SPARK: Physics-Guided Quantitative Augmentation for Dynamical System Modeling
Keywords: dynamical system, augmentation
Abstract: In dynamical system modeling, traditional numerical methods have a solid theoretical foundation but are limited by high computational costs and sensitivity to initial conditions. Current data-driven approaches use deep learning models to capture complex spatiotemporal features, but they rely heavily on large amounts of data and assume a stable data distribution, making them ineffective against data scarcity and distribution shifts. To address these challenges, we propose SPARK, a physics-guided quantized augmentation plugin. SPARK integrates boundary information and physical parameters, using a reconstruction autoencoder to build a physics-rich discrete memory bank for data compression. It then enhances selected samples for downstream tasks with this pre-trained memory bank. SPARK then utilizes an attention mechanism to model historical observations and combines fourier-enhanced graph ODE to efficiently predict long-term dynamical systems, enhancing robustness and adaptability to complex physical environments. Extensive experiments on benchmark datasets show that our approach significantly outperforms various baseline methods in handling distribution shifts and data scarcity.
Primary Area: learning on time series and dynamical systems
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Submission Number: 2890
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