A Multi-Branched Radial Basis Network Approach to Predicting Complex Chaotic Behaviours

TL;DR

This work addresses short-term forecasting of chaotic attractor dynamics by proposing a multi-branch Radial Basis Function neural network with an attention mechanism. The architecture consists of three parallel branches processing input feature pairs, each equipped with an inverse_multiquadric RBF layer and an attention module, with outputs merged to predict a 3D state $\hat{\boldsymbol{y}} \in \mathbb{R}^3$. Evaluated on a Kaggle Physics Attractor Time Series dataset of 36,700 points, the multi-branch model demonstrates more stable training and richer trajectory predictions than a single-branch baseline, highlighting improved capability to capture nonlinear temporal dependencies in chaotic systems. The work provides a reproducible framework and supports practical short-term forecasting in complex dynamical environments.

Abstract

In this study, we propose a multi branched network approach to predict the dynamics of a physics attractor characterized by intricate and chaotic behavior. We introduce a unique neural network architecture comprised of Radial Basis Function (RBF) layers combined with an attention mechanism designed to effectively capture nonlinear inter-dependencies inherent in the attractor's temporal evolution. Our results demonstrate successful prediction of the attractor's trajectory across 100 predictions made using a real-world dataset of 36,700 time-series observations encompassing approximately 28 minutes of activity. To further illustrate the performance of our proposed technique, we provide comprehensive visualizations depicting the attractor's original and predicted behaviors alongside quantitative measures comparing observed versus estimated outcomes. Overall, this work showcases the potential of advanced machine learning algorithms in elucidating hidden structures in complex physical systems while offering practical applications in various domains requiring accurate short-term forecasting capabilities.

Figures (6)

• Figure 1: Proposed multi layer architecture
• Figure 2: Single Sequential Proposed Layer
• Figure 3: Loss over iterations of the Single Sequential Network
• Figure 4: Loss over iterations of the Multi-Branched Network
• Figure 5: Output of the single sequential layer