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Neural PDEs & PINNs

The phaethon.pinns module provides deep integration with PyTorch, equipping artificial neural networks with absolute dimensional safety.

By bridging data-driven deep learning with fundamental physical laws, Phaethon introduces physics-aware autograd tensors, native calculus engines for Partial Differential Equations (PDEs), and advanced dimensional synthesis for operator learning.

Dependency Note

The PINNs module strictly requires the PyTorch backend. Install via: pip install 'phaethon[torch]'

PINNs Architecture

  • Physics Tensors & Ops

    The PTensor class. PyTorch tensors that dynamically track physical DNA and safely assemble heterogeneous data for neural ingestion.

  • Differential Calculus

    Native autograd engines (grad, laplace, div, curl) that automatically synthesize physical units during differentiation.

  • Fourier Neural Operators

    Spectral layers (1D Convolutions) and Buckingham Pi SVD projections for discovering dimensionless groups on-the-fly.

  • Physics Losses

    Strictly enforced PDE residuals and Axiom tribunals that penalize networks for mathematically valid but physically impossible predictions.