Composable and adaptive design of machine learning interatomic potentials guided by Fisher-information analysis

TL;DR

This work introduces an adaptive, physics-informed strategy for designing MLIPs by iteratively reconfiguring composable single-term submodels and evaluating them with a Fisher-information-matrix (FIM) based metric alongside four property-oriented RMSEs. It defines linear and nonlinear single-term models and constructs dual-term composites via addition and multiplication operators to capture higher-order interactions while controlling the FIM eigenspectrum (sloppiness) and numerical stability. Applied to a Nb dataset, the approach yields a dual-term sum model (E[G8L4] + N[E[G8L4]]) with $75$ parameters achieving force RMSE $0.172\ \mathrm{eV/\AA}$ and energy RMSE $0.013\ \mathrm{eV/atom}$, with the FIM guiding model selection and hyperparameter tuning. The framework highlights a trade-off space between accuracy, stability, and extensibility, and points to extensions with additional basis variants, recursive higher-order compositions, and integration with complementary uncertainty quantification methods.

Abstract

An adaptive physics-informed model design strategy for machine-learning interatomic potentials (MLIPs) is proposed. This strategy follows an iterative reconfiguration of composite models from single-term models, followed by a unified training procedure. A model evaluation method based on the Fisher information matrix (FIM) and multiple-property error metrics is proposed to guide model reconfiguration and hyperparameter optimization. Combining the model reconfiguration and the model evaluation subroutines, we provide an adaptive MLIP design strategy that balances flexibility and extensibility. In a case study of designing models against a structurally diverse niobium dataset, we managed to obtain an optimal configuration with 75 parameters generated by our framework that achieved a force RMSE of 0.172 eV/Å and an energy RMSE of 0.013 eV/atom.

Figures (7)

• Figure 1: An adaptive MLIP model design procedure is shown in the above diagram. Step 1: Choose a composable architecture framework that supports iterative combinations of submodel and basis-function components based on specified configurations. Step 2: Assemble an initial model configuration. Step 3: Train the model configuration based on a unified procedure. Step 4: Evaluate the performance of the model configuration based on both the training RMSEs and the Fisher information matrix. Based on the evaluation result, if the model configuration is accepted, it is then applied to test sets. Otherwise, by switching on and off the components in the framework (Step 1), a reconfigured model is generated (Step 2), trained (Step 3), and evaluated again (Step 4). So on and so forth, a final model configuration reaches the balance between performance and efficiency.
• Figure 2: The computation graphs of the two proposed nonlinear single-term models. The architecture of the exponentiated pair-cluster model $\hat{S}_{{\rm e}2}$ is visualized in (a) and (b), where (a) shows the overall pipeline and (b) shows the internal procedure of the model. The respective graphs for the neighboring-exponentiated pair-cluster interaction model $\hat{S}_{{\rm ne}2}$ are in (c) and (d).
• Figure 3: A dual-bipartite training procedure for a decomposable model $\hat{M}[\mathfrak{F}] \coloneq \hat{D}_m[\hat{A}_m,\, \hat{B}_m]$. The total parameters $\bm{\theta_{M[\mathfrak{F}]}}$ are divided into four parts based on Equation (\ref{['eq:sepPars']}). $\bm{c^{\braket{\hat{A}_m}}}$ ($\bm{d^{\braket{\hat{A}_m}}}$) and $\bm{c^{\braket{\hat{B}_m}}}$ ($\bm{d^{\braket{\hat{B}_m}}}$) are the linear (nonlinear) coefficients of submodels $\hat{A}_m$ and $\hat{B}_m$, respectively. During each training cycle, only a subset of $\bm{\theta_{M[\mathfrak{F}]}}$, controlled by the "Switches" (the yellow rhombuses), is optimized. The iteration ends whenever any "Stop Control" (the orange rhombuses) returns "true," either because the loss function has converged or the maximum of training cycles has been reached.
• Figure 4: Accuracy and stability ($\lg |\lambda|$) of $\hat{S}_{\,\rm l2}$ with Gaussian-based two-body cluster basis set of different sizes.
• Figure 5: Accuracy and stability ($\lg |\lambda|$) of $\hat{S}_{\rm e2}$ with Gaussian-based two-body cluster basis set of different sizes.