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Deep learning driven model discovery in biology and physics
Par Remy Kusters (CRI)
Le 19 Novembre 2019 à 11h00 - Salle de séminaires 5ème étage, Tour 32-33

Résumé

As scientific data sets become richer and increasingly complex, machine learning (ML) tools become more useful and widely applied. Discovering a mechanistic model, rather than predicting the outcome is paramount in the scientific endeavor and its lack in present day ML is limiting further integration of ML in quantitative science. In this talk I will present our development of quantitative tools to extract human interpretable models from quantitative biological and physical data sets. The work combines the predictive power of neural networks with the interpretability of symbolic regression to develop a framework of interpretable AI and discover mechanistic models from biological  and physical data. 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.