In this paper, a deep collocation method (DCM) for thin plate bending problems is proposed.
This method takes advantage of computational graphs and backpropagation algorithms …

Stochastic optimal control and games have a wide range of applications, from finance and
economics to social sciences, robotics, and energy management. Many real-world …

Mean Field Games (MFG) have been introduced to tackle games with a large number of
competing players. Considering the limit when the number of players is infinite, Nash …

We address scaling up equilibrium computation in Mean Field Games (MFGs) using Online
Mirror Descent (OMD). We show that continuous-time OMD provably converges to a Nash …

This chapter presents machine learning techniques and deep reinforcement learning-based
algorithms for the efficient resolution of nonlinear partial differential equations and dynamic …

We propose a numerical method for solving high dimensional fully nonlinear partial
differential equations (PDEs). Our algorithm estimates simultaneously by backward time …

How can we learn a dynamical system to make forecasts, when some variables are
unobserved? For instance, in COVID-19, we want to forecast the number of infected patients …

Machine learning-based modeling of physical systems has attracted significant interest in
recent years. Based solely on the underlying physical equations and initial and boundary …

Abstract Mean Field Games (MFGs) can potentially scale multi-agent systems to extremely
large populations of agents. Yet, most of the literature assumes a single initial distribution for …

Abstract The Fokker–Planck equation governs the uncertainty propagation of dynamical
systems driven by stochastic processes. The solution of the Fokker–Planck equation is a …