# AC-SINDy: Compositional Sparse Identification of Nonlinear Dynamics

arXiv: https://arxiv.org/abs/2604.18889 · HTML: https://mlsanity.com/paper/2604.18889/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 13 references that are in the map.
- First posted on arXiv 20 Apr 2026.

## Builds on (most cited first, 7 of 7)

- [SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamics](https://mlsanity.com/paper/2004.02322/) (2020)
- [DeepMoD: Deep learning for Model Discovery in noisy data](https://mlsanity.com/paper/1904.09406/) (2019)
- [Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modeling](https://mlsanity.com/paper/2109.05364/) (2021)
- [Scientific Machine Learning with Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2507.22959/) (2025)
- [Generalizing the SINDy approach with nested neural networks](https://mlsanity.com/paper/2404.15742/) (2024)
- [Sparse identification of nonlinear dynamics with library optimization mechanism: Recursive long-term prediction perspective](https://mlsanity.com/paper/2507.18220/) (2025)
- [LeARN: Learnable and Adaptive Representations for Nonlinear Dynamics in System Identification](https://mlsanity.com/paper/2412.12036/) (2024)

## Abstract (arXiv)

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.