Deep learning driven model discovery in biology and physics
In this talk I will introduce DeepMoD, a deep learning based model discovery algorithm which seeks the partial differential equation underlying a spatio-temporal 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.We illustrate this approach on several problems in the context of (bio)physics, mechanics and fluid dynamics, such as the Burgers', Korteweg-de Vries, advection-diffusion and Keller-Segel equations, and find that it requires as few as O(100) samples and works at noise levels up to 75%. This resilience to noise and high performance at very few samples allows to apply DeepMoD directly to noisy experimental time-series data, discovering e.g. the advection diffusion equation from a gel electrophoresis experiment.
ESADSE Saint-Etienne - Ecole d'art et de design de Saint-Etienne en partenariat avec le CRI