Title: Learning Physics with Deep Neural Networks

Abstract: Machine learning amounts to find low-dimensional models governing the properties of high dimensional functionals. This could almost be called physics.  Algorithms have considerably improved in the last 10 years through the processing of massive amounts of data. In particular, deep neural network have spectacular applications, to image classification, medical, industrial and physical data analysis.

We show that the approximation capabilities of deep convolution networks come from their ability to compute invariant at different scales over possibly high-dimensinal groups including diffeormophisms. We shall study the mathematical properties of simplified deep convolutional networks computed with wavelet. We give applications to  regression of molecular energies in quantum chemistry. We shall also introduce low-dimensional non-Gaussian intermittent models for statistical physics, with applications to Ising and high Reynold turbulences through cosmological data.