DeepMoD
Deep learning for automatic discovery of PDEs
DeepMoD (Deep learning for Model Discovery) automatically discovers the partial differential equations underlying noisy, sparse spatiotemporal datasets. It combines a neural network function approximator with sparse regression on a library of candidate PDE terms — making it extremely robust to noise and applicable with as few as ~100 data points.
Unlike other deep learning methods, DeepMoD does not require a separate training set and is not prone to overfitting, because the physics constraint is built directly into the network. It has been applied to a wide range of physical systems including Burgers’, Korteweg-de Vries, and Keller-Segel equations, as well as experimental biological data.
DeepMoD was one of the first AI4Science tools of its kind and has accumulated 187 citations since publication.
Key methods: Sparse regression · Neural networks · Physics-informed ML · PDE discovery
Related publication: Both, Choudhury, Sens, Kusters. DeepMoD: Deep learning for model discovery in noisy data. Journal of Computational Physics 428, 109985 (2021).