In this paper, we summarize some recent advances related to the energetic variational
approach (EnVarA), a general variational framework of building thermodynamically …

We design and compute first-order implicit-in-time variational schemes with high-order
spatial discretization for initial value gradient flows in generalized optimal transport metric …

Combining the classical theory of optimal transport with modern operator splitting
techniques, we develop a new numerical method for nonlinear, nonlocal partial differential …

We have created a functional framework for a class of non-metric gradient systems. The
state space is a space of nonnegative measures, and the class of systems includes the …

We review a class of gradient systems with dissipation potentials of hyperbolic-cosine type.
We show how such dissipation potentials emerge in large deviations of jump processes …

We consider dynamics driven by interaction energies on graphs. We introduce graph
analogues of the continuum nonlocal-interaction equation and interpret them as gradient …

We propose a novel deterministic particle method to numerically approximate the Landau
equation for plasmas. Based on a new variational formulation in terms of gradient flows of …

We consider in this paper random batch particle methods for efficiently solving the
homogeneous Landau equation in plasma physics. The methods are stochastic variations of …

We design a deterministic particle method for the solution of the spatially homogeneous
Landau equation with uncertainty. The deterministic particle approximation is based on the …

We consider the dynamic large deviation behaviour of Kac's collisional process for a range
of initial conditions including equilibrium. We prove an upper bound with a rate function of …