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This paper introduces a Constitutive Markov Physics-Informed Neural Operator (MPNO) designed to address autoregressive instability in transient dynamics predictions, particularly in scenarios with strong discontinuities. By incorporating physics-based edge weights into a row-stochastic propagation operator, MPNO ensures that the spectral radius of the propagator is constrained, effectively stabilizing autoregressive rollouts. The method achieves a significant reduction in error compared to existing models, demonstrating a single-step relative L2 error of 0.7304 卤 0.0008 while maintaining a fraction of the parameters used by the Fourier neural operator (FNO).
Autoregressive predictions in transient dynamics can be stabilized with a physics-informed approach that constrains spectral properties, outperforming traditional neural operators.
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.
