WKRR Improves Dynamical System Prediction from Noisy Data

This research addresses the significant challenge of accurately predicting complex dynamical systems when measurements are corrupted by noise. While traditional kernel ridge regression performs well with clean data, its effectiveness diminishes with noisy inputs. The authors build upon recent observations that a weak formulation can act as a filter for noisy data, enhancing noise robustness in various learning strategies. The paper introduces Weak-form Kernel Ridge Regression (WKRR), which combines a weak formulation with a kernel learning strategy. The authors provide an overview of the filtering mechanism and a bias-variance error decomposition to explain its effectiveness. WKRR is designed to be simple to implement and demonstrates superior performance compared to several baseline methods, handling both clean and noisy data efficiently. Experimental results showcase WKRR's capabilities on high-dimensional chaotic benchmark systems, including those with up to 64 dimensions, and on large-scale real-world fluid dynamics data reaching 15,000 dimensions. This indicates its potential for applications requiring robust modeling of complex, noisy dynamic processes.