Koopman Theory-Inspired Method for Learning Time Advancement Operators in Unstable Flame Front Evolution
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909424692494336 |
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| author | Yu, Rixin Herbert, Marco Klein, Markus Hodzic, Erdzan |
| author_facet | Yu, Rixin Herbert, Marco Klein, Markus Hodzic, Erdzan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_08426 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Koopman Theory-Inspired Method for Learning Time Advancement Operators in Unstable Flame Front Evolution Yu, Rixin Herbert, Marco Klein, Markus Hodzic, Erdzan Dynamical Systems Machine Learning Mathematical Physics 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. |
| title | Koopman Theory-Inspired Method for Learning Time Advancement Operators in Unstable Flame Front Evolution |
| topic | Dynamical Systems Machine Learning Mathematical Physics |
| url | https://arxiv.org/abs/2412.08426 |