让物理约束融入降维模型，提升燃烧模拟的稳定与精度
Physically consistent predictive reduced-order modeling by enhancing Operator Inference with state constraints
- 将物理约束嵌入算子推断，优化降维模型预测
- 在训练范围外拓展200%仍保持稳定且准确
- 适合需要高保真与高效计算的多物理系统模拟
复杂多物理系统（如本文研究的炭燃烧）的数值模拟会产生大量具有内在物理约束的状态变量。本文提出一种新方法，通过在降维模型预测中嵌入这些状态约束，增强算子推断（Operator Inference）——一种科学机器学习方法，用于从数据中学习由非线性偏微分方程支配的高维系统的低维表示。在模型学习过程中，我们提出基于关键性能指标的新方法来选择正则化超参数。由于嵌入状态约束可提升算子推断降维模型的稳定性，我们将其与标准算子推断及其他稳定性增强方法进行比较。针对炭燃烧的应用表明，该方法在稳定性与准确性上均优于其他方法，可在训练区间外外推超过200%，同时具备计算高效与物理一致的特点。
原文摘要 · Abstract (English)
Numerical simulations of complex multiphysics systems, such as char combustion considered herein, yield numerous state variables that inherently exhibit physical constraints. This paper presents a new approach to augment Operator Inference -- a methodology within scientific machine learning that enables learning from data a low-dimensional representation of a high-dimensional system governed by nonlinear partial differential equations -- by embedding such state constraints in the reduced-order model predictions. In the model learning process, we propose a new way to choose regularization hyperparameters based on a key performance indicator. Since embedding state constraints improves the stability of the Operator Inference reduced-order model, we compare the proposed state constraints-embedded Operator Inference with the standard Operator Inference and other stability-enhancing approaches. For an application to char combustion, we demonstrate that the proposed approach yields state predictions superior to the other methods regarding stability and accuracy. It extrapolates over 200\% past the training regime while being computationally efficient and physically consistent.
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