to discrete diffusion, and identify the corresponding reverse-time stochastic process and score function in the continuous-time setting, and the reverse-time mapping in the discrete-time setting. As an example of this framework, we introduce ``Blackout Diffusion'', which learns to produce samples from an empty image instead of from noise. Numerical experiments on the CIFAR-10, Binarized MNIST, and CelebA datasets confirm the feasibility of our approach. Generalizing from specific (Gaussian) forward processes to discrete-state processes without a variational approximation sheds light on how to interpret diffusion models, which we discuss.

Javier Santos, Ying Yin, Honggeun Jo et al.

The permeability of complex porous materials can be obtained via direct flow simulation, which provides the most accurate results, but is very computationally expensive. In particular, the simulation convergence time scales poorly as simulation domains become tighter or more heterogeneous. Semi-analytical models that rely on averaged structural properties (i.e. porosity and tortuosity) have been proposed, but these features only summarize the domain, resulting in limited applicability. On the other hand, data-driven machine learning approaches have shown great promise for building more general models by virtue of accounting for the spatial arrangement of the domains solid boundaries. However, prior approaches building on the Convolutional Neural Network (ConvNet) literature concerning 2D image recognition problems do not scale well to the large 3D domains required to obtain a Representative Elementary Volume (REV). As such, most prior work focused on homogeneous samples, where a small REV entails that that the global nature of fluid flow could be mostly neglected, and accordingly, the memory bottleneck of addressing 3D domains with ConvNets was side-stepped. Therefore, important geometries such as fractures and vuggy domains could not be well-modeled. In this work, we address this limitation with a general multiscale deep learning model that is able to learn from porous media simulation data. By using a coupled set of neural networks that view the domain on different scales, we enable the evaluation of large images in approximately one second on a single Graphics Processing Unit. This model architecture opens up the possibility of modeling domain sizes that would not be feasible using traditional direct simulation tools on a desktop computer.

Justin S. Smith, Nicholas Lubbers, Aidan P. Thompson et al.

Abstract Machine learning models, trained on data from ab initio quantum simulations, are yielding molecular dynamics potentials with unprecedented accuracy. One limiting factor is the quantity of available training data, which can be expensive to obtain. A quantum simulation often provides all atomic forces, in addition to the total energy of the system. These forces provide much more information than the energy alone. It may appear that training a model to this large quantity of force data would introduce significant computational costs. Actually, training to all available force data should only be a few times more expensive than training to energies alone. Here, we present a new algorithm for efficient force training, and benchmark its accuracy by training to forces from real-world datasets for organic chemistry and bulk aluminum.

Javier E. Santos, Mohammed Mehana, Hao Wu et al.

Predicting the spatial configuration of gas molecules in nanopores of shale formations is crucial for fluid flow forecasting and hydrocarbon reserves estimation. The key challenge in these tight formations is that the majority of the pore sizes are less than 50 nm. At this scale, the fluid properties are affected by nanoconfinement effects due to the increased fluid-solid interactions. For instance, gas adsorption to the pore walls could account for up to 85% of the total hydrocarbon volume in a tight reservoir. Although there are analytical solutions that describe this phenomenon for simple geometries, they are not suitable for describing realistic pores, where surface roughness and geometric anisotropy play important roles. To describe these, molecular dynamics (MD) simulations are used since they consider fluid-solid and fluid-fluid interactions at the molecular level. However, MD simulations are computationally expensive, and are not able to simulate scales larger than a few connected nanopores. We present a method for building and training physics-based deep learning surrogate models to carry out fast and accurate predictions of molecular configurations of gas inside nanopores. Since training deep learning models requires extensive databases that are computationally expensive to create, we employ active learning (AL). AL reduces the overhead of creating comprehensive sets of high-fidelity data by determining where the model uncertainty is greatest, and running simulations on the fly to minimize it. The proposed workflow enables nanoconfinement effects to be rigorously considered at the mesoscale where complex connected sets of nanopores control key applications such as hydrocarbon recovery and CO2 sequestration.

Justin S. Smith, Benjamin Nebgen, Nithin Mathew et al.

