arXiv subjects

Nicholas Lubbers

Publications and source records attributed to Nicholas Lubbers.

At least 19 recordsLinked to original sources

arXiv2026

Projected Hessian Learning: Fast Curvature Supervision for Accurate Machine-Learning Interatomic Potentials

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.

physics.chem-ph↗

arXiv2026

Knowledge Distillation of Noisy Force Labels for Improved Coarse-Grained Force Fields

Molecular dynamics simulations are an integral tool for studying the atomistic behavior of materials under diverse conditions. However, they can be computationally demanding in wall-clock time, especially for large systems, which limits the time and length scales accessible. Coarse-grained (CG) models reduce computational expense by grouping atoms into simplified representations commonly called beads, but sacrifice atomic detail and introduce mapping noise, complicating the training of machine-learned surrogates. Moreover, because CG models inherently include entropic contributions, they cannot be fit directly to all-atom energies, leaving instantaneous, noisy forces as the only state-specific quantities available for training. Here, we apply a knowledge distillation framework by first training an initial CG neural network potential (the teacher) solely on AA-to-CG mapped forces to denoise those labels, then distill its force and energy predictions to train refined CG models (the student) in both single- and ensemble-training setups while exploring different force and energy target combinations. We validate this framework on a complex molecular fluid, a deep eutectic solvent, by evaluating two-, three-, and many-body properties and compare the CG and all-atom results. Our findings demonstrate that training a student model on ensemble teacher-predicted forces and per-bead energies improves the quality and stability of CG force fields.

physics.chem-ph↗

arXiv2026

Effects of Structural Allocation of Geometric Task Diversity in Linear Meta-Learning Models

Meta-learning aims to leverage information across related tasks to improve prediction on unlabeled data for new tasks when only a small number of labeled observations are available ("few-shot" learning). Increased task diversity is often believed to enhance meta-learning by providing richer information across tasks. However, recent work by Kumar et al. (2022) shows that increasing task diversity, quantified through the overall geometric spread of task representations, can in fact degrade meta-learning prediction performance across a range of models and datasets. In this work, we build on this observation by showing that meta-learning performance is affected not only by the overall geometric variability of task parameters, but also by how this variability is allocated relative to an underlying low-dimensional structure. Similar to Pimonova et al. (2025), we decompose task-specific regression effects into a structurally informative component and an orthogonal, non-informative component. We show theoretically and through simulation that meta-learning prediction degrades when a larger fraction of between-task variability lies in orthogonal, non-informative directions, even when the overall geometric variability of tasks is held fixed.

stat.ML↗

arXiv2025

Enhancing Molecular Dipole Moment Prediction with Multitask Machine Learning

We present a multitask machine learning strategy for improving the prediction of molecular dipole moments by simultaneously training on quantum dipole magnitudes and inexpensive Mulliken atomic charges. With dipole magnitudes as the primary target and assuming only scalar dipole values are available without vector components we examine whether incorporating lower quality labels that do not quantitatively reproduce the target property can still enhance model accuracy. Mulliken charges were chosen intentionally as an auxiliary task, since they lack quantitative accuracy yet encode qualitative physical information about charge distribution. Our results show that including Mulliken charges with a small weight in the loss function yields up to a 30% improvement in dipole prediction accuracy. This multitask approach enables the model to learn a more physically grounded representation of charge distributions, thereby improving both the accuracy and consistency of dipole magnitude predictions. These findings highlight that even auxiliary data of limited quantitative reliability can provide valuable qualitative physical insights, ultimately strengthening the predictive power of machine learning models for molecular properties.

physics.chem-ph↗

arXiv2025

Multi-fidelity learning for interatomic potentials: Low-level forces and high-level energies are all you need

