Related papers: The Energy-Dissipation Principle for stochastic pa…
The Weighted Inertia-Energy-Dissipation (WIDE) principle is a global variational approach to nonlinear evolution equations of parabolic and hyperbolic type. The minimization of the parameter-dependent WIDE functional on trajectories…
We prove the applicability of the Weighted Energy-Dissipation (WED) variational principle [50] to nonlinear parabolic stochastic partial differential equations in abstract form. The WED principle consists in the minimization of a…
Variational principles play a fundamental role in deriving evolution equations of physics. They are working well in case of nondissipative evolution but for dissipative systems they are not unique, not predictive and not constructive. With…
In this paper, we investigate a system of parabolic partial differential equations with unknown-dependent coefficients that integrates two models: an anisotropic orientation-adaptive denoising process in image processing and a phase-field…
In this article, we introduce the concept of energy-variational solutions for a large class of systems of nonlinear evolutionary partial differential equations. Under certain convexity assumptions, the existence of such solutions can be…
The stochastic differential equations for a model of dissipative particle dynamics with both total energy and total momentum conservation in the particle-particle interactions are presented. The corresponding Fokker-Planck equation for the…
We advance a variational method to prove qualitative properties such as symmetries, monotonicity, upper and lower bounds, sign properties, and comparison principles for a large class of doubly-nonlinear evolutionary problems including…
Extracting governing physical laws from computational or experimental data is crucial across various fields such as fluid dynamics and plasma physics. Many of those physical laws are dissipative due to fluid viscosity or plasma collisions.…
This paper develops the so-called Weighted Energy-Dissipation (WED) variational approach for the analysis of gradient flows in metric spaces. This focuses on the minimization of the parameter-dependent global-in-time functional of…
In the variational principle leading to the Euler equation for a perfect fluid, we can use the method of undetermined multiplier for holonomic constraints representing mass conservation and adiabatic condition. For a dissipative fluid, the…
A general stochastic maximum principle is proved for optimal controls of semilinear stochastic evolution equations. Stochastic evolution operators, and the control with values in a general set enter into both drift and diffusion terms.
We establish a notion of universality for the parabolic Anderson model via an invariance principle for a wide family of parabolic stochastic partial differential equations. We then use this invariance principle in order to provide an…
In this paper, we consider a system of initial boundary value problems for parabolic equations, as a generalized version of the "$ \phi $-$ \eta $-$ \theta $ model" of grain boundary motion, proposed by Kobayashi [16]. The system is a…
The stochastic differential equations for a model of dissipative particle dynamics, with both total energy and total momentum conservation at every time-step, are presented. The algorithm satisfies detailed balance as well as the…
A general maximum principle is proved for optimal controls of abstract semilinear stochastic evolution equations. The control variable, as well as linear unbounded operators, acts in both drift and diffusion terms, and the control set need…
We provide a novel existence result for energy-variational solutions to a general class of evolutionary partial differential equations. Compared to previous works on this solution concept, the generalization is mainly twofold: a relaxation…
A variational principle is further developed for out of equilibrium dynamical systems by using the concept of maximum entropy. With this new formulation it is obtained a set of two first-order differential equations, revealing the same…
We consider a general optimal control problem in the setting of gradient flows. Two approximations of the problem are presented, both relying on the variational reformulation of gradient-flow dynamics via the Weighted-Energy-Dissipation…
Fluid dynamics accompanies with the entropy production thus increases the local temperature, which plays an important role in charged systems such as the ion channel in biological environment and electrodiffusion in capacitors/batteries. In…
Learning the underlying potential energy of stochastic gradient systems from partial and noisy observations is a fundamental problem arising in physics, chemistry, and data-driven modeling. Classical approaches often rely on direct…