2026-10-14T21:34:48Z https://api.figshare.com/v2/oai

oai:figshare.com:article/34033356 2026-09-30T15:09:07Z category_146 category_873 category_734 category_931 portal_63 item_type_6 month_year_09_2026

Efficient Tensorized Evaluation of Permutation Invariant Polynomials for Representing Potential Energy Surfaces Junhong Li (8040599) Kaisheng Song (19324102) Hua Guo (305546) Jun Li (6494) Space Science Chemical Sciences not elsewhere classified Biological Sciences not elsewhere classified Information Systems not elsewhere classified permutation invariant polynomials order derivatives ). monomial symmetrization approach fully vectorized manner diffusion monte carlo contain identical atoms scale batch evaluation evaluation becomes regular allows efficient execution qct ), path integral molecular dynamics based invariant descriptors efficient tensorized evaluation enables fast evaluation scalable gpu execution replacing recursive factorization pips ), together recursive factorization fi evaluation efficient simulations pimd ), molecular systems fis ), enables large based implementation widely used time compilation segmented summation related polynomial reformulates pip practical route jaxpip provides introduce jaxpip fundamental invariants exp transformation constructing high classical trajectory Permutation invariant polynomials (PIPs), together with related polynomial-based invariant descriptors such as fundamental invariants (FIs), are widely used in constructing high-fidelity global potential energy surfaces (PESs) of molecules that contain identical atoms. Although the monomial symmetrization approach (MSA) enables fast evaluation of PIPs through recursive factorization, it leads to deeply nested computational graphs that may require large memory and are inefficient in modern automatic differentiation frameworks. In this work, we introduce JaxPIP, a JAX-based implementation that reformulates PIP/FI evaluation into tensorized linear algebra operations. By replacing recursive factorization with dense matrix operations combined with log-exp transformation and segmented summation, the evaluation becomes regular and GPU-friendly. This allows efficient execution with just-in-time compilation and enables large-scale batch evaluation of energies and forces (as well as higher-order derivatives). The resulting architecture supports ensemble simulations such as quasi-classical trajectory (QCT), path-integral molecular dynamics (PIMD), and diffusion Monte Carlo (DMC) in a fully vectorized manner. As demonstrated in examples, JaxPIP provides a practical route for efficient simulations of molecular systems with scalable GPU execution. 2026-09-30T00:00:00Z Text Journal contribution 10.1021/acs.jctc.6c01659.s001 https://figshare.com/articles/journal_contribution/Efficient_Tensorized_Evaluation_of_Permutation_Invariant_Polynomials_for_Representing_Potential_Energy_Surfaces/34033356 CC BY-NC 4.0