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Onsager's 1931 `reciprocity relations' result connects microscopic time-reversibility with a symmetry property of corresponding macroscopic evolution equations. Among the many consequences is a variational characterization of the…
The Cahn-Hilliard equation is the most common model to describe phase separation processes of a mixture of two components. For a better description of short-range interactions of the material with the solid wall, various dynamic boundary…
A recent line of work has shown remarkable behaviors of the generalization error curves in simple learning models. Even the least-squares regression has shown atypical features such as the model-wise double descent, and further works have…
This research is concerned with evolution equations and their forward-backward discretizations. Our first contribution is an estimation for the distance between iterates of sequences generated by forward-backward schemes, useful in the…
We study the global convergence of a Fisher-Rao policy gradient flow for infinite-horizon entropy-regularised Markov decision processes with Polish state and action space. The flow is a continuous-time analogue of a policy mirror descent…
In this paper we intend to give a comprehensive approach of functional inequalities for diffusion processes under some "curvature" assumptions. Our notion of curvature coincides with the usual $\Gamma_2$ curvature of Bakry and Emery in the…
Near the beginning of the century, Wright and Fisher devised an elegant, mathematically tractable model of gene reproduction and replacement that laid the foundation for contemporary population genetics. The Wright-Fisher model and its…
We propose a new evolutionary dynamics for population games with a discrete strategy set, inspired by the theory of optimal transport and Mean field games. The dynamics can be described as a Fokker-Planck equation on a discrete strategy…
We perform a convergence analysis of a discrete-in-time minimization scheme approximating a finite dimensional singularly perturbed gradient flow. We allow for different scalings between the viscosity parameter $\varepsilon$ and the time…
A finite element method for the evolution of a two-phase membrane in a sharp interface formulation is introduced. The evolution equations are given as an $L^2$--gradient flow of an energy involving an elastic bending energy and a line…
We explore the transition to hydrodynamics in a weakly-coupled model of quark-gluon plasma given by kinetic theory in the relaxation time approximation with conformal symmetry. We demonstrate that the gradient expansion in this model has a…
This is the first of a series of papers devoted to a thorough analysis of the class of gradient flows in a metric space $(X,\mathsf{d})$ that can be characterized by Evolution Variational Inequalities. We present new results concerning the…
The aim of this paper is to study relaxation rates for the Cahn-Hilliard equation in dimension larger than one. We follow the approach of Otto and Westdickenberg based on the gradient flow structure of the equation and establish…
Modelling incompressible ideal fluids as a finite collection of vortex filaments is important in physics (super-fluidity, models for the onset of turbulence) as well as for numerical algorithms used in computer graphics for the real time…
We consider differential-difference equations that determine the continuous symmetries of discrete equations on the triangular lattice. It is shown that a certain combination of continuous flows can be represented as a scalar evolution…
We analyze the gradient flow of a potential energy in the space of probability measures when we substitute the optimal transport geometry with a geometry based on Sinkhorn divergences, a debiased version of entropic optimal transport. This…
We introduce a non-diffusive spatial coupling term into the replicator equation of evolutionary game theory. The spatial flux is based on motion due to local gradients in the relative fitness of each strategy, providing a game-dependent…
We consider the forward Kolmogorov equation corresponding to measure-valued processes stemming from a class of interacting particle systems in population dynamics, including variations of the Bolker-Pacala-Dieckmann-Law model. Under the…
Motivated by recent developments in the fields of large deviations for interacting particle system and mean field control, we establish a comparison principle for the Hamilton--Jacobi equation corresponding to linearly controlled gradient…
Bayesian nonparametric mixture models provide a flexible framework for data analysis but are often hindered by the computational expense of traditional inference methods like MCMC. A fast, recursive algorithm proposed by Newton (2002)…