G-AlignNet: Geometry-Driven Quality Alignment for Robust Dynamical Systems Modeling

Haoran Li, CHENHAN XIAO, Muhao Guo, Yang Weng

Keywords: adaptive physical systems, dynamical modeling, data quality alignment, geometric representation learning, geometric optimization

TL;DR: This paper proposes a unified geometric perspective to model adaptive physical dynamics and align data qualities with provable guarantees.

Abstract: The Neural ODE family has shown promise in modeling complex systems but often assumes consistent data quality, making them less effective in real-world applications with irregularly sampled, incomplete, or multi-resolution data. Current methods, such as ODE-RNN, aim to address these issues but lack formal performance guarantees and can struggle with highly evolving dynamical systems. To tackle this, we propose a novel approach that leverages parameter manifolds to improve robustness in system dynamical modeling. Our method utilizes the orthogonal group as the underlying structure for the parameter manifold, facilitating both quality alignment and dynamical learning in a unified framework. Unlike previous methods, which primarily focus on empirical performance, our approach offers stronger theoretical guarantees of error convergence thanks to the novel architecture and well-posed optimization with orthogonality. Numerical experiments demonstrate significant improvements in interpolation and prediction tasks, particularly in scenarios involving high- and low-resolution data, irregular sampling intervals, etc. Our framework provides a step toward more reliable dynamics learning in changing environments where data quality cannot be assumed.

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

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Submission Number: 11781