Related papers: Entropy solutions to macroscopic IPM
We propose a general framework for solving quantum state estimation problems using the minimum relative entropy criterion. A convex optimization approach allows us to decide the feasibility of the problem given the data and, whenever…
Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated…
The montecarlo method, which is quite commonly used to solve maximum entropy problems in statistical physics, can actually be used to solve inverse problems in a much wider context. The probability distribution which maximizes entropy can…
We derive entropy conserving and entropy dissipative overlapping domain formulations for systems of nonlinear hyperbolic equations in conservation form, such as would be approximated by overset mesh methods. The entropy conserving…
We describe an energy-enstrophy conserving discretisation for the rotating shallow water equations with slip boundary conditions. This relaxes the assumption of boundary-free domains (periodic solutions or the surface of a sphere, for…
Solutions to conservation laws satisfy the monotonicity property: the number of local extrema is a non-increasing function of time, and local maximum/minimum values decrease/increase monotonically in time. This paper investigates this…
We introduce the notion of entropy solutions (e.s.) to a conservation law with an arbitrary jump continuous flux vector and prove existence of the largest and the smallest e.s. to the Cauchy problem. The monotonicity and stability…
This paper deals with a splitting method applied to a conservation law model of manufacturing system incorporating yield loss. A splitting scheme has been proposed. The yield loss term is treated by solving implicitly an ordinary…
We consider the problem of finding optimally stable polynomial approximations to the exponential for application to one-step integration of initial value ordinary and partial differential equations. The objective is to find the largest…
We use the entropy method to analyze the nonlinear dynamics and stability of a continuum kinetic model of an active nematic suspension. From the time evolution of the relative entropy -- an energy-like quantity in the kinetic model -- we…
We consider well-balanced schemes for the following 1D scalar conservation law with source term: d_t u + d_x f(u) + z'(x) b(u) = 0. More precisely, we are interested in the numerical approximation of the initial boundary value problem for…
This article presents a constrained policy optimization approach for the optimal control of systems under nonstationary uncertainties. We introduce an assumption that we call Markov embeddability that allows us to cast the stochastic…
Machine learning interatomic potentials (MLIPs) balance high accuracy and lower costs compared to density functional theory calculations, but their performance often depends on the size and diversity of training datasets. Large datasets…
We study the entropy solution for a class of systems of nonlocal conservation laws in which the convective flux is convoluted with a kernel in both spatial and temporal variables. This formulation models the flux dependence on the solution…
An asymptotic preserving and energy stable scheme for the Euler-Poisson system under the quasineutral scaling is designed and analysed. Correction terms are introduced in the convective fluxes and the electrostatic potential, which lead to…
We present a framework to address a class of sequential decision making problems. Our framework features learning the optimal control policy with robustness to noisy data, determining the unknown state and action parameters, and performing…
We consider the gradient flow of a quadratic non-autonomous energy under monotonicity constraint in time and natural regularity assumptions. We provide first a notion of weak solution, inspired by the theory of curves of maximal slope, and…
In this paper, we consider solving discounted Markov Decision Processes (MDPs) under the constraint that the resulting policy is stabilizing. In practice MDPs are solved based on some form of policy approximation. We will leverage recent…
We investigate the problem of synthesizing optimal control policies for Markov decision processes (MDPs) with both qualitative and quantitative objectives. Specifically, our goal is to achieve a given linear temporal logic (LTL) task with…
This paper addresses the design of linear and nonlinear stabilization procedures for high-order continuous Galerkin (CG) finite element discretizations of scalar conservation laws. We prove that the standard CG method is entropy…