Comparing EPGP Surrogates and Finite Elements Under Degree-of-Freedom Parity
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915602692571136 |
|---|---|
| author | Amo, Obed Ghosh, Samit Lange-Hegermann, Markus Raiţă, Bogdan Pokojovy, Michael |
| author_facet | Amo, Obed Ghosh, Samit Lange-Hegermann, Markus Raiţă, Bogdan Pokojovy, Michael |
| contents | We present a new benchmarking study comparing a boundary-constrained Ehrenpreis--Palamodov Gaussian Process (B-EPGP) surrogate with a classical finite element method combined with Crank--Nicolson time stepping (CN-FEM) for solving the two-dimensional wave equation with homogeneous Dirichlet boundary conditions. The B-EPGP construction leverages exponential-polynomial bases derived from the characteristic variety to enforce the PDE and boundary conditions exactly and employs penalized least squares to estimate the coefficients. To ensure fairness across paradigms, we introduce a degrees-of-freedom (DoF) matching protocol. Under matched DoF, B-EPGP consistently attains lower space-time $L^2$-error and maximum-in-time $L^{2}$-error in space than CN-FEM, improving accuracy by roughly two orders of magnitude. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04518 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Comparing EPGP Surrogates and Finite Elements Under Degree-of-Freedom Parity Amo, Obed Ghosh, Samit Lange-Hegermann, Markus Raiţă, Bogdan Pokojovy, Michael Machine Learning Numerical Analysis 68T05, 62J07, 65M20, 65M60 I.2.6; G.1.2; G.1.8 We present a new benchmarking study comparing a boundary-constrained Ehrenpreis--Palamodov Gaussian Process (B-EPGP) surrogate with a classical finite element method combined with Crank--Nicolson time stepping (CN-FEM) for solving the two-dimensional wave equation with homogeneous Dirichlet boundary conditions. The B-EPGP construction leverages exponential-polynomial bases derived from the characteristic variety to enforce the PDE and boundary conditions exactly and employs penalized least squares to estimate the coefficients. To ensure fairness across paradigms, we introduce a degrees-of-freedom (DoF) matching protocol. Under matched DoF, B-EPGP consistently attains lower space-time $L^2$-error and maximum-in-time $L^{2}$-error in space than CN-FEM, improving accuracy by roughly two orders of magnitude. |
| title | Comparing EPGP Surrogates and Finite Elements Under Degree-of-Freedom Parity |
| topic | Machine Learning Numerical Analysis 68T05, 62J07, 65M20, 65M60 I.2.6; G.1.2; G.1.8 |
| url | https://arxiv.org/abs/2511.04518 |