arXiv:2604.18889v1 Announce Type: new Abstract: We present AC-SINDy, a compositional extension of the Sparse Identification of Nonlinear Dynamics (SINDy) framework that replaces explicit feature libraries with a structured representation based on arithmetic circuits. Rather than enumerating candidate basis functions, the proposed approach constructs nonlinear features through compositions of linear functions and multiplicative interactions, yielding a compact and scalable parameterization and enabling sparsity to be enforced directly over the computational graph. We also introduce a formulation that separates state estimation from dynamics identification by combining latent state inference with shared dynamics and multi-step supervision, improving robustness to noise while preserving interpretability. Experiments on nonlinear and chaotic systems demonstrate that the method recovers accurate and interpretable governing equations while scaling more favorably than standard SINDy.