用算术电路自动构建非线性项，让方程发现更高效可解释。
AC-SINDy: Compositional Sparse Identification of Nonlinear Dynamics
- 用算术电路组合线性项和乘积项生成非线性特征
- 在混沌系统上准确恢复了真实微分方程，且参数量更少
- 适合需要可解释性与抗噪能力的物理建模场景
我们提出AC-SINDy，一种基于算术电路的非线性动力学稀疏识别方法。该方法用结构化计算图替代传统显式基函数库，通过线性函数与乘积交互组合生成非线性特征，实现紧凑且可扩展的参数化，并直接在计算图上施加稀疏约束。同时引入分离状态估计与动力学识别的框架，结合隐变量推断、共享动力学和多步监督，提升对噪声的鲁棒性并保持可解释性。在非线性及混沌系统上的实验表明，该方法能准确恢复可解释的控制方程，且在规模扩展上优于标准SINDy。
原文摘要 · Abstract (English)
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.
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