用于瞬态动力学自回归稳定性的本构马尔可夫物理信息神经算子（MPNO）
A Constitutive Markov Physics-Informed Neural Operator (MPNO) for Autoregressive Stability in Transient Dynamics
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中文总结 AI 辅助
针对瞬态动力学神经算子的自回归不稳定性问题，提出构造性稳定的MPNO，在三类PDE测试中表现优异，参数量少且推理速度远超LS-DYNA。
中文摘要 AI 辅助
应用于含强间断瞬态动力学偏微分方程（PDE）的神经算子会出现自回归不稳定性：在混凝土侵入应力场预测中，小波神经算子（WNO）的自回归rollout会发散，而MeshGraphNets则坍缩为零预测。WNO的不稳定性源于其传播算子的谱半径缺乏结构约束；傅里叶神经算子（FNO）在这些测量中是稳定的，但仅为涌现性稳定，而非构造性稳定。我们提出一种本构马尔可夫物理信息神经算子（MPNO），将一步演化建模为马尔可夫（行随机）传播算子。物理耦合边权重（声阻抗调和均值、接触面积和牵引力幅值）将材料界面本构信息编码为非负对称邻接矩阵W；通过lambda_max归一化图拉普拉斯算子L = D - W后，传播子P = I - alpha*L~被构造性地约束为谱半径rho(P) ≤ 1，从而抑制自回归误差的指数放大。因此，稳定性是可设计的架构属性，而非优化的损失目标。在三个PDE（Burgers方程和二维横截面混凝土侵入问题）上，MPNO在100/135/165 m/s的所有测试种子上均以有界误差稳定rollout；单步相对L2误差为0.7304 ± 0.0008，优于WNO，且参数量仅为FNO的约四分之一，与FNO相当。边权重公式可通过替换材料属性变量跨场景迁移。MPNO仅约2万个参数，推理速度较LS-DYNA提升约10^5倍。
英文摘要
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.
发表机构
- School of Environment and Safety Engineering, North University of China（中北大学环境与安全工程学院）
机构由 AI 辅助整理，请以论文原文为准。
