Numerical wave propagation aided by deep learning

Nguyen, Hieu; Tsai, Richard

doi:10.1016/j.jcp.2022.111828

Cited by 7 publications

(2 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They also observe that the trained coarse propagator improves Parareal convergence compared to a simplified analytical coarse model. Nguyen and Tsai [17] do not fully replace the numerical coarse propagator but use supervised learning to enhance its accuracy for wave propagation modeling. They observe that this enhances stability and accuracy of Parareal, provided the training data contains sufficiently representative examples.…”

Section: Related Workmentioning

confidence: 99%

Parareal with a Physics-Informed Neural Network as Coarse Propagator

Ibrahim,

Götschel,

Ruprecht

2023

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Parallel-in-time algorithms provide an additional layer of concurrency for the numerical integration of models based on time-dependent differential equations. Methods like Parareal, which parallelize across multiple time steps, rely on a computationally cheap and coarse integrator to propagate information forward in time, while a parallelizable expensive fine propagator provides accuracy. Typically, the coarse method is a numerical integrator using lower resolution, reduced order or a simplified model. Our paper proposes to use a physics-informed neural network (PINN) instead. We demonstrate for the Black-Scholes equation, a partial differential equation from computational finance, that Parareal with a PINN coarse propagator provides better speedup than a numerical coarse propagator. Training and evaluating a neural network are both tasks whose computing patterns are well suited for GPUs. By contrast, mesh-based algorithms with their low computational intensity struggle to perform well. We show that moving the coarse propagator PINN to a GPU while running the numerical fine propagator on the CPU further improves Parareal’s single-node performance. This suggests that integrating machine learning techniques into parallel-in-time integration methods and exploiting their differences in computing patterns might offer a way to better utilize heterogeneous architectures.

show abstract

Section: Related Workmentioning

confidence: 99%

Parareal with a Physics-Informed Neural Network as Coarse Propagator

Ibrahim,

Götschel,

Ruprecht

2023

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

“…The wave equation provides a mathematical framework for understanding and predicting how waves propagate through various physical systems. While numerous numerical methods have been developed for solving wave equations, the emergence of PINNs has garnered significant interest as a data-driven approach [24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Physics-Informed Neural Networks for High-Frequency and Multi-Scale Problems Using Transfer Learning

Mustajab,

Lyu,

Rizvi

et al. 2024

Applied Sciences

View full text Add to dashboard Cite

Physics-Informed Neural Network (PINN) is a data-driven solver for partial and ordinary differential equations (ODEs/PDEs). It provides a unified framework to address both forward and inverse problems. However, the complexity of the objective function often leads to training failures. This issue is particularly prominent when solving high-frequency and multi-scale problems. We proposed using transfer learning to boost the robustness and convergence of training PINN, starting training from low-frequency problems and gradually approaching high-frequency problems through fine-tuning. Through two case studies, we discovered that transfer learning can effectively train PINNs to approximate solutions from low-frequency problems to high-frequency problems without increasing network parameters. Furthermore, it requires fewer data points and less training time. We compare the PINN results using direct differences and L2 relative error showing the advantage of using transfer learning techniques. We describe our training strategy in detail, including optimizer selection, and suggest guidelines for using transfer learning to train neural networks to solve more complex problems.

show abstract

An enhanced V-cycle MgNet model for operator learning in numerical partial differential equations

Zhu

Huang

2023

Comput Geosci

View full text Add to dashboard Cite

Numerical wave propagation aided by deep learning

Cited by 7 publications

References 37 publications

Parareal with a Physics-Informed Neural Network as Coarse Propagator

Parareal with a Physics-Informed Neural Network as Coarse Propagator

Physics-Informed Neural Networks for High-Frequency and Multi-Scale Problems Using Transfer Learning

An enhanced V-cycle MgNet model for operator learning in numerical partial differential equations

Contact Info

Product

Resources

About