arXiv subjects

Yangshuai Wang

Publications and source records attributed to Yangshuai Wang.

At least 37 records · Page 2Linked to original sources

arXiv2025

Beyond Adam: Disentangling Optimizer Effects in the Fine-Tuning of Atomistic Foundation Models

Atomistic foundation models constitute a paradigm shift in computational materials science by providing universal machine-learned interatomic potentials with broad transferability across chemical spaces. Although fine-tuning is essential for adapting these pretrained models to specific target systems, the influence of the optimization algorithm on this process remains insufficiently characterized. In this work, we perform a rigorous benchmark of seven first-order optimizers, including Adam, AdamW, RAdam, SGD, LAMB, Ranger, and ScheduleFree, for the fine-tuning of foundation models across molecular, crystalline, and liquid regimes. We evaluate these algorithms based on energy and force accuracy for both in-distribution and out-of-distribution configurations, as well as their impact on downstream physical properties such as elastic moduli, phonon spectra, and interfacial dynamics. We interpret these empirical results through a preconditioning framework that views each optimizer as a data-dependent linear transformation of the gradient. This analysis clarifies how different update rules impose specific spectral filters on the effective loss Hessian. Across all regimes, AdamW and ScheduleFree achieve superior curvature conditioning and force accuracy, whereas stochastic gradient descent exhibits slow convergence and instability. Furthermore, we demonstrate that a brief second-order refinement stage reduces residual anisotropy in the loss landscape and enhances the fidelity of physical observables without increasing inference costs. These findings provide conceptual insight and practical guidance for selecting and designing optimizers to ensure the stable and efficient fine-tuning of universal interatomic potentials.

physics.comp-ph↗

arXiv2025

MicroEvoEval: A Systematic Evaluation Framework for Image-Based Microstructure Evolution Prediction

Simulating microstructure evolution (MicroEvo) is vital for materials design but demands high numerical accuracy, efficiency, and physical fidelity. Although recent studies on deep learning (DL) offer a promising alternative to traditional solvers, the field lacks standardized benchmarks. Existing studies are flawed due to a lack of comparing specialized MicroEvo DL models with state-of-the-art spatio-temporal architectures, an overemphasis on numerical accuracy over physical fidelity, and a failure to analyze error propagation over time. To address these gaps, we introduce MicroEvoEval, the first comprehensive benchmark for image-based microstructure evolution prediction. We evaluate 14 models, encompassing both domain-specific and general-purpose architectures, across four representative MicroEvo tasks with datasets specifically structured for both short- and long-term assessment. Our multi-faceted evaluation framework goes beyond numerical accuracy and computational cost, incorporating a curated set of structure-preserving metrics to assess physical fidelity. Our extensive evaluations yield several key insights. Notably, we find that modern architectures (e.g., VMamba), not only achieve superior long-term stability and physical fidelity but also operate with an order-of-magnitude greater computational efficiency. The results highlight the necessity of holistic evaluation and identify these modern architectures as a highly promising direction for developing efficient and reliable surrogate models in data-driven materials science.

cond-mat.mtrl-sci↗

arXiv2025

Amplitude Expansion Phase Field Crystal (APFC) Modeling based Efficient Dislocation Simulations using Fourier Pseudospectral Method

Crystalline defects critically influence material properties, necessitating accurate simulation methods. Existing approaches, from atomic-scale configurations to continuum elasticity, face inherent limitations in modeling dislocation-induced lattice deformation. The amplitude expansion of the phase field crystal (APFC) model bridges this gap with a mesoscopic description. This paper introduces a computationally efficient Fourier pseudospectral method for solving the APFC equations. The method exploits system periodicity and solution analyticity--the latter's rigorous proof remaining an open question, as discussed herein--to enable precise implementation of periodic boundary conditions. Numerical experiments on 2D triangular and 3D body-centered cubic lattices demonstrate that the method accurately reproduces the strain fields of edge dislocations, matching continuum theory predictions. These results confirm the APFC model's potential for capturing complex defect structures at the mesoscale, paving the way for simulating more intricate defect dynamics.

