omnibias.fields

The backend-agnostic field substrate that PINN, geometry, and score/SDE build on. Hosts FieldState, the attribute-DSL views, the lazy σⁿ(z) cache, the op-extension registry, and the torch + jax closed-form operator surface.

import omnibias.fields as of

Lazy backends

Importing omnibias.fields does not import torch or jax. The backend kernels live in omnibias.fields.torch / omnibias.fields.jax and load lazily.

Core schemas and views

Symbol	Role
FieldState	the value object: a field plus its closed-form operator views
FieldBase	base class for fields
CoordinateSpec	input coordinate names/order
ComponentSpec	output components and named groups
ComponentView	scalar-component view (.grad, .lap, .hess, …)
VectorView	vector-group view (.div, .curl, .jacobian, …)
SigmaCache	lazy, memoized σⁿ(z) evaluations
OperatorInfo	metadata describing a registered operator
DOMAINS	the recognized operator domains

Operator registry

Symbol	Role
ops_registry	the registry object
get_operator(name)	look up an operator
list_operators() / operator_names()	enumerate operators
did_you_mean(name)	suggestion helper for typos

The operator surface

Through the attribute DSL on a FieldState, the backends expose closed-form gradient, divergence, curl, laplacian, hessian, jacobian, plus quadrature / inner-product / norm / tensor-divergence and Wirtinger ops. Dispatch to the closed-form σ-tower is selected by a class marker, so the substrate never imports a downstream package.

Example

state = field(coords)          # a FieldState
u = state.u                    # ComponentView
u.lap                          # Δu (closed form)
state.velocity.div             # ∇·u (closed form)

See also

• Field substrate — the design.
• pinn, geometry — built on this substrate.