A Constitutive Markov Physics-Informed Neural Operator (MPNO) for Autoregressive Stability in Transient Dynamics
Wenpu Du, Peng Zhou, Yunlong Xia, Sinuo Xin, Congcong Zhang, Boyang Zhang, Yi Zhang, Wenzheng Xu
Abstract
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 (acoustic-impedance harmonic mean, contact area, and traction amplitude) encode material-interface constitutive information into a nonnegative symmetric adjacency matrix W; after normalizing the graph Laplacian L = D - W by lambda_max, the propagator P = I - alpha*L~ is constructively constrained to spectral radius rho(P) <= 1, suppressing exponential amplification of autoregressive errors. Stability is thus a designable architectural property, not an optimized loss objective. On three PDEs (Burgers and two-dimensional transverse-section concrete penetration), MPNO rolls out stably with bounded error on all test seeds at 100/135/165 m/s; the single-step relative L2 error is 0.7304 +/- 0.0008, better than WNO and comparable to FNO at about one quarter of FNO's parameters. The edge-weight formula transfers across scenarios by replacing material-property variables. With about 20K parameters, MPNO delivers roughly 10^5x inference speedup over LS-DYNA.
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Classified with taxonomy v2 on Sat, 5 Sept 2026.