cond-mat.mtrl-sci↗

arXiv2025

Higher-Order Boundary Conditions for Atomistic Dislocation Simulations

We present a higher-order boundary condition for atomistic simulations of dislocations that address the slow convergence of standard supercell methods. The method is based on a multipole expansion of the equilibrium displacement, combining continuum predictor solutions with discrete moment corrections. The continuum predictors are computed by solving a hierarchy of singular elliptic PDEs via a Galerkin spectral method, while moment coefficients are evaluated from force-moment identities with controlled approximation error. A key feature is the coupling between accurate continuum predictors and moment evaluations, enabling the construction of systematically improvable high-order boundary conditions. We thus design novel algorithms, and numerical results for screw and edge dislocations confirm the predicted convergence rates in geometry and energy norms, with reduced finite-size effects and moderate computational cost.

math.NA↗

arXiv2025

An Atomic Cluster Expansion Potential for Twisted Multilayer Graphene

Twisted multilayer graphene, characterized by its moiré patterns arising from inter-layer rotational misalignment, serves as a rich platform for exploring quantum phenomena. Machine learning interatomic potentials (MLIPs) are a promising approach to model such systems. Our work develops a method to generate training and test datasets for fitting MLIPs that capture all possible misalignments but remain small-scale to facilitate efficient data generation and parameter estimation. To achieve this, we generate configurations with periodic boundary conditions suitable for DFT calculations, and then introduce an internal twist and shift within those supercell structures. Using this technique, supplemented with an active learning workflow, we fit an Atomic Cluster Expansion potential for simulating twisted multilayer graphene and test it for accuracy and robustness on a range of simulation tasks.

physics.comp-ph↗

arXiv2025

Flexible Uncertainty Calibration for Machine-Learned Interatomic Potentials

Reliable uncertainty quantification (UQ) is essential for developing machine-learned interatomic potentials (MLIPs) in predictive atomistic simulations. Conformal prediction (CP) is a statistical framework that constructs prediction intervals with guaranteed coverage under minimal assumptions, making it an attractive tool for UQ. However, existing CP techniques, while offering formal coverage guarantees, often lack accuracy, scalability, and adaptability to the complexity of atomic environments. In this work, we present a flexible uncertainty calibration framework for MLIPs, inspired by CP but reformulated as a parameterized optimization problem. This formulation enables the direct learning of environment-dependent quantile functions, producing sharper and more adaptive predictive intervals at negligible computational cost. Using the foundation model MACE-MP-0 as a representative case, we demonstrate the framework across diverse benchmarks, including ionic crystals, catalytic surfaces, and molecular systems. Our results show order-of-magnitude improvements in uncertainty-error correlation, enhanced data efficiency in active learning, and strong generalization performance, together with reliable transfer of calibrated uncertainties across distinct exchange-correlation functionals. This work establishes a principled and data-efficient approach to uncertainty calibration in MLIPs, providing a practical route toward more trustworthy and transferable atomistic simulations.

physics.chem-ph↗

arXiv2025

A Conformal Prediction Framework for Uncertainty Quantification in Physics-Informed Neural Networks

Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving PDEs, yet existing uncertainty quantification (UQ) approaches for PINNs generally lack rigorous statistical guarantees. In this work, we bridge this gap by introducing a distribution-free conformal prediction (CP) framework for UQ in PINNs. This framework calibrates prediction intervals by constructing nonconformity scores on a calibration set, thereby yielding distribution-free uncertainty estimates with rigorous finite-sample coverage guarantees for PINNs. To handle spatial heteroskedasticity, we further introduce local conformal quantile estimation, enabling spatially adaptive uncertainty bands while preserving theoretical guarantee. Through systematic evaluations on typical PDEs (damped harmonic oscillator, Poisson, Allen-Cahn, and Helmholtz equations) and comprehensive testing across multiple uncertainty metrics, our results demonstrate that the proposed framework achieves reliable calibration and locally adaptive uncertainty intervals, consistently outperforming heuristic UQ approaches. By bridging PINNs with distribution-free UQ, this work introduces a general framework that not only enhances calibration and reliability, but also opens new avenues for uncertainty-aware modeling of complex PDE systems.

