PDE-Constrained Optimization Models and Pseudospectral Methods for Multiscale Particle Dynamics

by   Mildred Aduamoah, et al.

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 investigate problems where the control acts as an advection 'flow' vector or a source term of the partial differential equation, and the constraint is equipped with boundary conditions of Dirichlet or no-flux type. After deriving continuous first-order optimality conditions for such problems, we solve the resulting systems by developing a link with computational methods for statistical mechanics, deriving pseudospectral methods in both space and time variables, and utilizing variants of existing fixed point methods. Numerical experiments indicate the effectiveness of our approach for a range of problem set-ups, boundary conditions, as well as regularization and model parameters.



There are no comments yet.


page 1

page 2

page 3

page 4


A New Treatment of Boundary Conditions in PDE Solutions with Galerkin Methods via Partial Integral Equation Framework

We present a new framework for solution of Partial Differential Equation...

Bulk-surface Lie splitting for parabolic problems with dynamic boundary conditions

This paper studies bulk-surface splitting methods of first order for (se...

An iterative splitting method for pricing European options under the Heston model

In this paper, we propose an iterative splitting method to solve the par...

Analysis of boundary effects on PDE-based sampling of Whittle-Matérn random fields

We consider the generation of samples of a mean-zero Gaussian random fie...

Model Reduction of Swing Equations with Physics Informed PDE

This manuscript is the first step towards building a robust and efficien...

Deep Learning for Constrained Utility Maximisation

This paper proposes two algorithms for solving stochastic control proble...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.