Improved deep learning of chaotic dynamical systems with multistep penalty losses
<|reference_start|>Improved deep learning of chaotic dynamical systems with multistep penalty losses: Predicting the long-term behavior of chaotic systems remains a formidable challenge due to their extreme sensitivity to initial conditions and the inherent limitations of traditional data-driven modeling approaches. This paper introduces a novel framework that addresses these challenges by leveraging the recently proposed multi-step penalty (MP) optimization technique. Our approach extends the applicability of MP optimization to a wide range of deep learning architectures, including Fourier Neural Operators and UNETs. By introducing penalized local discontinuities in the forecast trajectory, we effectively handle the non-convexity of loss landscapes commonly encountered in training neural networks for chaotic systems. We demonstrate the effectiveness of our method through its application to two challenging use-cases: the prediction of flow velocity evolution in two-dimensional turbulence and ocean dynamics using reanalysis data. Our results highlight the potential of this approach for accurate and stable long-term prediction of chaotic dynamics, paving the way for new advancements in data-driven modeling of complex natural phenomena.<|reference_end|>
@article{chakraborty2024improved,
    title={Improved deep learning of chaotic dynamical systems with multistep
  penalty losses},
    author={Dibyajyoti Chakraborty, Seung Whan Chung, Ashesh Chattopadhyay, Romit
  Maulik},
    journal={arXiv preprint arXiv:2410.05572},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.05572},
    primaryClass={cs.LG cs.AI math.DS}
}