A Constitutive Markov Physics-Informed Neural Operator (MPNO) for Autoregressive Stability in Transient Dynamics
Read the original on arXiv Machine Learning →The paper introduces a constitutive Markov physics‑informed neural operator (MPNO) designed to stabilize autoregressive predictions for transient‑dynamics PDEs with strong discontinuities. By modeling one‑step evolution as a row‑stochastic propagation operator and embedding material‑interface physics into a non‑negative symmetric adjacency matrix, MPNO guarantees a spectral radius ≤1, preventing exponential error growth. Experiments on Burgers’ equation and concrete‑penetration stress‑field prediction show that MPNO rolls out stably with bounded error, achieving comparable accuracy to the Fourier neural operator while using only a quarter of its parameters and delivering a 10^5× speedup over LS‑DYNA.
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