Related papers: Numerical optimization using flow equations
Several deterministic and stochastic multi-variable global optimization algorithms (Conjugate Gradient, Nelder-Mead, Quasi-Newton, and Global) are investigated in conjunction with energy minimization principle to resolve the pressure and…
In this paper, we study a maximization and a minimization problem associated with a Poisson boundary value problem. Optimal solutions in a set of rearrangements of a given function define stationary and stable flows of an ideal fluid in two…
We show that accelerated optimization methods can be seen as particular instances of multi-step integration schemes from numerical analysis, applied to the gradient flow equation. In comparison with recent advances in this vein, the…
Recently, the nonlinearity continuation method has been used to numerically solve boundary value problems for steady-state Richards equation. The method can be considered as a predictor-corrector procedure with the simplest form which has…
This article serves as a summary outlining the mathematical entropy analysis of the ideal magnetohydrodynamic (MHD) equations. We select the ideal MHD equations as they are particularly useful for mathematically modeling a wide variety of…
In this paper, we study porous media flows in heterogeneous stochastic media. We propose an efficient forward simulation technique that is tailored for variational Bayesian inversion. As a starting point, the proposed forward simulation…
We propose a general approach to freezing out fluctuations in heavy-ion collisions using the principle of maximum entropy. We find the results naturally expressed as a direct relationship between the irreducible relative correlators…
Error estimates are proved for an evolving surface finite element semi-discretization for anisotropic mean curvature flow of closed surfaces. For the geometric surface flow, a system coupling the anisotropic evolution law to parabolic…
The boundary conditions prescribing the constant traction or the so-called do-nothing conditions are frequently taken on artificial boundaries in the numerical simulations of steady flow of incompressible fluids, despite the fact that they…
Nonequilibrium statistical models of point vortex systems are constructed using an optimal closure method, and these models are employed to approximate the relaxation toward equilibrium of systems governed by the two-dimensional Euler…
Inverse problems of partial differential equations are ubiquitous across various scientific disciplines and can be formulated as statistical inference problems using Bayes' theorem. To address large-scale problems, it is crucial to develop…
This paper presents a systematic approach for computing local solutions to motion planning problems in non-convex environments using numerical optimal control techniques. It extends the range of use of state-of-the-art numerical optimal…
We propose practical extensions to Bayesian optimization for solving dynamic problems. We model dynamic objective functions using spatiotemporal Gaussian process priors which capture all the instances of the functions over time. Our…
In this paper we study the distributions of the number of real solutions to the power flow equations over varying electrical parameters. We introduce a new monodromy and parameter homotopy continuation method for quickly finding all…
We derive novel algorithms for optimization problems constrained by partial differential equations describing multiscale particle dynamics, including non-local integral terms representing interactions between particles. In particular, we…
Multiscale problems can usually be approximated through numerical homogenization by an equation with some effective parameters that can capture the macroscopic behavior of the original system on the coarse grid to speed up the simulation.…
We study the dynamics of piecewise affine surface homeomorphisms from the point of view of their entropy. Under the assumption of positive topological entropy, we establish the existence of finitely many ergodic and invariant probability…
In this article, we propose high-order finite-difference entropy stable schemes for the two-fluid relativistic plasma flow equations. This is achieved by exploiting the structure of the equations, which consists of three independent flux…
Extreme events play a crucial role in fluid turbulence. Inspired by methods from field theory, these extreme events, their evolution and probability can be computed with help of the instanton formalism as minimizers of a suitable action…
This article concerns the problem of computing solutions to state-constrained optimal control problems whose trajectory is affected by a flow field. This general mathematical framework is particularly pertinent to the requirements…