Structural Inference of Dynamical Systems with Conjoined State Space Models

Abstract

This paper introduces SICSM, a novel structural inference framework that integrates Selective State Space Models (selective SSMs) with Generative Flow Networks (GFNs) to handle the challenges posed by dynamical systems with irregularly sampled trajectories and partial observations. By utilizing the robust temporal modeling capabilities of selective SSMs, our approach learns input-dependent transition functions that adapt to non-uniform time intervals, thereby enhancing the accuracy of structural inference. By aggregating dynamics across diverse temporal dependencies and channeling them into the GFN, the SICSM adeptly approximates the posterior distribution of the system's structure. This process not only enables precise inference of complex interactions within partially observed systems but also ensures the seamless integration of prior knowledge, enhancing the model’s accuracy and robustness.Extensive evaluations on sixteen diverse datasets demonstrate that SICSM outperforms existing methods, particularly in scenarios characterized by irregular sampling and incomplete observations, which highlight its potential as a reliable tool for scientific discovery and system diagnostics in disciplines that demand precise modeling of complex interactions.