A Constitutive Markov Physics-Informed Neural Operator (MPNO) for Autoregressive Stability in Transient Dynamics
Neural operators applied to transient-dynamics PDEs with strong discontinuities exhibit autoregressive instability: in concrete-penetration stress-field prediction, the wavelet neural operator (WNO) diverges in autoregressive rollout, while MeshGraphNets collapse to zero predictions. WNO's instability stems from the lack of a structural constraint on the spectral radius of its propagation operator; the Fourier neural operator (FNO) is stable in these measurements but only emergently, not by construction. We propose a constitutive Markov physics-informed neural operator (MPNO) modeling one-step evolution as a Markov (row-stochastic) propagation operator. Physics-coupled edge weights (acous...
| Authors | Wenpu Du, Peng Zhou, Yunlong Xia et al. |
|---|---|
| Primary category | cs.LG |
| Published | 26 August 2026 |
| Last updated at source | 26 August 2026 |
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