cs.LG↗

arXiv2025

A foundation model for atomistic materials chemistry

Atomistic simulations of matter, especially those that leverage first-principles (ab initio) electronic structure theory, provide a microscopic view of the world, underpinning much of our understanding of chemistry and materials science. Over the last decade or so, machine-learned force fields have transformed atomistic modeling by enabling simulations of ab initio quality over unprecedented time and length scales. However, early ML force fields have largely been limited by: (i) the substantial computational and human effort of developing and validating potentials for each particular system of interest; and (ii) a general lack of transferability from one chemical system to the next. Here we show that it is possible to create a general-purpose atomistic ML model, trained on a public dataset of moderate size, that is capable of running stable molecular dynamics for a wide range of molecules and materials. We demonstrate the power of the MACE-MP-0 model - and its qualitative and at times quantitative accuracy - on a diverse set of problems in the physical sciences, including properties of solids, liquids, gases, chemical reactions, interfaces and even the dynamics of a small protein. The model can be applied out of the box as a starting or "foundation" model for any atomistic system of interest and, when desired, can be fine-tuned on just a handful of application-specific data points to reach ab initio accuracy. Establishing that a stable force-field model can cover almost all materials changes atomistic modeling in a fundamental way: experienced users get reliable results much faster, and beginners face a lower barrier to entry. Foundation models thus represent a step towards democratising the revolution in atomic-scale modeling that has been brought about by ML force fields.

physics.chem-ph↗

arXiv2025

Fine-Tuning Universal Machine-Learned Interatomic Potentials: A Tutorial on Methods and Applications

Universal machine-learned interatomic potentials (U-MLIPs) have demonstrated broad applicability across diverse atomistic systems but often require fine-tuning to achieve task-specific accuracy. While the number of available U-MLIPs and their fine-tuning applications is rapidly expanding, there remains a lack of systematic guidance on how to effectively fine-tune these models. This tutorial provides a comprehensive, step-by-step guide to fine-tuning U-MLIPs for computational materials modeling. Using the recently released MACE-MP-0 as a representative foundation model, we illustrate the full workflow of dataset preparation, hyperparameter selection, model training, and validation. Beyond methodological guidance, we conduct systematic case studies on solid-state electrolytes, stacking fault defects in metals, semiconductors, solid-liquid interfacial interactions in low-dimensional systems, and more complicated heterointerfaces. These examples demonstrate that fine-tuning substantially improves predictive accuracy while maintaining affordable computational cost, accelerates training convergence, enhances out-of-distribution generalization, and achieves superior data efficiency. Remarkably, fine-tuned foundation models can even capture aspects of long-range physics without explicit corrections. Together, these results highlight that fine-tuning not only provides a practical recipe for applying U-MLIPs, but also offers new insights into their physical fidelity and potential for advancing large-scale atomistic simulations. To support practical applications, we include code examples that enable researchers, particularly those new to the field, to efficiently incorporate fine-tuned U-MLIPs into their workflows.

physics.comp-ph↗

arXiv2025

A Study on the Fine-Tuning Performance of Universal Machine-Learned Interatomic Potentials (U-MLIPs)

Universal machine-learned interatomic potentials (U-MLIPs) have demonstrated effectiveness across diverse atomistic systems but often require fine-tuning for task-specific accuracy. We investigate the fine-tuning of two MACE-based foundation models, MACE-MP-0 and its variant MACE-MP-0b, and identify key insights. Fine-tuning on task-specific datasets enhances accuracy and, in some cases, outperforms models trained from scratch. Additionally, fine-tuned models benefit from faster convergence due to the strong initial predictions provided by the foundation model. The success of fine-tuning also depends on careful dataset selection, which can be optimized through filtering or active learning. We further discuss practical strategies for achieving better fine-tuning foundation models in atomistic simulations and explore future directions for their development and applications.

