PDECheck: A Diagnostic Software Suite for Auditing Learned PDE Simulators
Abstract
PDECheck audits learned PDE simulators through callable propagators or saved predictions. It evaluates relative L2 error, temporal composition, finite-difference generators, and equation-specific physical residuals, retaining horizons and missing prerequisites. Analytic and manufactured defects verify the kernels. A heat-equation sweep quantifies generator sensitivity to timestep, frequency, grid, and precision. A three-equation, five-seed FNO study compares supervised, PINO-style, and composition-regularized training. An accuracy-matched advection comparison has state errors below 0.3% and a semigroup-error ratio of 1.48 (95% interval 1.34-1.62). The composition penalty lowers semigroup error but increases composed-state and longer-rollout prediction error. A time-reparameterization check produces identical low-error endpoints with different compositions. Applications to five external equation families exercise the readers and physical contracts on coarse grids. The release includes reproducibility artifacts and measured CPU/CUDA costs.
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BibTeX
@misc{shikhman2026pdecheck,
title = {{PDECheck: A Diagnostic Software Suite for Auditing Learned PDE Simulators}},
author = {Lennon J. Shikhman},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.18200},
eprint = {2606.18200},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.18200},
}
RIS
TY - UNPB
TI - PDECheck: A Diagnostic Software Suite for Auditing Learned PDE Simulators
AU - Lennon J. Shikhman
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2606.18200
UR - https://arxiv.org/abs/2606.18200
AB - PDECheck audits learned PDE simulators through callable propagators or saved predictions. It evaluates relative L^2 error, temporal composition, finite-difference generators, and equation-specific physical residuals, retaining horizons and missing prerequisites. Analytic and manufactured defects verify the kernels. A heat-equation sweep quantifies generator sensitivity to timestep, frequency, grid, and precision. A three-equation, five-seed FNO study compares supervised, PINO-style, and composition-regularized training. An accuracy-matched advection comparison has state errors below 0.3% and a semigroup-error ratio of 1.48 (95% interval 1.34-1.62). The composition penalty lowers semigroup error but increases composed-state and longer-rollout prediction error. A time-reparameterization check produces identical low-error endpoints with different compositions. Applications to five external equation families exercise the readers and physical contracts on coarse grids. The release includes reproducibility artifacts and measured CPU/CUDA costs.
ER -