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Scope: PINNs and PDE surrogates

TL;DR — classical physics-informed neural networks (PINNs) for PDEs are out of scope for Jaxonomy. Jaxonomy is a simulation engine for systems governed by ODEs and DAEs evolving in time; it has no spatial discretization, no collocation-point sampling, and no PDE residual machinery, and we do not plan to add them.

What "PINN" means here

The term is used for two quite different things. Only one of them belongs in Jaxonomy:

Classical PDE PINN Physics-informed dynamics learning
Governing equations PDEs over space(-time): Burgers, Navier–Stokes, heat equation ODEs / DAEs over time: mechanics, circuits, thermal networks, chemistry
Unknown A neural field u(x, t) trained to satisfy the PDE residual at collocation points Parameters and/or a neural correction term inside a simulated model
Core machinery Spatial sampling, residual losses, boundary/initial-condition penalties A differentiable time-stepping simulator
In Jaxonomy? No Yes — this is a core capability

Out of scope (use these instead)

If you want to train u(x, t) against a PDE residual — surrogate models for fluid fields, heat maps over a plate, wave propagation — use a library built for it:

  • DeepXDE — the reference PINN library (PDEs, IDEs, fractional PDEs; TensorFlow/PyTorch/JAX backends).
  • NVIDIA PhysicsNeMo (formerly Modulus) — industrial-scale physics-ML, including PINNs and neural operators.
  • Neuromancer — differentiable programming for constrained optimization and physics-informed system identification in PyTorch.

A spatially discretized PDE (method of lines) can be simulated in Jaxonomy — a finite-volume battery-electrode model or a discretized heat rod is just a large ODE/DAE system — but Jaxonomy does not own the discretization, and we will not add collocation/residual training utilities for neural fields.

In scope (what Jaxonomy does instead)

Physics-informed learning where the physics enters through a differentiable simulation in time:

  • Universal differential equations (UDE) — a neural term inside an ODE right-hand side, trained end-to-end through simulate (see the UDE + symbolic regression example).
  • Neural DAE — a neural correction inside an acausal, constrained DAE (NeuralDAEBlock; see the constrained pendulum drag-recovery example). The index-reduction pipeline (Pantelides) runs unchanged with the neural term in place.
  • Neural ODE blocks — MLP (Equinox) and imported PyTorch / TensorFlow / ONNX networks as blocks inside a diagram.
  • SINDy — sparse symbolic regression of dynamics from data (Sindy block).
  • Differentiable parameter estimation — fit_parameters, lookup-table fitting, and the whole autodiff/optimization workflow.

The dividing line: if the "physics" constraint is enforced by simulating a dynamical system forward in time, it belongs here; if it is enforced by a residual loss over a spatial domain, it does not.