physics.comp-ph↗

arXiv2025

Formulation and Analysis of Blended Atomistic to Higher-Order Continuum Coupling Methods for Crystalline Defects

Concurrent multiscale methods play an important role in modeling and simulating materials with defects, aiming to achieve the balance between accuracy and efficiency. Atomistic-to-continuum (a/c) coupling methods, a typical class of concurrent multiscale methods, link atomic-scale simulations with continuum mechanics. Existing a/c methods adopt the classic second-order Cauchy-Born approximation as the continuum mechanics model. In this work, we employ a higher-order Cauchy-Born model to study the potential accuracy improvement of the coupling scheme. In particular, we develop an energy-based blended atomistic to higher-order continuum method and present a rigorous a priori error analysis. We show that the overall accuracy of the energy-based blended method is not actually improved due the coupling interface error which is of lower order and may not be improved. On the contrast, higher order accuracy is achieved by the force-based blended atomistic to higher-order continuum method. Our theoretical results are demonstrated by a detailed numerical study.

math.NA↗

arXiv2025

Adaptive Quasicontinuum Methods and Simulations for Crystal Defects with a Theory based Unified a Posteriori Error Estimate

Adaptive quasicontinuum (QC) methods are important methodologies in molecular mechanics for the simulations of materials with defects, intending to achieve the optimal balance of accuracy and efficiency on the fly. In this study, we propose a residual-force based a posteriori error estimate that is simple and is unified for consistent quasicontinuum methods, as opposed to the widely adopted residual-stress based a posteriori error estimates which are complicated and need to be derived for the particular QC method under consideration. The simple and unified formulation of the estimator, together with certain sampling techniques, leads to a highly efficient and adaptable implementation. We also prove in theory that the unified error estimator provides an upper bound of the true error. We develop adaptive algorithms based on this unified estimator and validate the algorithms by several representative quasicontinuum methods for various types of crystalline defects, in terms of convergence and efficiency. In particular, the adaptive simulations of the anti-plane crack, of which we possess little a priori knowledge, demonstrate the necessity and significance of the proposed a posteriori estimates and the adaptive strategies.

math.NA↗

arXiv2025

A General Framework of Linear Elasticity Enhanced Multiscale Coupling Methods for Crystalline Defects

The atomistic-to-continuum (a/c) coupling methods, also known as the quasicontinuum (QC) methods, are a important class of concurrent multisacle methods for modeling and simulating materials with defects. The a/c methods aim to balance the accuracy and efficiency by coupling a molecular mechanics model (also termed as the atomistic model) in the vicinity of localized defects with the Cauchy-Born approximation of the atomistic model in the elastic far field. However, since both the molecular mechanics model and its Cauchy-Born approximation are usually a nonlinear, it potentially leads to a high computational cost for large-scale simulations. In this work, we propose an advancement of the classic quasinonlocal (QNL) a/c coupling method by incorporating a linearized Cauchy-Born model to reduce the computational cost. We present a rigorous a priori error analysis for this QNL method with linear elasticity enhancement (QNLL method), and show both analytically and numerically that it achieves the same convergence behavior as the classic (nonlinear) QNL method by proper determination of certain parameters relating to domain decomposition and finite element discretization. More importantly, our numerical experiments demonstrate that the QNLL method perform an substantial improvement of the computational efficiency in term of CPU times.

math.NA↗

arXiv2025

Many-Body Coarse-Grained Molecular Dynamics with the Atomic Cluster Expansion

Molecular dynamics (MD) simulations provide detailed insight into atomic-scale mechanisms but are inherently restricted to small spatio-temporal scales. Coarse-grained molecular dynamics (CGMD) techniques allow simulations of much larger systems over extended timescales. In theory, these techniques can be quantitatively accurate, but common practice is to only target qualitatively correct behaviour of coarse-grained models. Recent advances in applying machine learning methodology in this setting are now being applied to create also quantitatively accurate CGMD models. We demonstrate how the Atomic Cluster Expansion parameterization (Drautz, 2019) can be used in this task to construct highly efficient, interpretable and accurate CGMD models. We focus in particular on exploring the role of many-body effects.

