Koopman Theory-Inspired Method for Learning Time Advancement Operators in Unstable Flame Front Evolution
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Abstract (arXiv)
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.
Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 5 of its 47 references that are in the map. First posted on arXiv 11 Dec 2024.
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5 of 47 references.
References · 5
- 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
- 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
- 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
- 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 734
- 2021Neural Operator: Learning Maps Between Function Spacescited by 414
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