Problem

Has symbolic regression but missing PINNs and neural operators for scientific computing.

Existing

• src/Regression/SymbolicRegression.cs

Missing Implementations

Physics-Informed NNs (CRITICAL):

• PINN (Physics-Informed Neural Network)
• Deep Ritz Method
• Variational Physics-Informed Neural Networks

Neural Operators (HIGH):

• FNO (Fourier Neural Operator)
• DeepONet (Deep Operator Network)
• Graph Neural Operators

Scientific ML (MEDIUM):

• Universal Differential Equations
• Hamiltonian Neural Networks
• Lagrangian Neural Networks
• Symbolic Physics Learner

Use Cases

• PDE solving (Navier-Stokes, heat equation)
• Climate modeling
• Molecular dynamics
• Fluid dynamics

Architecture

• src/Scientific ML/PINNs/
• src/ScientificML/NeuralOperators/
• PDE specification interface

Success Criteria

• Standard PDE benchmarks (Burgers, Allen-Cahn)
• Operator learning benchmarks
• Comparison with traditional PDE solvers