Predicting the evolution of complex systems governed by partial differential equations remains challenging, especially for nonlinear, chaotic behaviors. This study introduces Koopman-inspired Fourier neural operators and convolutional neural networks 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.Â
The authors gratefully acknowledge the financial support by the Swedish Research Council (Grant No. VR-2019-05648) and the AI Lund initiative grant. The stay abroad of M.H. was supported by the Federal Ministry of Defence. The computations were enabled by resources provided by the National Academic Infrastructure for Supercomputing in Sweden (NAISS), at ALVIS and Tetralith, partially funded by the Swedish Research Council (Grant Agreement No. 2022-06725).