🤖 AI Summary
This study addresses the challenge of enhancing the long-term prediction accuracy and stability of deep learning surrogate models for chaotic dynamical systems while maintaining computational efficiency. By employing a unified training protocol and matching model capacity, the authors systematically evaluate the rolling prediction performance of several mainstream neural network architectures on the double pendulum, the Kuramoto–Sivashinsky equation, and Kolmogorov flow. They propose an integrator-inspired update structure that significantly reduces prediction bias and the amplification of perturbations. Stability differences among models are quantified using metrics including the Jacobian matrix, one-step relative error, and finite-time Lyapunov exponents. Experimental results demonstrate that the proposed architecture not only improves long-term predictive accuracy but also more faithfully reproduces the geometric structure of the system’s attractor.
📝 Abstract
Temporal surrogate models are effective for predicting chaotic dynamical systems where computational cost can be prohibitive. Several deep neural network architectures can be used for such purposes. In this work, a few commonly used architectures are compared using a common training protocol. The objective is to fairly assess the impact of model architectures for long-horizon prediction stability. Experiments are carried out for three problems, the double pendulum, the Kuramoto-Sivashinsky equations, and the Kolmogorov flow. The experiments are carried out with matching model capacity. Analysis is also carried out for a scenario where each model is individually optimized. It is observed that in both scenarios, the models exhibit categorical differences in long-horizon rollouts. For a concrete quantification, stepwise error injections and perturbation amplifications are analyzed using metrics such as local jacobian, relative one-step bias, and finite-time Lyapunov growth. Additionally, an attractor analysis is also conducted to assess how well the learned models replicate the underlying system geometry. An ablation study to isolate the impact of each component of a continuous-update architecture is also carried out. It is concluded that models that having integrator-like updates show lower bias and perturbation amplification yielding stable long-horizon rollout and more accurate predictions.