arXiv subjects

Sakib Matin

Publications and source records attributed to Sakib Matin.

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↗

arXiv2025

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↗

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/{\AA} in force accuracy and over 0.1 eV in activation energy reproduction.

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

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

Kitaev interaction and proximate higher-order skyrmion crystal in the triangular lattice van der Waals antiferromagnet NiI2

Topological spin textures, such as magnetic skyrmions, are a spectacular manifestation of magnetic frustration and anisotropy. Most known skyrmion systems are restricted to a topological charge of one, require an external magnetic field for stabilization, and are only reported in a few materials. Here, we investigate the possibility that the Kitaev anisotropic-exchange interaction stabilizes a higher-order skyrmion crystal in the insulating van der Waals magnet NiI2. We unveil and explain the incommensurate static and dynamic magnetic correlations across three temperature-driven magnetic phases of this compound using neutron scattering measurements, simulations, and modeling. Our parameter optimisation yields a minimal Kitaev-Heisenberg Hamiltonian for NiI2 which reproduces the experimentally observed magnetic excitations. Monte Carlo simulations for this model predict the emergence of the higher-order skyrmion crystal but neutron diffraction and optical experiments in the candidate intermediate temperature regime are inconclusive. We discuss possible deviations from the Kitaev-Heisenberg model that explains our results and conclude that NiI2, in addition to multiferroic properties in the bulk and few-layer limits, is a Kitaev bulk material proximate to the finite temperature higher-order skyrmion crystal phase.

cond-mat.mtrl-sci↗

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

Sunny.jl: A Julia Package for Spin Dynamics

Sunny is a Julia package designed to serve the needs of the quantum magnetism community. It supports the specification of a very broad class of spin models and a diverse suite of numerical solvers. These include powerful methods for simulating spin dynamics both in and out of equilibrium. Uniquely, it features a broad generalization of classical and semiclassical approaches to SU(N) coherent states, which is useful for studying systems exhibiting strong spin-orbit coupling or local entanglement effects. Sunny also offers a well-developed framework for calculating the dynamical spin structure factor, enabling direct comparison with scattering experiments. Ease of use is a priority, with tools for symmetry-guided modeling and interactive visualization.

quant-ph↗

arXiv2024

Spin dynamics of triple-Q magnetic orderings in a triangular lattice: Implications for multi-Q orderings in general two-dimensional lattices

Multi-Q magnetic structures on two-dimensional (2D) lattices provide a key route to realizing topological physics in 2D magnetism. A major experimental challenge is to unambiguously confirm their formation by excluding the possibility of topologically trivial multi-domain single- or double-Q magnetic orders, which cannot be distinguished using conventional diffraction techniques. Here, we propose that long-wavelength spin dynamics offers a universal diagnostic for triangular lattices: triple-Q orders that preserve rotational symmetry and single- or double-Q orders that break it exhibit qualitatively distinct anisotropies in their Goldstone mode velocities, stemming from fundamental differences in their underlying spin configurations. We validate this concept using the metallic triangular lattice antiferromagnet Co$_{0.325}$TaS$_{2}$, which hosts both a stripe-type single-Q state and a triple-Q tetrahedral ordering at different temperatures. Using inelastic neutron scattering (INS) and spin dynamics simulations, we first refine the spin Hamiltonian by fitting the paramagnetic excitation spectra, allowing us to develop an unbiased model independent of magnetic ordering. We then show that the observed velocity profiles of the Goldstone modes agree with the high-temperature model's predictions: markedly anisotropic for the single-Q phase and near isotropic for the triple-Q phase. Importantly, this contrast persists across various exchange parameters, highlighting its model-independent nature and suggesting potential applicability to other 2D lattice systems. This work provides universal insight into the dynamical properties of topological multi-Q magnetic orderings in 2D lattice structures, offering a broadly applicable diagnostic to distinguishing them from topologically trivial single- or double-Q counterparts. (For the full abstract, please refer to the manuscript)

cond-mat.str-el↗

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↗

arXiv2023

Machine learning potentials with Iterative Boltzmann Inversion: training to experiment

Methodologies for training machine learning potentials (MLPs) to quantum-mechanical simulation data have recently seen tremendous progress. Experimental data has a very different character than simulated data, and most MLP training procedures cannot be easily adapted to incorporate both types of data into the training process. We investigate a training procedure based on Iterative Boltzmann Inversion that produces a pair potential correction to an existing MLP, using equilibrium radial distribution function data. By applying these corrections to a MLP for pure aluminum based on Density Functional Theory, we observe that the resulting model largely addresses previous overstructuring in the melt phase. Interestingly, the corrected MLP also exhibits improved performance in predicting experimental diffusion constants, which are not included in the training procedure. The presented method does not require auto-differentiating through a molecular dynamics solver, and does not make assumptions about the MLP architecture. The results suggest a practical framework of incorporating experimental data into machine learning models to improve accuracy of molecular dynamics simulations.

physics.app-ph↗

arXiv2023

Learning Together: Towards foundational models for machine learning interatomic potentials with meta-learning

The development of machine learning models has led to an abundance of datasets containing quantum mechanical (QM) calculations for molecular and material systems. However, traditional training methods for machine learning models are unable to leverage the plethora of data available as they require that each dataset be generated using the same QM method. Taking machine learning interatomic potentials (MLIPs) as an example, we show that meta-learning techniques, a recent advancement from the machine learning community, can be used to fit multiple levels of QM theory in the same training process. Meta-learning changes the training procedure to learn a representation that can be easily re-trained to new tasks with small amounts of data. We then demonstrate that meta-learning enables simultaneously training to multiple large organic molecule datasets. As a proof of concept, we examine the performance of a MLIP refit to a small drug-like molecule and show that pre-training potentials to multiple levels of theory with meta-learning improves performance. This difference in performance can be seen both in the reduced error and in the improved smoothness of the potential energy surface produced. We therefore show that meta-learning can utilize existing datasets with inconsistent QM levels of theory to produce models that are better at specializing to new datasets. This opens new routes for creating pre-trained, foundational models for interatomic potentials.

