[2502.00472] Binned Spectral Power Loss for Improved Prediction of Chaotic Systems

Computer Science > Machine Learning arXiv:2502.00472 (cs) [Submitted on 1 Feb 2025 (v1), last revised 27 Mar 2026 (this version, v3)] Title:Binned Spectral Power Loss for Improved Prediction of Chaotic Systems Authors:Dibyajyoti Chakraborty, Arvind T. Mohan, Romit Maulik View a PDF of the paper titled Binned Spectral Power Loss for Improved Prediction of Chaotic Systems, by Dibyajyoti Chakraborty and 2 other authors View PDF HTML (experimental) Abstract:Forecasting multiscale chaotic dynamical systems, such as turbulent flows, with deep learning remains a formidable challenge due to the spectral bias of neural networks, which hinders the accurate representation of fine-scale structures in long-term predictions. This issue is exacerbated when models are deployed autoregressively, leading to compounding errors and instability. In this work, we introduce a novel approach to mitigate the spectral bias, which we call the Binned Spectral Power (BSP) Loss. The BSP loss is a frequency-domain loss function that adaptively weighs errors in predicting both larger and smaller scales of the dataset. Unlike traditional losses that focus on pointwise misfits, our BSP loss explicitly penalizes deviations in the energy distribution across different scales, promoting stable and physically consistent predictions. We demonstrate that the BSP loss mitigates the well-known problem of spectral bias in deep learning. We further validate our approach for the data-driven high-dimensional time-serie...