Deep Operator Networks for Bayesian Parameter Estimation in PDEs
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912515430023168 |
|---|---|
| author | Raj, Amogh Gudumotou, Carol Eunice Bun, Sakol Srinivasa, Keerthana Sarshar, Arash |
| author_facet | Raj, Amogh Gudumotou, Carol Eunice Bun, Sakol Srinivasa, Keerthana Sarshar, Arash |
| contents | We present a novel framework combining Deep Operator Networks (DeepONets) with Physics-Informed Neural Networks (PINNs) to solve partial differential equations (PDEs) and estimate their unknown parameters. By integrating data-driven learning with physical constraints, our method achieves robust and accurate solutions across diverse scenarios. Bayesian training is implemented through variational inference, allowing for comprehensive uncertainty quantification for both aleatoric and epistemic uncertainties. This ensures reliable predictions and parameter estimates even in noisy conditions or when some of the physical equations governing the problem are missing. The framework demonstrates its efficacy in solving forward and inverse problems, including the 1D unsteady heat equation and 2D reaction-diffusion equations, as well as regression tasks with sparse, noisy observations. This approach provides a computationally efficient and generalizable method for addressing uncertainty quantification in PDE surrogate modeling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10684 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Deep Operator Networks for Bayesian Parameter Estimation in PDEs Raj, Amogh Gudumotou, Carol Eunice Bun, Sakol Srinivasa, Keerthana Sarshar, Arash Machine Learning Computational Engineering, Finance, and Science 65K10, 35R30, 68T07 I.2.9; G.1.8; I.6.5 We present a novel framework combining Deep Operator Networks (DeepONets) with Physics-Informed Neural Networks (PINNs) to solve partial differential equations (PDEs) and estimate their unknown parameters. By integrating data-driven learning with physical constraints, our method achieves robust and accurate solutions across diverse scenarios. Bayesian training is implemented through variational inference, allowing for comprehensive uncertainty quantification for both aleatoric and epistemic uncertainties. This ensures reliable predictions and parameter estimates even in noisy conditions or when some of the physical equations governing the problem are missing. The framework demonstrates its efficacy in solving forward and inverse problems, including the 1D unsteady heat equation and 2D reaction-diffusion equations, as well as regression tasks with sparse, noisy observations. This approach provides a computationally efficient and generalizable method for addressing uncertainty quantification in PDE surrogate modeling. |
| title | Deep Operator Networks for Bayesian Parameter Estimation in PDEs |
| topic | Machine Learning Computational Engineering, Finance, and Science 65K10, 35R30, 68T07 I.2.9; G.1.8; I.6.5 |
| url | https://arxiv.org/abs/2501.10684 |