omnibias-fields

Status: Beta (v0.1.0).

The backend-agnostic field substrate for omnibias: the FieldState value object, the attribute-DSL views (state.u.grad, state.velocity.div, ...), the lazy sigma^(n)(z) cache, the op-extension registry, and the cross-backend (torch + jax) closed-form differential-operator surface.

Why this is the substrate

• One forward pass per derivative order — the SigmaCache evaluates sigma^(n)(z) exactly once per (layer, order) pair and feeds every downstream op (grad, div, curl, laplacian, hessian, jacobian, Sobolev norms, tensor divergence, Wirtinger).
• Cross-backend bit-identity — the torch and JAX op surfaces are arithmetic twins over the sigma tower the caller supplies, and that tower comes from the one shared omnibias.core.polynomials recurrence via omnibias.torch / omnibias.jax. A Laplacian on torch is therefore ULP-equal to the same Laplacian on JAX in float64.
• One extension surface — omnibias-pinn, omnibias-geometry, omnibias-score (and any external package that registers ops through ops_registry) all share one FieldState. The same state.u.grad syntax works everywhere.

This package was extracted from omnibias-pinn so that every field-based extension can build on one shared, bit-identical substrate. omnibias-pinn re-exports the moved symbols through back-compat shims, so existing omnibias.pinn._core and omnibias.pinn.<backend>.ops imports keep working unchanged.

Install

pip install "omnibias-fields[torch]"   # or [jax], or [all]

What's here

Building on top of this

A field is any object implementing the FieldBase protocol that, when called on a (B, D) coordinate tensor, returns a FieldState. To make the closed-form ops dispatch correctly, set the class attribute named by omnibias.fields._core.DISPATCH_ATTR (default "_omnibias_dispatch") to one of the dispatch tags: "one_layer" selects the closed-form sigma-tower reduction; any other tag selects the state-method path (the field implements value_component, derivative, mixed_partial taking the FieldState).

To add a new op without modifying this package, register it:

from omnibias.fields import ops_registry

@ops_registry.register("symmetric_laplacian")
def symmetric_laplacian(state, name):
    ...
# now available as state.u.symmetric_laplacian

See FIELDS_DERIVATIONS.md for the math behind each op and the numerical-stability notes.

Invariants

• Pure-Python core. omnibias.fields._core imports no torch / jax / numpy.
• Cross-backend bit-identity. The torch and jax ops are arithmetic twins over the same pure-Python schemas; the sigma tower they consume comes from the shared omnibias-core polynomial coefficients. They agree to rtol=1e-12, atol=1e-12 on the parity tests.
• One sigma evaluation per (order, axis). The SigmaCache is filled lazily and reused across all ops in a residual.

License

Apache-2.0. See LICENSE and ../../LICENSING.md. You never need a commercial licence for this package.