Bayesian hyper-parameter optimization of physics-informed neural networks to a nonlocal nonlinear Schrödinger...

Area of Science:

• Computational Physics
• Machine Learning
• Numerical Analysis

Background:

• Manual hyper-parameter tuning in Physical Information Neural Networks (PINNs) is inefficient and suboptimal.
• Achieving optimal performance in PINNs requires effective hyper-parameter optimization strategies.

Purpose of the Study:

• To introduce a Bayesian hyper-parameter optimization method for PINNs (BHPO-PINN) using Gaussian processes.
• To enhance the training performance and solution accuracy of PINNs.
• To apply BHPO-PINN to solve the nonlocal reverse-time nonlinear Schrödinger equation.

Main Methods:

• Developed a Bayesian hyper-parameter optimization framework (BHPO-PINN) based on Gaussian processes.
• Applied the BHPO-PINN method to solve the nonlocal reverse-time nonlinear Schrödinger equation.
• Conducted numerical simulations for one-soliton and four types of two-soliton solutions, analyzing relative and maximum absolute errors.

Main Results:

• BHPO-PINN identified optimal hyper-parameter combinations, significantly enhancing training performance.
• Numerical simulations demonstrated improved accuracy and stability compared to traditional PINNs.
• Error variations under different training iterations were analyzed to validate hyper-parameter optimization.

Conclusions:

• The BHPO-PINN method offers a more efficient and effective approach to hyper-parameter tuning for PINNs.
• BHPO-PINN achieves superior accuracy and stability in solving complex nonlinear equations.
• This optimization technique is crucial for advancing the application of PINNs in scientific computing.