The promise of machine learning interatomic potentials (MLIPs) has led to an abundance of public quantum mechanical (QM) training datasets. The quality of an MLIP is directly limited by the accuracy of the energies and atomic forces in the training dataset. Unfortunately, most of these datasets are computed with relatively low-accuracy QM methods, e.g., density functional theory with a moderate basis set. Due to the increased computational cost of more accurate QM methods, e.g., coupled-cluster theory with a complete basis set extrapolation, most high-accuracy datasets are much smaller and often do not contain atomic forces. The lack of high-accuracy atomic forces is quite troubling, as training with force data greatly improves the stability and quality of the MLIP compared to training to energy alone. Because most datasets are computed with a unique level of theory, traditional single-fidelity learning is not capable of leveraging the vast amounts of published QM data. In this study, we apply multi-fidelity learning to train an MLIP to multiple QM datasets of different levels of accuracy, i.e., levels of fidelity. Specifically, we perform three test cases to demonstrate that multi-fidelity learning with both low-level forces and high-level energies yields an extremely accurate MLIP -- far more accurate than a single-fidelity MLIP trained solely to high-level energies and almost as accurate as a single-fidelity MLIP trained directly to high-level energies and forces. Therefore, multi-fidelity learning greatly alleviates the need for generating large and expensive datasets containing high-accuracy atomic forces and allows for more effective training to existing high-accuracy energy-only datasets. Indeed, low-accuracy atomic forces and high-accuracy energies are all that are needed to achieve a high-accuracy MLIP with multi-fidelity learning.

physics.comp-ph↗

arXiv2025

Meta-Learning Linear Models for Molecular Property Prediction

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.

cs.LG↗

arXiv2025

Reactive Chemistry at Unrestricted Coupled Cluster Level: High-throughput Calculations for Training Machine Learning Potentials

Accurately modeling chemical reactions at the atomistic level requires high-level electronic structure theory due to the presence of unpaired electrons and the need to properly describe bond breaking and making energetics. Commonly used approaches such as Density Functional Theory (DFT) frequently fail for this task due to deficiencies that are well recognized. However, for high-fidelity approaches, creating large datasets of energies and forces for reactive processes to train machine learning interatomic potentials or force fields is daunting. For example, the use of the unrestricted coupled cluster level of theory has previously been seen as unfeasible due to high computational costs, the lack of analytical gradients in many computational codes, and additional challenges such as constructing suitable basis set corrections for forces. In this work, we develop new methods and workflows to overcome the challenges inherent to automating unrestricted coupled cluster calculations. Using these advancements, we create a dataset of gas-phase reactions containing energies and forces for 3119 different organic molecules configurations calculated at the gold-standard level of unrestricted CCSD(T) (coupled cluster singles doubles and perturbative triples). With this dataset, we provide an analysis of the differences between the density functional and unrestricted CCSD(T) descriptions. We develop a transferable machine learning interatomic potential for gas-phase reactions, trained on unrestricted CCSD(T) data, and demonstrate the advantages of transitioning away from DFT data. Transitioning from training to DFT to training to UCCSD(T) datasets yields an improvement of more than 0.1 eV/Å in force accuracy and over 0.1 eV in activation energy reproduction.

physics.chem-ph↗

arXiv2025

Teacher-student training improves accuracy and efficiency of machine learning interatomic potentials

Machine learning interatomic potentials (MLIPs) are revolutionizing the field of molecular dynamics (MD) simulations. Recent MLIPs have tended towards more complex architectures trained on larger datasets. The resulting increase in computational and memory costs may prohibit the application of these MLIPs to perform large-scale MD simulations. Here, we present a teacher-student training framework in which the latent knowledge from the teacher (atomic energies) is used to augment the students' training. We show that the light-weight student MLIPs have faster MD speeds at a fraction of the memory footprint compared to the teacher models. Remarkably, the student models can even surpass the accuracy of the teachers, even though both are trained on the same quantum chemistry dataset. Our work highlights a practical method for MLIPs to reduce the resources required for large-scale MD simulations.

physics.chem-ph↗

arXiv2025

Ensemble Knowledge Distillation for Machine Learning Interatomic Potentials

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.

physics.chem-ph↗

arXiv2025

Toward machine learning interatomic potentials for modeling uranium mononitride

Uranium mononitride (UN) is a promising accident-tolerant fuel because of its high fissile density and high thermal conductivity. In this study, we developed the first machine learning interatomic potentials for reliable atomic-scale modeling of UN at finite temperatures. We constructed a training set using density functional theory (DFT) calculations that was enriched through an active learning procedure, and two neural network potentials were generated. Both potentials successfully reproduce key thermophysical properties of interest, such as temperature-dependent lattice parameter, specific heat capacity, and bulk modulus. We also evaluated the energy of stoichiometric defect reactions and defect migration barriers and found close agreement with DFT predictions, demonstrating that our potentials can be used for modeling defects in UN. Additional tests provide evidence that our potentials are reliable for simulating diffusion, noble gas impurities, and radiation damage.

