Computing the ground state energy of quantum many particle systems is of fundamental importance in a variety of fields, including chemistry, physics and materials science, amongst others. However, the complexity of such quantum mechanical computations grows rapidly with the number of particles. Machine learning algorithms do not simulate the physical system, but instead estimate solutions by interpolating values provided by a training set of known examples. However, precise interpolations may require a number of examples that is exponential in the system dimension, and are thus intractable. Tractable algorithms compute interpolations in low dimensional approximation spaces, which leverage the underlying physical properties of the system.

In this talk I will give an overview of machine learning algorithms for computing the ground state energy of quantum many particle systems, describing the core principles of such algorithms and illustrating the common themes that emerge. I will then present in more detail our approach to the problem, which is based on a type of multiscale, multilayer convolutional neural network, called a wavelet scattering transform. Through a cascade of multiscale wavelet transforms and nonlinearities, the scattering transform encodes the appropriate invariants and regularity properties of the physical system. Wavelet scattering regressions, computed over databases of organic molecules and amorphous materials, achieve errors on the order of quantum mechanical simulations, but at a fraction of the computational cost.