Accuracy of molecular dynamics simulations depends crucially on the interatomic potential used to generate forces. The gold standard would be first-principles quantum mechanics (QM) calculations, but these become prohibitively expensive at large simulation scales. Machine learning (ML) based potentials aim for faithful emulation of QM at drastically reduced computational cost. The accuracy and robustness of an ML potential is primarily limited by the quality and diversity of the training dataset. Using the principles of active learning (AL), we present a highly automated approach to dataset construction. The strategy is to use the ML potential under development to sample new atomic configurations and, whenever a configuration is reached for which the ML uncertainty is sufficiently large, collect new QM data. Here, we seek to push the limits of automation, removing as much expert knowledge from the AL process as possible. All sampling is performed using MD simulations starting from an initially disordered configuration, and undergoing non-equilibrium dynamics as driven by time-varying applied temperatures. We demonstrate this approach by building an ML potential for aluminum (ANI-Al). After many AL iterations, ANI-Al teaches itself to predict properties like the radial distribution function in melt, liquid-solid coexistence curve, and crystal properties such as defect energies and barriers. To demonstrate transferability, we perform a 1.3M atom shock simulation, and show that ANI-Al predictions agree very well with DFT calculations on local atomic environments sampled from the nonequilibrium dynamics. Interestingly, the configurations appearing in shock appear to have been well sampled in the AL training dataset, in a way that we illustrate visually.

Justin S. Smith, Ben Nebgen, Nicholas Lubbers et al.

The development of accurate and transferable machine learning (ML) potentials for predicting molecular energetics is a challenging task. The process of data generation to train such ML potentials is a task neither well understood nor researched in detail. In this work, we present a fully automated approach for the generation of datasets with the intent of training universal ML potentials. It is based on the concept of active learning (AL) via Query by Committee (QBC), which uses the disagreement between an ensemble of ML potentials to infer the reliability of the ensemble's prediction. QBC allows the presented AL algorithm to automatically sample regions of chemical space where the ML potential fails to accurately predict the potential energy. AL improves the overall fitness of ANAKIN-ME (ANI) deep learning potentials in rigorous test cases by mitigating human biases in deciding what new training data to use. AL also reduces the training set size to a fraction of the data required when using naive random sampling techniques. To provide validation of our AL approach we develop the COMP6 benchmark (publicly available on GitHub), which contains a diverse set of organic molecules. Through the AL process, it is shown that the AL-based potentials perform as well as the ANI-1 potential on COMP6 with only 10% of the data, and vastly outperforms ANI-1 with 25% the amount of data. Finally, we show that our proposed AL technique develops a universal ANI potential (ANI-1x) that provides accurate energy and force predictions on the entire COMP6 benchmark. This universal ML potential achieves a level of accuracy on par with the best ML potentials for single molecule or materials, while remaining applicable to the general class of organic molecules comprised of the elements CHNO.

Nicholas Lubbers, Justin S. Smith, Kipton Barros

We introduce the Hierarchically Interacting Particle Neural Network (HIP-NN) to model molecular properties from datasets of quantum calculations. Inspired by a many-body expansion, HIP-NN decomposes properties, such as energy, as a sum over hierarchical terms. These terms are generated from a neural network--a composition of many nonlinear transformations--acting on a representation of the molecule. HIP-NN achieves state-of-the-art performance on a dataset of 131k ground state organic molecules, and predicts energies with 0.26 kcal/mol mean absolute error. With minimal tuning, our model is also competitive on a dataset of molecular dynamics trajectories. In addition to enabling accurate energy predictions, the hierarchical structure of HIP-NN helps to identify regions of model uncertainty.

Nicholas Lubbers, Turab Lookman, Kipton Barros

We apply recent advances in machine learning and computer vision to a central problem in materials informatics: The statistical representation of microstructural images. We use activations in a pre-trained convolutional neural network to provide a high-dimensional characterization of a set of synthetic microstructural images. Next, we use manifold learning to obtain a low-dimensional embedding of this statistical characterization. We show that the low-dimensional embedding extracts the parameters used to generate the images. According to a variety of metrics, the convolutional neural network method yields dramatically better embeddings than the analogous method derived from two-point correlations alone.