标题： 基于Koopman理论的学习不稳定火焰前沿演化时间推进算子的方法 显示英文标题

标题： Koopman Theory-Inspired Method for Learning Time Advancement Operators in Unstable Flame Front Evolution

摘要： 预测由偏微分方程(PDE)支配的复杂系统的演化仍然具有挑战性，尤其是在非线性、混沌行为方面。 本研究引入了受Koopman启发的傅里叶神经算子(kFNO)和卷积神经网络(kCNN)，以学习火焰前沿不稳定性的问题进展算子。 通过将数据转换到高维潜在空间，这些模型相比传统方法实现了更准确的多步预测。 在二维和二维火焰前沿场景中的基准测试表明，所提出的方法在短期准确性及长期统计再现方面表现出优越性能，为建模复杂动力系统提供了一个有前景的框架。 显示英文摘要

摘要： 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.