omnibias.pinn
Physics-informed neural networks on closed-form derivatives. Typed PINN fields, differential operators, hard-conservation cages, conditioned losses, prebuilt PDE residuals, and diagnostics.
from omnibias.pinn import CoordinateSpec, ComponentSpec
from omnibias.pinn.torch.fields import OneLayerVectorField
Pick a backend extra
omnibias.pinn.torch requires omnibias-pinn[torch]; omnibias.pinn.jax
requires omnibias-pinn[jax]. The backend subpackages are not imported
eagerly, so one extra is enough.
Top-level schemas
The backend-agnostic types re-exported from the field substrate.
| Symbol | Role |
|---|---|
CoordinateSpec | names/ordering of input coordinates |
ComponentSpec | output components and named groups |
FieldState | the value object holding a field and its closed-form ops |
FieldBase | base class for fields |
ComponentView, VectorView | attribute-DSL views into a FieldState |
EquationSpec | a PDE residual specification |
SigmaCache | lazy σⁿ(z) cache |
IncompressibilityPolicy, ResidualPolicy | policy enums |
ops_registry, registry | operator / field registries |
register_lim_along, unregister_lim_along | limit-op extension hooks |
Backend surfaces (omnibias.pinn.torch / .jax)
Each backend carries bit-identical implementations of:
- fields — e.g.
OneLayerVectorField, field MLPs. - ops — closed-form
grad,div,curl,lap,hess,jacobian, accessed via the attribute DSL (state.u.lap,state.velocity.curl). - cage — hard-constraint layers (
StreamfunctionField,VectorPotentialField); see structural cages. - equations — prebuilt residuals (
Heat,Biharmonic,KuramotoSivashinsky,CahnHilliard, Navier–Stokes, …). - losses / diagnostics — conditioned losses and training diagnostics.
Example
state = field(coords) # FieldState
state.u.lap # Δu, closed form
state.velocity.curl # ∇×u, closed form