Reproduce “AC-SINDy: Compositional Sparse Identification of Nonlinear Dynamics” on OpenResearch

About this paper

Peter Racioppo

AC-SINDy, a compositional extension of the Sparse Identification of Nonlinear Dynamics (SINDy) framework, identifies nonlinear dynamics from observational data using a structured neural architecture and gradient-based pruning. It successfully recovers accurate and interpretable governing equations, demonstrating improved parameter efficiency and robustness to noise compared to traditional SINDy methods.

Key insights

• Compositional, factorized representations based on arithmetic circuits can effectively replace explicit feature libraries, providing a more compact and scalable parameterization for identifying sparse nonlinear dynamics.
• Sparsity can be robustly enforced directly on the structure of a learned computational graph using gradient-based importance estimates for pruning, even in the presence of shared intermediate computations.
• Robustness to noisy data can be achieved by decoupling state estimation from dynamics learning via latent state inference combined with multi-step predictive consistency, which implicitly suppresses noise.
• Feature Normalization is crucial for stabilizing optimization and ensuring identifiability and interpretability in compositional models that incorporate multiplicative interactions.

Summary by alphaXiv.