Binned Spectral Power Loss for Improved Prediction of Chaotic Systems

2025-02-01

AI Summary

Deep learning models suffer from spectral bias in long-term forecasting of chaotic systems, leading to fine-scale distortions, error accumulation, and instability. To address this, we propose the frequency-domain-driven Binned Spectral Power (BSP) loss function—a novel adaptive spectral weighting mechanism based on energy distribution across frequency bands. BSP explicitly enforces multi-scale spectral power consistency without modifying network architecture, thereby mitigating spectral bias. By integrating frequency-domain analysis, spectral power binning with adaptive weighting, and autoregressive deep models (LSTM/Transformer), our method significantly improves prediction stability and spectral fidelity across multiple high-dimensional chaotic benchmarks. Experimental results demonstrate up to a 37% reduction in long-term prediction error and over 50% decrease in spectral energy distribution error compared to standard losses.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Multiagent Systems: Adversarial Agents
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Web Mining and Content Analysis: Large pretrained models with web data
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

Forecasting multiscale chaotic dynamical systems 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-series forecasting of a range of benchmark chaotic systems which are typically intractable due to spectral bias. Our results demonstrate that the BSP loss significantly improves the stability and spectral accuracy of neural forecasting models without requiring architectural modifications. By directly targeting spectral consistency, our approach paves the way for more robust deep learning models for long-term forecasting of chaotic dynamical systems.

Problem

• Deep Learning
• Complex Chaotic Systems
• Prediction Instability

Innovation

• BSP Loss
• Energy Distribution
• Complex Chaotic Systems