DeepMoD: Deep learning for Model Discovery in noisy data

Institut Curie, PSL Research University, CNRS UMR168, Paris, France We introduce DeepMoD, a deep learning based model discovery algorithm which seeks the partial differential equation underlying a spatiotemporal data set. DeepMoD employs sparse regression on a library of basis functions and their corresponding spatial derivatives. A feed-forward neural network approximates the data set and automatic differentiation is used to construct this function library and perform regression within the neural network. This construction makes it extremely robust to noise and applicable to small data sets and, contrary to other deep learning methods, does not require a training set and is impervious to overfitting. We illustrate this approach on several physical problems, such as the Burgers', Korteweg-de Vries, advection-diffusion and Keller-Segel equations, and This resilience to noise and high performance at very few samples highlights the potential of this method to be applied on experimental data. The increasing ability to generate large amounts of model discovery turns into finding a sparse representation data from complex physical, biological, chemical and social of the coefficient vector ξ. Rudy et al. [3] introduce the systems is beginning to transform quantitative science.regression