Robust PDE discovery under sparse and highly noisy conditions via attention neural networks

Nianyu Yi; Shihan Zhang; Shilin Zhang; Yunqing Huang

Robust PDE discovery under sparse and highly noisy conditions via attention neural networks

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arxiv 2506.17908 v1 pith:V7VJK33F submitted 2025-06-22 math.NA cs.NA

Robust PDE discovery under sparse and highly noisy conditions via attention neural networks

Shilin Zhang , Yunqing Huang , Nianyu Yi , shihan Zhang This is my paper

classification math.NA cs.NA

keywords ann-pysrdiscoverynetworkssparseattentionconditionsdataframework

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The discovery of partial differential equations (PDEs) from experimental data holds great promise for uncovering predictive models of complex physical systems. In this study, we introduce an efficient automatic model discovery framework, ANN-PYSR, which integrates attention neural networks with the state-of-the-art PySR symbolic regression library. Our approach successfully identifies the governing PDE in six benchmark examples. Compared to the DLGA framework, numerical experiments demonstrate ANN-PYSR can extract the underlying dynamic model more efficiently and robustly from sparse, highly noisy data (noise level up to 200%, 5000 sampling points). It indicates an extensive variety of practical applications of ANN-PYSR, particularly in conditions with sparse sensor networks and high noise levels, where traditional methods frequently fail.

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