Machine Learning-Enabled Time-Skipping Method: Theory and Perturbation-Based Verification
Abstract
Simulating the time evolution of practical mechanics problems requires many time steps. This cost is further compounded by the iterative nature of implicit solvers. We present a cycle-based Machine Learning-enabled Time-skipping (MLT) method. In each cycle, several time steps are skipped, a machine learning (ML) prediction bridges the gap to initialize one solver step, and the physics-based solver then runs for several steps to correct any accumulated errors. Using the Implicit Function Theorem, we derive first-order estimates that characterize how ML prediction errors propagate. These estimates identify when errors remain bounded across cycles and guide the choice of cycle parameters, independent of model architecture. We verify these estimates on the Allen-Cahn equation and a forced variant using controlled synthetic perturbations that emulate ML errors. Wall-clock measurements confirm the theoretical speedup is realizable in practice. The MLT method provides a robust framework for accelerating time-marching in dynamic simulations.
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BibTeX
@misc{bannerman2026machine,
title = {{Machine Learning-Enabled Time-Skipping Method: Theory and Perturbation-Based Verification}},
author = {Isaac C. Bannerman and Shaowu Pan and Lucy T. Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41152},
eprint = {2610.41152},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41152},
}
RIS
TY - UNPB
TI - Machine Learning-Enabled Time-Skipping Method: Theory and Perturbation-Based Verification
AU - Isaac C. Bannerman
AU - Shaowu Pan
AU - Lucy T. Zhang
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41152
UR - https://arxiv.org/abs/2610.41152
AB - Simulating the time evolution of practical mechanics problems requires many time steps. This cost is further compounded by the iterative nature of implicit solvers. We present a cycle-based Machine Learning-enabled Time-skipping (MLT) method. In each cycle, several time steps are skipped, a machine learning (ML) prediction bridges the gap to initialize one solver step, and the physics-based solver then runs for several steps to correct any accumulated errors. Using the Implicit Function Theorem, we derive first-order estimates that characterize how ML prediction errors propagate. These estimates identify when errors remain bounded across cycles and guide the choice of cycle parameters, independent of model architecture. We verify these estimates on the Allen-Cahn equation and a forced variant using controlled synthetic perturbations that emulate ML errors. Wall-clock measurements confirm the theoretical speedup is realizable in practice. The MLT method provides a robust framework for accelerating time-marching in dynamic simulations.
ER -