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arXiv · 2412.08426

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

Rixin Yu·Marco Herbert·Markus Klein·Erdzan Hodzic
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Abstract

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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BibTeXRIS

Rixin Yu, Marco Herbert, Markus Klein, Erdzan Hodzic. 2024-12-11. Koopman Theory-Inspired Method for Learning Time Advancement Operators in Unstable Flame Front Evolution. https://arxiv.org/abs/2412.08426

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