mlsanityData to 14 Oct 2026

A Constitutive Markov Physics-Informed Neural Operator (MPNO) for Autoregressive Stability in Transient Dynamics

arXiv 2608.25744 ↗First posted 26 Aug 2026cs.LGcited by 0

Not on the map. Why?

Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 23 of its 43 references that are in the map. First posted on arXiv 26 Aug 2026.

Builds on

23 of 43 references.

References · 23

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  2. 2017Graph Attention Networkscited by 8,923
  3. 2017Neural Message Passing for Quantum Chemistrycited by 3,487
  4. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  5. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
  6. 2018Spectral Normalization for Generative Adversarial Networkscited by 1,636
  7. 2019Simplifying Graph Convolutional Networkscited by 1,477
  8. 2018Predict then Propagate: Graph Neural Networks meet Personalized PageRankcited by 993
  9. 2020Learning to Simulate Complex Physics with Graph Networkscited by 880
  10. 2020Learning Mesh-Based Simulation with Graph Networkscited by 868
  11. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 734
  12. 2016Input Convex Neural Networkscited by 414
11 more
  1. 2021Neural Operator: Learning Maps Between Function Spacescited by 414
  2. 2022PDEBENCH: An Extensive Benchmark for Scientific Machine Learningcited by 413
  3. 2022Message Passing Neural PDE Solverscited by 386
  4. 2022U-NO: U-shaped Neural Operatorscited by 230
  5. 2023PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solverscited by 216
  6. 2017Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equationscited by 208
  7. 2022A new family of Constitutive Artificial Neural Networks towards automated model discoverycited by 49
  8. 2025Thermalizer: Stable autoregressive neural emulation of spatiotemporal chaoscited by 21
  9. 2024Peridynamic Neural Operators: A Data-Driven Nonlocal Constitutive Model for Complex Material Responsescited by 18
  10. 2024Physics-informed MeshGraphNets (PI-MGNs): Neural finite element solvers for non-stationary and nonlinear simulations on arbitrary meshescited by 12
  11. 2026Bridging Spectral Operator Learning and U-Net Hierarchies: SpectraNet for Stable Autoregressive PDE Surrogatescited by 1

Built on by

Not cited yet.

Similar, not cited

Close in wording, no citation either way

  1. 2026Autoregression-Free Neural Operators for Time-Dependent PDEs
  2. 2025History-Aware Neural Operator: Robust Data-Driven Constitutive Modeling of Path-Dependent Materials
  3. 2025Merging Memory and Space: A State Space Neural Operator
  4. 2024On the Benefits of Memory for Modeling Time-Dependent PDEs
  5. 2025Physically consistent and uncertainty-aware learning of spatiotemporal dynamics
  6. 2025CFO: Learning Continuous-Time PDE Dynamics via Flow-Matched Neural Operators
  7. 2026Geometry-aware Latent Autoregressive Generative Model for PDEs in Complex Domains
  8. 2026Learning to Discretize: Diffusion-Based Adaptive Mesh with Spectral Guidance