Danny Pérez

Andrew Binder, Mitchell Luskin, Danny Perez et al.

Spatial multiscale methods have established themselves as useful tools for extending the length scales accessible by conventional statics (i.e., zero temperature molecular dynamics). Recently, extensions of these methods, such as the finite-temperature quasicontinuum (hot-QC) or Coarse-Grained Molecular Dynamics (CGMD) methods, have allowed for multiscale molecular dynamics simulations at finite temperature. Here, we assess the quality of the long-time dynamics these methods generate by considering canonical transition rates. Specifically, we analyze the transition state theory (TST) rates in CGMD and compare them to the corresponding TST rate of the fully atomistic system. The ability of such an approach to reliably reproduce the TST rate is verified through a relative error analysis, which is then used to highlight the major contributions to the error and guide the choice of degrees of freedom. Finally, our analytical results are compared with numerical simulations for the case of a 1-D chain.

Thomas D Swinburne, Danny Perez

Bayesian regression determines model parameters by minimizing the expected loss, an upper bound to the true generalization error. However, the loss ignores misspecification, where models are imperfect. Parameter uncertainties from Bayesian regression are thus significantly underestimated and vanish in the large data limit. This is particularly problematic when building models of low-noise, or near-deterministic, calculations, as the main source of uncertainty is neglected. We analyze the generalization error of misspecified, near-deterministic surrogate models, a regime of broad relevance in science and engineering. We show posterior distributions must cover every training point to avoid a divergent generalization error and design an ansatz that respects this constraint, which for linear models incurs minimal overhead. This is demonstrated on model problems before application to thousand dimensional datasets in atomistic machine learning. Our efficient misspecification-aware scheme gives accurate prediction and bounding of test errors where existing schemes fail, allowing this important source of uncertainty to be incorporated in computational workflows.

Sk Md Ahnaf Akif Alvi, Mrinalini Mulukutla, Nicolas Flores et al.

Surrogate modeling techniques have become indispensable in accelerating the discovery and optimization of high-entropy alloys(HEAs), especially when integrating computational predictions with sparse experimental observations. This study systematically evaluates the fitting performance of four prominent surrogate models conventional Gaussian Processes(cGP), Deep Gaussian Processes(DGP), encoder-decoder neural networks for multi-output regression and XGBoost applied to a hybrid dataset of experimental and computational properties in the AlCoCrCuFeMnNiV HEA system. We specifically assess their capabilities in predicting correlated material properties, including yield strength, hardness, modulus, ultimate tensile strength, elongation, and average hardness under dynamic and quasi-static conditions, alongside auxiliary computational properties. The comparison highlights the strengths of hierarchical and deep modeling approaches in handling heteroscedastic, heterotopic, and incomplete data commonly encountered in materials informatics. Our findings illustrate that DGP infused with machine learning-based prior outperform other surrogates by effectively capturing inter-property correlations and input-dependent uncertainty. This enhanced predictive accuracy positions advanced surrogate models as powerful tools for robust and data-efficient materials design.