Physics-Informed Neural Networks (PINNs)

This section of the user guide delves into the Physics-Informed Neural Networks (PINNs) available within the fusionlab-learn library. These models represent a cutting-edge approach that merges the pattern-recognition power of deep learning with the fundamental principles of physics, expressed as Partial Differential Equations (PDEs).

Unlike purely data-driven models, PINNs are trained to satisfy both observational data and the underlying physical laws of a system. This makes them exceptionally powerful for scientific and engineering applications where data may be sparse or noisy, as the physics provides a strong inductive bias, leading to more robust and generalizable solutions.

The models in this section are designed for complex spatio-temporal forecasting tasks, such as those found in geohydrology, where respecting the physical processes is crucial for accurate and meaningful predictions.

PINN Models:

• Hybrid Physics-Data Models: PiHALNet & PIHALNet
  • Common Key Features
  • Physical Formulation and Hybrid Loss
  • Architectural & Feature Differences
  • PIHALNet (Modern, BaseAttentive-based)
  • PiHALNet (Legacy Version)
  • Next Steps
• TransFlowSubsNet: A Physics-Informed Hybrid Forecasting Model
  • The Hybrid Loss Function: Fusing Data and Physics
  • Governing Physical Equations
  • Architectural Workflow: A Deep Dive
  • Key Configuration Parameters for Physics
  • Complete Usage Example
  • Next Steps
• Physics-Informed Transient Groundwater Flow (PiTGWFlow)
  • Key Features
  • When to Use PiTGWFlow
  • The Governing Equation
  • Architectural Workflow: A Deep Dive
  • Complete Example
  • Next Steps