Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.12145 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915113395552256 |
|---|---|
| author | De Ryck, T. Mishra, S. Shang, Y. Wang, F. |
| author_facet | De Ryck, T. Mishra, S. Shang, Y. Wang, F. |
| contents | We present approximation results and numerical experiments for the use of randomized neural networks within physics-informed extreme learning machines to efficiently solve high-dimensional PDEs, demonstrating both high accuracy and low computational cost. Specifically, we prove that RaNNs can approximate certain classes of functions, including Sobolev functions, in the $H^2$-norm at dimension-independent convergence rates, thereby alleviating the curse of dimensionality. Numerical experiments are provided for the high-dimensional heat equation, the Black-Scholes model, and the Heston model, demonstrating the accuracy and efficiency of randomized neural networks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12145 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs De Ryck, T. Mishra, S. Shang, Y. Wang, F. Numerical Analysis We present approximation results and numerical experiments for the use of randomized neural networks within physics-informed extreme learning machines to efficiently solve high-dimensional PDEs, demonstrating both high accuracy and low computational cost. Specifically, we prove that RaNNs can approximate certain classes of functions, including Sobolev functions, in the $H^2$-norm at dimension-independent convergence rates, thereby alleviating the curse of dimensionality. Numerical experiments are provided for the high-dimensional heat equation, the Black-Scholes model, and the Heston model, demonstrating the accuracy and efficiency of randomized neural networks. |
| title | Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2501.12145 |