physics.chem-ph↗

arXiv2023

Cluster Scaling and Critical Points: A Cautionary Tale

Many systems in nature are conjectured to exist at a critical point, including the brain and earthquake faults. The primary reason for this conjecture is that the distribution of clusters (avalanches of firing neurons in the brain or regions of slip in earthquake faults) can be described by a power law. Because there are other mechanisms such as $1/f$ noise that can produce power laws, other criteria that the cluster critical exponents must satisfy can be used to conclude whether or not the observed power law behavior indicates an underlying critical point rather than an alternate mechanism. We show how a possible misinterpretation of the cluster scaling data can lead to incorrectly conclude that the measured critical exponents do not satisfy these criteria. Examples of the possible misinterpretation of the data for one-dimensional random site percolation and the one-dimensional Ising model are presented. We stress that the interpretation of a power law cluster distribution indicating the presence of a critical point is subtle, and its misinterpretation might lead to the abandonment of a promising area of research.

cond-mat.stat-mech↗

arXiv2021

Scaling of causal neural avalanches in a neutral model

Neural avalanches are collective firings of neurons that exhibit emergent scale-free behavior. Understanding the nature and distribution of these avalanches is an important element in understanding how the brain functions. We study a model of neural avalanches for which the dynamics are governed by neutral theory. The neural avalanches are defined using causal connections between the firing neurons. We analyze the scaling of causal neural avalanches as the critical point is approached from the absorbing phase. By using cluster analysis tools from percolation theory, we characterize the critical properties of the neural avalanches. We identify the tuning parameters consistent with experiments. The scaling hypothesis provides a unified explanation of the power laws which characterize the critical point. The critical exponents characterizing the avalanche distributions and divergence of the response functions are consistent with the predictions of the scaling hypothesis. We use a universal scaling function for the avalanche profile to find that the firing rates for avalanches of different durations show data collapse after appropriate rescaling. We also find data collapse for the avalanche distribution functions, which is stronger evidence of criticality than just the existence of power laws. Critical slowing-down and power law relaxation of avalanches is observed as the system is tuned to its critical point. We discuss how our results motivate future empirical studies of criticality in the brain.

physics.bio-ph↗

arXiv2020

Pinned, locked, pushed, and pulled traveling waves in structured environments

Traveling fronts describe the transition between two alternative states in a great number of physical and biological systems. Examples include the spread of beneficial mutations, chemical reactions, and the invasions by foreign species. In homogeneous environments, the alternative states are separated by a smooth front moving at a constant velocity. This simple picture can break down in structured environments such as tissues, patchy landscapes, and microfluidic devices. Habitat fragmentation can pin the front at a particular location or lock invasion velocities into specific values. Locked velocities are not sensitive to moderate changes in dispersal or growth and are determined by the spatial and temporal periodicity of the environment. The synchronization with the environment results in discontinuous fronts that propagate as periodic pulses. We characterize the transition from continuous to locked invasions and show that it is controlled by positive density-dependence in dispersal or growth. We also demonstrate that velocity locking is robust to demographic and environmental fluctuations and examine stochastic dynamics and evolution in locked invasions.

cond-mat.stat-mech↗

arXiv2019

Novel effective ergodicity breaking phase transition in a driven-dissipative system

We show that the Olami-Feder-Christensen model exhibits an effective ergodicity breaking transition as the noise is varied. Above the critical noise, the average stress on each site converges to the global average. Below the critical noise, the stress on individual sites becomes trapped in different limit cycles. We use ideas from the study of dynamical systems and compute recurrence plots and the recurrence rate. We identify the order parameter as the recurrence rate averaged over all sites and find numerical evidence that the transition can be characterized by exponents that are consistent with hyperscaling.

nlin.CD↗

arXiv2019

Prediction in a driven-dissipative system displaying a continuous phase transition

Prediction in complex systems at criticality is believed to be very difficult, if not impossible. Of particular interest is whether earthquakes, whose distribution follows a power law (Gutenberg-Richter) distribution, are in principle unpredictable. We study the predictability of event sizes in the Olmai-Feder-Christensen model at different proximities to criticality using a convolutional neural network. The distribution of event sizes satisfies a power law with a cutoff for large events. We find that prediction decreases as criticality is approached and that prediction is possible only for large, non-scaling events. Our results suggest that earthquake faults that satisfy Gutenberg-Richter scaling are difficult to forecast.

cond-mat.stat-mech↗

arXiv2019

Genetic drift in range expansions is very sensitive to density feedback in dispersal and growth

Theory predicts rapid genetic drift during invasions, yet many expanding populations maintain high genetic diversity. We find that genetic drift is dramatically suppressed when dispersal rates increase with the population density because many more migrants from the diverse, high-density regions arrive at the expansion edge. When density-dependence is weak or negative, the effective population size of the front scales only logarithmically with the carrying capacity. The dependence, however, switches to a sublinear power law and then to a linear increase as the density-dependence becomes strongly positive. We develop a unified framework revealing that the transitions between different regimes of diversity loss are controlled by a single, universal parameter: the ratio of the expansion velocity to the geometric mean of dispersal and growth rates at expansion edge. Our results suggest that positive density-dependence could dramatically alter evolution in expanding populations even when its contributions to the expansion velocity is small.

q-bio.PE↗