Theory2 Physics Machine Learning

Train and use physics-informed machine learning models.

Fourier Neural Operators (FNO)

Learn PDE solution operators:

# Standard FNO configuration
/home/mikeb/theory2/.venv/bin/theory --json ml train-fno \
  --modes=16 --width=64 --layers=4

# Memory-efficient with Tucker factorization
/home/mikeb/theory2/.venv/bin/theory --json ml train-fno \
  --modes=32 --width=128 --factorization=tucker

# Check available models
/home/mikeb/theory2/.venv/bin/theory --json ml info

FNO Parameters

• modes: Fourier modes to keep (12-64, higher = more resolution)
• width: Hidden channel dimension (32-256)
• layers: Number of Fourier layers (2-6)
• factorization: dense, tucker, cp (tucker reduces memory 10x)

E(3)-Equivariant Networks (E3NN)

For molecular and atomic systems with geometric symmetry:

# Standard E3NN
/home/mikeb/theory2/.venv/bin/theory --json ml train-e3nn \
  --irreps-hidden="16x0e+16x1o+16x2e" --layers=3

# With gated nonlinearities
/home/mikeb/theory2/.venv/bin/theory --json ml train-e3nn \
  --irreps-hidden="32x0e+16x1o+8x2e" --use-gates

Irreps Format

NxLp where:

• N: Multiplicity
• L: Angular momentum (0=scalar, 1=vector, 2=tensor)
• p: Parity (e=even, o=odd)

Example: 16x0e + 16x1o + 8x2e = 16 scalars + 16 vectors + 8 symmetric tensors

Physics-Informed Neural Networks (PINNs)

Solve PDEs without training data:

# Heat equation
/home/mikeb/theory2/.venv/bin/theory --json ml solve-pde \
  --pde-type=heat --alpha=0.01 --iterations=10000

# Poisson equation
/home/mikeb/theory2/.venv/bin/theory --json ml solve-pde \
  --pde-type=poisson --iterations=20000

Available PDEs

• heat: 1D heat diffusion ∂u/∂t = α∂²u/∂x²
• poisson: 2D Poisson ∇²u = f

Argument Parsing

1. train-fno or fno: Train Fourier Neural Operator
2. train-e3nn or e3nn: Train equivariant network
3. solve-pde or pinn: Solve PDE with PINN
4. info: Show available models and status

Always use --json for structured output.