cond-mat.mtrl-sci↗

arXiv2025

Discrete Spatial Diffusion: Intensity-Preserving Diffusion Modeling

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.

cs.GR↗

arXiv2025

Flexible Moment-Invariant Bases from Irreducible Tensors

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.

cs.CV↗

arXiv2025

Optimal Invariant Bases for Atomistic Machine Learning

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.

physics.chem-ph↗

arXiv2025

GPU-Accelerated Charge-Equilibration for Shadow Molecular Dynamics in Python

With recent advancements in machine learning for interatomic potentials, Python has become the go-to programming language for exploring new ideas. While machine-learning potentials are often developed in Python-based frameworks, existing molecular dynamics software is predominantly written in lower-level languages. This disparity complicates the integration of machine learning potentials into these molecular dynamics libraries. Additionally, machine learning potentials typically focus on local features, often neglecting long-range electrostatics due to computational complexities. This is a key limitation as applications can require long-range electrostatics and even flexible charges to achieve the desired accuracy. Recent charge equilibration models can address these issues, but they require iterative solvers to assign relaxed flexible charges to the atoms. Conventional implementations also demand very tight convergence to achieve long-term stability, further increasing computational cost. In this work, we present a scalable Python implementation of a recently proposed shadow molecular dynamics scheme based on a charge equilibration model, which avoids the convergence problem while maintaining long-term energy stability and accuracy of observable properties. To deliver a functional and user-friendly Python-based library, we implemented an efficient neighbor list algorithm, Particle Mesh Ewald, and traditional Ewald summation techniques, leveraging the GPU-accelerated power of Triton and PyTorch. We integrated these approaches with the Python-based shadow molecular dynamics scheme, enabling fast charge equilibration for scalable machine learning potentials involving systems with hundreds of thousands of atoms.

physics.comp-ph↗

arXiv2025

Model-Agnostic Knowledge Guided Correction for Improved Neural Surrogate Rollout

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.

cs.LG↗

arXiv2024

Thermodynamic Transferability in Coarse-Grained Force Fields using Graph Neural Networks

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.

physics.chem-ph↗

arXiv2024

Machine Learning Framework for Modeling Exciton-Polaritons in Molecular Materials

A light-matter hybrid quasiparticle, called a polariton, is formed when molecules are strongly coupled to an optical cavity. Recent experiments have shown that polariton chemistry can manipulate chemical reactions. Polariton chemistry is a collective phenomenon and its effects increase with the number of molecules in a cavity. However, simulating an ensemble of molecules in the excited state coupled to a cavity mode is theoretically and computationally challenging. Recent advances in machine learning techniques have shown promising capabilities in modeling ground state chemical systems. This work presents a general protocol to predict excited-state properties, such as energies, transition dipoles, and non-adiabatic coupling vectors with the hierarchically interacting particle neural network. Machine learning predictions are then applied to compute potential energy surfaces and electronic spectra of a prototype azomethane molecule in the collective coupling scenario. These computational tools provide a much-needed framework to model and understand many molecules' emerging excited-state polariton chemistry.

physics.chem-ph↗

arXiv2023

Learning a General Model of Single Phase Flow in Complex 3D Porous Media

Modeling effective transport properties of 3D porous media, such as permeability, at multiple scales is challenging as a result of the combined complexity of the pore structures and fluid physics - in particular, confinement effects which vary across the nanoscale to the microscale. While numerical simulation is possible, the computational cost is prohibitive for realistic domains, which are large and complex. Although machine learning models have been proposed to circumvent simulation, none so far has simultaneously accounted for heterogeneous 3D structures, fluid confinement effects, and multiple simulation resolutions. By utilizing numerous computer science techniques to improve the scalability of training, we have for the first time developed a general flow model that accounts for the pore-structure and corresponding physical phenomena at scales from Angstrom to the micrometer. Using synthetic computational domains for training, our machine learning model exhibits strong performance (R$^2$=0.9) when tested on extremely diverse real domains at multiple scales.

physics.geo-ph↗