Tutorial

To make full use of IDRLnet. We strongly suggest following the following examples:

1. Simple Poisson. This example introduces the primary usage of IDRLnet. Including creating sampling domains, neural networks, partial differential equations, training, monitoring, and inference.

2. Euler-Bernoulli beam. The example introduces how to use symbols to construct a PDE node efficiently.

3. Burgers’ Equation. The case presents how to include time in the sampling domains.

4. Allen-Cahn Equation. The example introduces the representation of periodic boundary conditions. Receiver acting as callbacks are also introduced, including implementing user-defined algorithms and post-processing during the training.

5. Inverse wave equation. The example introduces how to discover unknown parameters in PDEs.

6. Parameterized poisson equation. The example introduces how to train a surrogate with parameters.

7. Variational Minimization. The example introduces how to solve variational minimization problems.

8. Volterra integral differential equation. The example introduces the way to solve IDEs.

9. Navier-Stokes equation. The example introduces how to use the LBFGS optimizer.

10. Deepritz method. The example introduces the way to solve PDEs with the Deepritz method.

• Solving Simple Poisson Equation
  • Define Symbols
  • Define Geometric Objects
  • Define Sampling Methods and Constraints
  • Define Neural Networks and PDEs
  • Define A Solver
  • Inference
  • Performance Issues
• Euler–Bernoulli beam
  • Expression Node
  • Seperate Inference Domain
• Burgers’ Equation
  • Time-dependent Domain
  • Use TensorBoard
• Allen-Cahn Equation
  • Periodic Boundary Conditions
  • Receivers acting as Callbacks
• Inverse Wave Equation
  • Importing External Data
  • Define Unknown Parameters
  • Loss Metrics
• Parameterized Poisson
  • Train A Surrogate
• Variational Minimization
  • Load a Pretrained Network
  • Integral Domain
• Volterra Integral Differential Equation
  • 1D integral with Variable Limits
• Navier-Stokes equations
  • Steady 2D NS equations
  • Unsteady 2D N-S equations with unknown parameters
• Deepritz
  • Define Sampling Methods and Constraints
  • Define Neural Networks and PDEs