🤖 AI Summary
In training nonlinear state-space models, state trajectories often undergo severe distortion, leading to sparse state-space coverage and structural deformation—thereby compromising interpretability and robustness. To address this, we propose a data-distribution-aware trajectory regularization method tailored for locally affine state-space models. Our approach introduces two distribution-aware regularizers: (i) an affine consistency constraint imposed on local model parameters to preserve local linearity, and (ii) a density-aware uniform coverage penalty applied along state trajectories to encourage balanced exploration of the state space. Integrating system modeling priors with experimental design principles, our method seamlessly integrates into spatially guided training frameworks. Experiments on standard system identification benchmarks demonstrate that our method significantly improves the quality of state-space distribution, enhances training stability, boosts model interpretability, and strengthens robustness against input perturbations and distributional shifts.
📝 Abstract
The state space dynamics representation is the most general approach for nonlinear systems and often chosen for system identification. During training, the state trajectory can deform significantly leading to poor data coverage of the state space. This can cause significant issues for space-oriented training algorithms which e.g. rely on grid structures, tree partitioning, or similar. Besides hindering training, significant state trajectory deformations also deteriorate interpretability and robustness properties. This paper proposes a new type of space-filling regularization that ensures a favorable data distribution in state space via introducing a data-distribution-based penalty. This method is demonstrated in local model network architectures where good interpretability is a major concern. The proposed approach integrates ideas from modeling and design of experiments for state space structures. This is why we present two regularization techniques for the data point distributions of the state trajectories for local affine state space models. Beyond that, we demonstrate the results on a widely known system identification benchmark.