Multi-Fidelity Physics-Informed Neural Networks with Bayesian Uncertainty Quantification and Adaptive Residual Learning for Efficient Solution of Parametric Partial Differential Equations
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910007723819008 |
|---|---|
| author | Imanov, Olaf Yunus Laitinen |
| author_facet | Imanov, Olaf Yunus Laitinen |
| contents | Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding physical laws directly into neural network training. However, solving high-fidelity PDEs remains computationally prohibitive, particularly for parametric systems requiring multiple evaluations across varying parameter configurations. This paper presents MF-BPINN, a novel multi-fidelity framework that synergistically combines physics-informed neural networks with Bayesian uncertainty quantification and adaptive residual learning. Our approach leverages abundant low-fidelity simulations alongside sparse high-fidelity data through a hierarchical neural architecture that learns nonlinear correlations across fidelity levels. We introduce an adaptive residual network with learnable gating mechanisms that dynamically balances linear and nonlinear fidelity discrepancies. Furthermore, we develop a rigorous Bayesian framework employing Hamiltonian Monte Carlo. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_01176 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multi-Fidelity Physics-Informed Neural Networks with Bayesian Uncertainty Quantification and Adaptive Residual Learning for Efficient Solution of Parametric Partial Differential Equations Imanov, Olaf Yunus Laitinen Machine Learning Numerical Analysis Computational Physics 68T07, 62F15, 65M06, 65N06, 35R30 I.2.6; G.3; G.1.8 Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding physical laws directly into neural network training. However, solving high-fidelity PDEs remains computationally prohibitive, particularly for parametric systems requiring multiple evaluations across varying parameter configurations. This paper presents MF-BPINN, a novel multi-fidelity framework that synergistically combines physics-informed neural networks with Bayesian uncertainty quantification and adaptive residual learning. Our approach leverages abundant low-fidelity simulations alongside sparse high-fidelity data through a hierarchical neural architecture that learns nonlinear correlations across fidelity levels. We introduce an adaptive residual network with learnable gating mechanisms that dynamically balances linear and nonlinear fidelity discrepancies. Furthermore, we develop a rigorous Bayesian framework employing Hamiltonian Monte Carlo. |
| title | Multi-Fidelity Physics-Informed Neural Networks with Bayesian Uncertainty Quantification and Adaptive Residual Learning for Efficient Solution of Parametric Partial Differential Equations |
| topic | Machine Learning Numerical Analysis Computational Physics 68T07, 62F15, 65M06, 65N06, 35R30 I.2.6; G.3; G.1.8 |
| url | https://arxiv.org/abs/2602.01176 |