用数学理论指导神经网络，精准预测不稳定的火焰前沿演化。
Koopman Theory-Inspired Method for Learning Time Advancement Operators in Unstable Flame Front Evolution
- 基于库普曼理论构建新型神经网络，将数据映射到高维空间学习演化规律。
- 在1D与2D火焰场景中，多步预测精度和长期统计特性均优于传统方法。
- 适合研究复杂非线性动力系统、燃烧模拟与混沌行为建模的科研人员。
预测由偏微分方程（PDE）支配的复杂系统演化仍具挑战性，尤其在非线性、混沌行为下。本研究提出受库普曼理论启发的傅里叶神经算子（kFNO）与卷积神经网络（kCNN），用于学习火焰前沿不稳定性解决方案的推进算子。通过将数据转换至高维隐空间，这些模型在多步预测上实现更高精度。在1维与2维火焰前沿场景中的基准测试表明，所提方法在短期预测准确性和长期统计再现性方面均表现更优，为复杂动力系统建模提供了一个有前景的框架。
原文摘要 · Abstract (English)
Predicting the evolution of complex systems governed by partial differential equations (PDEs) remains challenging, especially for nonlinear, chaotic behaviors. This study introduces Koopman-inspired Fourier Neural Operators (kFNO) and Convolutional Neural Networks (kCNN) to learn solution advancement operators for flame front instabilities. By transforming data into a high-dimensional latent space, these models achieve more accurate multi-step predictions compared to traditional methods. Benchmarking across one- and two-dimensional flame front scenarios demonstrates the proposed approaches' superior performance in short-term accuracy and long-term statistical reproduction, offering a promising framework for modeling complex dynamical systems.
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