Multifidelity Modeling for Physics-Informed Neural Networks (PINNs)
arXiv:2106.13361 · doi:10.1016/j.jcp.2021.110844
Abstract
Multifidelity simulation methodologies are often used in an attempt to judiciously combine low-fidelity and high-fidelity simulation results in an accuracy-increasing, cost-saving way. Candidates for this approach are simulation methodologies for which there are fidelity differences connected with significant computational cost differences. Physics-informed Neural Networks (PINNs) are candidates for these types of approaches due to the significant difference in training times required when different fidelities (expressed in terms of architecture width and depth as well as optimization criteria) are employed. In this paper, we propose a particular multifidelity approach applied to PINNs that exploits low-rank structure. We demonstrate that width, depth, and optimization criteria can be used as parameters related to model fidelity, and show numerical justification of cost differences in training due to fidelity parameter choices. We test our multifidelity scheme on various canonical forward PDE models that have been presented in the emerging PINNs literature.
References in corpus (13)
- B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data
- Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations
- On the Number of Linear Regions of Deep Neural Networks
- PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEs
- Integrating Machine Learning and Multiscale Modeling: Perspectives, Challenges, and Opportunities in the Biological, Biomedical, and Behavioral Sciences
- Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems
- Representation Benefits of Deep Feedforward Networks
- On the number of response regions of deep feed forward networks with piece-wise linear activations
- Complexity of Linear Regions in Deep Networks
- A Radial Basis Function (RBF)-Finite Difference Method for the Simulation of Reaction-Diffusion Equations on Stationary Platelets within the Augmented Forcing Method
- Parametric Topology Optimization with Multi-Resolution Finite Element Models
- Multi-fidelity uncertainty quantification of irradiated particle-laden turbulence
- Kernel optimization for Low-Rank Multi-Fidelity Algorithms