Multiscale Physics-Informed Neural Network for Complex Fluid Flows with Long-Range Dependencies
Summary: arXiv:2604.05652v1 Announce Type: cross
Abstract: Fluid flows are governed by the nonlinear Navier-Stokes equations, which can manifest multiscale dynamics even from predictable initial conditions. Predicting such phenomena remains a formidable challenge in scientific machine learning, particularly regarding convergence speed, data requirements, and solution accuracy.
In complex fluid flows, these challenges are exacerbated by long-range spatial dependencies arising from distant boundary conditions, which typically necessitate extensive supervision data to achieve acceptable results. To address these issues, researchers have proposed the Domain-Decomposed and Shifted Physics-Informed Neural Network (DDS-PINN), a novel framework designed to resolve such multiscale interactions with minimal supervision.
Key Features of DDS-PINN
The DDS-PINN framework incorporates several innovative features:
- Localized Networks: By employing localized networks, DDS-PINN can effectively capture the multiscale interactions present in fluid flows.
- Unified Global Loss: The framework utilizes a unified global loss function that allows it to maintain local precision while capturing global dependencies.
- Minimal Supervision: DDS-PINN is designed to work with minimal supervision data, significantly reducing the data requirements typically needed for accurate predictions.
Benchmarking and Results
The robustness of DDS-PINN has been demonstrated across a suite of benchmarks, including:
- A multiscale linear differential equation
- The nonlinear Burgers’ equation
- Data-free Navier-Stokes simulations of flat-plate boundary layers
One of the most compelling applications of DDS-PINN is in solving the computationally challenging backward-facing step (BFS) problem. For laminar regimes (Re = 100), the model produced results comparable to traditional computational fluid dynamics (CFD) methods without the need for any data, accurately predicting key parameters such as:
- Boundary layer thickness
- Separation lengths
- Reattachment lengths
Turbulent Flows and Performance
For turbulent BFS flow at Reynolds number Re = 10,000, DDS-PINN achieved convergence to O(10^-4) using only 500 random supervision points, which is less than 0.3% of the total domain. This performance outperformed established methods, including Residual-based Attention-PINN, in terms of accuracy.
Conclusion
The DDS-PINN framework demonstrates significant potential for the super-resolution of complex turbulent flows from sparse experimental measurements. By combining localized networks with a global loss approach, this innovative method offers a promising avenue for advancing the field of scientific machine learning in fluid dynamics.