Using the Implicit Function Theorem, first-order estimates are derived that characterize how ML prediction errors propagate and guide the choice of cycle parameters, independent of model architecture.
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.
Multistep sCD (MS-sCD), a continuous-time, segment-conditioned multistep generalization of sCD, a continuous-time, segment-conditioned multistep generalization of sCD borrowed from the discrete-time multistep consistency distillation of Heek et al.
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