Gradient-Driven Physics Informed Neural Networks for Conduction Heat Transfer and Incompressible Laminar Flow

Area of Science:

• Computational physics
• Numerical analysis
• Machine learning for science

Background:

• Physics-Informed Neural Networks (PINNs) integrate physical laws into neural networks for solving partial differential equations (PDEs).
• Traditional PINNs face challenges in accurately resolving sharp gradients and complex solution features, limiting their application scope.

Purpose of the Study:

• Introduce Gradient-Driven Physics-Informed Neural Networks (GDPINNs) to enhance the resolution of sharp gradients in PINNs.
• Improve the accuracy and effectiveness of neural network-based PDE solvers in complex physical scenarios.

Main Methods:

• Developed GDPINNs by incorporating gradient information directly into the neural network's loss function.
• Validated GDPINNs on steady-state and transient heat conduction problems with varying boundary conditions.
• Applied GDPINNs to incompressible laminar flow in a lid-driven cavity problem.

Main Results:

• GDPINNs demonstrated superior performance in capturing sharp gradients compared to traditional PINNs.
• Achieved strong agreement with reference solutions in heat conduction and fluid flow simulations.
• GDPINNs showed consistent higher accuracy and better feature capture in high-gradient problems.

Conclusions:

• GDPINNs offer a significant improvement over standard PINNs for problems involving sharp gradients.
• The method shows broad applicability across different physics domains, including heat transfer and fluid dynamics.
• GDPINNs represent a promising advancement for tackling complex physical problems with PINNs.