# jNO — jax Numerical Operators

> A JAX-native library for differentiable numerical methods. Classical solvers (FEM, FDM,
> spectral/RCWA) and scientific machine learning (PINNs, neural operators, Bayesian inference) on
> one substrate: you write the math — a weak form, a strong-form stencil, a PDE residual, a data
> loss — and it lowers to a single GPU-ready, end-to-end reverse-mode-differentiable,
> jit-compiled graph. Import name `jno`, PyPI `jax-numerical-operators`.

The complete LLM briefing — house conventions, API vocabulary, measured gotchas, verified
end-to-end examples — is one file:

- [Full guide](https://fhg-iisb.github.io/jNO/llms-full.txt): paste-into-a-system-prompt complete

## Docs

- [Installation](https://fhg-iisb.github.io/jNO/Installation/): pip / extras / pixi / Docker; CPU by default, GPU via the [cuda] extra
- [Getting started](https://fhg-iisb.github.io/jNO/Getting-Started/): first end-to-end problem
- [Concepts](https://fhg-iisb.github.io/jNO/concepts/): the trace, constraints, crux, models
- [Domain and geometry](https://fhg-iisb.github.io/jNO/Domain-and-Geometry/): jno.Shape / jno.Path CSG, tags, sampling
- [FEM](https://fhg-iisb.github.io/jNO/fem/): weak forms as term lists, solver slots, eigenproblems, contact
- [FDM](https://fhg-iisb.github.io/jNO/fdm/): strong-form collocation from the same term lists
- [RCWA](https://fhg-iisb.github.io/jNO/rcwa/): periodic-layered electromagnetics
- [Inverse problems](https://fhg-iisb.github.io/jNO/inverse-problems/): parameters, fields, regularization
- [Tutorials](https://fhg-iisb.github.io/jNO/#tutorials): 29 worked, verified examples

## Source

- [Repository](https://github.com/FhG-IISB/jNO)
- [Paper](https://arxiv.org/abs/2605.10159)