Work

The Deep Ritz Method for parametric p-Dirichlet problems

Year: 2025

Type: article

Abstract: We establish error estimates for the approximation of parametric p -Dirichlet problems deploying the Deep Ritz Method. Parametric dependencies include, e.g. , varying geometries and exponents $p\in (1,\infty )$ p ∈ ( 1 , ∞ ) . Combining the derived error estimates with quantitative approximation theorems yields error decay rates and establishes that the Deep Ritz Method retains the favorable approximation capabilities of neural networks in the approximation of high-dimensional functions, which demonstrates the method’s suitability for parametric problems. Finally, we present numerical experiments that illustrate potential applications.

Source: Advances in Continuous and Discrete Models

DOI: 10.1186/s13662-025-04043-2

Authors: Alex Kaltenbach, Marius Zeinhofer

Institutions: Technische Universität Berlin, Simula Research Laboratory

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: $1,890

Funders: Norges Forskningsråd, Technische Universität Berlin