用神经网络保持系统结构，提升非多项式动态建模精度
NN-OpInf: an operator inference approach using structure-preserving composable neural networks
- 设计结构保持的可组合神经网络，学习数据中的隐藏动力学
- 在非多项式系统上比传统方法更准更稳，尤其在参数变化时
- 适合需要高精度建模的复杂系统，如流体或结构力学
我们提出神经网络算子推断（NN-OpInf）：一种结构保持、可组合且限制最小的非侵入式降维建模框架，用于动态系统的算子推断。该方法从快照数据中学习潜在动力学，强制施加局部算子结构，如斜对称性、（半）正定性和梯度保持性，同时通过支持异质算子的加法组合来反映复杂动态。我们提出了实用的训练策略，并分析了计算成本相对于线性和二次多项式算子推断（P-OpInf）的差异。在多个非线性和参数化问题上的数值实验表明，与P-OpInf及先前的神经网络降阶模型相比，其在准确性、稳定性和鲁棒性方面均有提升，尤其是在动力学无法由多项式模型良好表示时。结果表明，当目标动力学包含非多项式非线性时，NN-OpInf可作为P-OpInf的有效替代方案，在牺牲更高训练计算成本和更难的非凸学习问题的前提下，带来精度和分布外性能的提升。
原文摘要 · Abstract (English)
We propose neural network operator inference (NN-OpInf): a structure-preserving, composable, and minimally restrictive operator inference framework for the non-intrusive reduced-order modeling of dynamical systems. The approach learns latent dynamics from snapshot data, enforcing local operator structure such as skew-symmetry, (semi-)positive definiteness, and gradient preservation, while also reflecting complex dynamics by supporting additive compositions of heterogeneous operators. We present practical training strategies and analyze computational costs relative to linear and quadratic polynomial OpInf (P-OpInf). Numerical experiments across several nonlinear and parametric problems demonstrate improved accuracy, stability, and robustness over P-OpInf and prior NN-ROM formulations, particularly when the dynamics are not well represented by polynomial models. These results suggest that NN-OpInf can serve as an effective drop-in replacement for P-OpInf when the dynamics to be modeled contain non-polynomial nonlinearities, offering potential gains in accuracy and out-of-distribution performance at the expense of higher training computational costs and a more difficult, non-convex learning problem.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。