physics.comp-ph↗

arXiv2024

Higher-order Far-field Boundary Conditions for Crystalline Defects

Crystalline materials exhibit long-range elastic fields due to the presence of defects, leading to significant domain size effects in atomistic simulations. A rigorous far-field expansion of these long-range fields identifies low-rank structure in the form of a sum of discrete multipole terms and continuum correctors. We propose a novel numerical scheme that exploits this low-rank structure to accelerate material defect simulations by minimizing the domain size effects. Our approach iteratively improves the boundary condition, systematically following the asymptotic expansion of the far field. We provide both rigorous error estimates for the method and a range of empirical numerical tests, to assess it's convergence and robustness.

math.NA↗

arXiv2024

Surrogate models for vibrational entropy based on a spatial decomposition

The temperature-dependent behavior of defect densities within a crystalline structure is intricately linked to the phenomenon of vibrational entropy. Traditional methods for evaluating vibrational entropy are computationally intensive, limiting their practical utility. We show that total entropy can be decomposed into atomic site contributions and rigorously estimate the locality of site entropy. This analysis suggests that vibrational entropy can be effectively predicted using a surrogate model for site entropy. We employ machine learning to develop such a surrogate models employing the Atomic Cluster Expansion model. We supplement our rigorous analysis with an empirical convergence study. In addition we demonstrate the performance of our method for predicting vibrational formation entropy and attempt frequency of the transition rates, on point defects such as vacancies and interstitials.

physics.comp-ph↗

arXiv2024

A Posteriori Error Estimate and Adaptivity for QM/MM Models of Crystalline Defects

Hybrid quantum/molecular mechanics (QM/MM) models play a pivotal role in molecular simulations. These models provide a balance between accuracy, surpassing pure MM models, and computational efficiency, offering advantages over pure QM models. Adaptive approaches have been developed to further improve this balance by allowing on-the-fly selection of the QM and MM subsystems as necessary. We propose a novel and robust adaptive QM/MM method for practical material defect simulations. To ensure mathematical consistency with the QM reference model, we employ machine-learning interatomic potentials (MLIPs) as the MM models. Our adaptive QM/MM method utilizes a residual-based error estimator that provides both upper and lower bounds for the approximation error, thus indicating its reliability and efficiency. Furthermore, we introduce a novel adaptive algorithm capable of anisotropically updating the QM/MM partitions. This update is based on the proposed residual-based error estimator and involves solving a free interface motion problem, which is efficiently achieved using the fast marching method. We demonstrate the robustness of our approach via numerical tests on a wide range of crystalline defects.

physics.comp-ph↗

arXiv2024

MeshAC: A 3D Mesh Generation and Adaptation Package for Multiscale Coupling Methods

This paper introduces the MeshAC package, which generates three-dimensional adaptive meshes tailored for the efficient and robust implementation of multiscale coupling methods. While Delaunay triangulation is commonly used for mesh generation across the entire computational domain, generating meshes for multiscale coupling methods is more challenging due to intrinsic discrete structures such as defects, and the need to match these structures to the continuum domain at the interface. The MeshAC package tackles these challenges by generating meshes that align with fine-level discrete structures. It also incorporates localized modification and reconstruction operations specifically designed for interfaces. These enhancements improve both the implementation efficiency and the quality of the coupled mesh. Furthermore, MeshAC introduces a novel adaptive feature that utilizes gradient-based a posteriori error estimation, which automatically adjusts the atomistic region and continuum mesh, ensuring an optimal balance between accuracy and efficiency. This package can be directly applied to the geometry optimization problems of a/c coupling in static mechanics, with potential extensions to many other scenarios. Its capabilities are demonstrated for complex material defects, including straight edge dislocation in BCC W and double voids in FCC Cu. These results suggest that MeshAC can be a valuable tool for researchers and practitioners in computational mechanics.

cs.GR↗