Physics-informed Machine Learning  

Project description

Machine learning strategies for fluid flows have been extensively developed in recent years. Particular attention has been paid to physics-informed deep neural networks in a statistical learning context. Such models combine measurements with physical properties to improve the reconstruction quality, especially when there are not enough velocity measurements. In this project, we aim to reconstruct the velocity field of incompressible flows given a finite set of measurements.

This project will focus on developing novel machine-learning techniques with spectral properties and mathematical guarantees. Within this physics-informed type of statistical learning framework, we will adaptively build a sparse set of Fourier basis functions with corresponding coefficients by solving a sequence of minimization problems where the set of basis functions is augmented greedily at each optimization problem. We regularize our minimization problems with the seminorm of the fractional Sobolev space in a Tikhonov fashion. Our computational framework will thus combine supervised and unsupervised learning techniques.