.png){kind=icon}
Return
The Deep Ritz Method for parametric p-Dirichlet problems
.png){kind=icon}
OA
AI
DOI：10.1186/s13662-025-04043-2.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
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 $p\in (1,\infty )$. 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.
Keywords:
Deep Ritz method
Parametric problems
Neural networks
Non-linear variational problems
Journal
A
IF:
1.8
Papers:
167
Citations:
0
Organization
Cited Papers
ShareSaveApproximation rates for neural networks with encodable weights in smoothness spaces.png)
NEURAL NETWORKS
OAAI
NEURAL NETWORKSIF6.3
OAAIShareSaveShareSave
View more