Interacting Particle Systems: Fast algorithms and non-convex optimization (Jin, Shanghai Jiao Tong University)

Jun 24
24-06-2020 12:00 Uhr bis 13:00 Uhr
Online (contact marius.yamakou@fau to get the data for the VC)

Interacting Particle Systems: Fast algorithms and non-convex optimization

Speaker: Prof. Dr. Shi Jin

Affiliation: Shanghai Jiao Tong University

Abstract: We first develop random batch methods for classical and quantum interacting particle systems with large number of particles. These methods use small but random batches for particle interactions, thus the computational cost is reduced from O(N^2) per time step to O(N), for a system with N particles with binary interactions. For classical particles we give a particle number independent error estimate under some special interactions. For quantum N-body Schrodinger equation, we obtain, for pair-wise random interactions, a convergence estimate for the Wigner transform of the single-particle reduced density matrix of the particle system at time t that is uniform in N > 1 and independent of the Planck constant hbar. We then introduce a stochastic interacting particle consensus system for global optimization of high dimensional non-convex functions. This algorithm does not use gradient of the function thus is suitable for non-smooth functions. We prove that under dimension-independent conditions on the parameters and with suitable initial data the algorithms converge to the neighborhood of the global minimum almost surely.

https://en.www.math.fau.de/applied-analysis/

Friedrich-Alexander-Universität Erlangen-Nürnberg