DeepMoD: Deep learning for model discovery in noisy data

We introduce DeepMoD, a Deep learning based Model Discovery algorithm. DeepMoD discovers the partial differential equation underlying spatio-temporal data set using sparse regression on library of possible functions and their derivatives. A neural network is used as function approximator its output to construct library, allowing perform within network. This construction makes it extremely robust noise, applicable small sets, and, contrary other deep methods, does not require training set. benchmark our approach several physical problems such Burgers', Korteweg-de Vries Keller-Segel equations, find that requires few O(102) samples works at noise levels up 75%. Motivated by these results, we apply directly noisy experimental time-series from gel electrophoresis experiment advection-diffusion describing this system.