Work

Optimal Bounds for POD Approximations of Infinite Horizon Control Problems Based on Time Derivatives

Year: 2025

Type: book-chapter

Abstract: In this paper we consider the numerical approximation of infinite horizon problems via the dynamic programming approach. The value function of the problem solves a Hamilton–Jacobi–Bellman equation that is approximated by a fully discrete method. It is known that the numerical problem is difficult to handle by the so called curse of dimensionality. To mitigate this issue we apply a reduction of the order by means of a new proper orthogonal decomposition (POD) method based on time derivatives. We carry out the error analysis of the method using recently proved optimal bounds for the fully discrete approximations. Moreover, the use of snapshots based on time derivatives allows us to bound some terms of the error that could not be bounded in a standard POD approach. Some numerical experiments show the good performance of the method in practice.

Source: Journal of Scientific Computing

DOI: 10.1007/s10915-025-02833-0

Authors: Javier de Frutos, Bosco García-Archilla, Julia Novo

Institutions: Universidad de Valladolid, Universidad de Sevilla, Universidad Autónoma de Madrid

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funders: Universidad de Sevilla, Universidad Autónoma de Madrid, Junta de Castilla y León, Agencia Estatal de Investigación