Research Roadmap

This page summarizes research directions and promotion criteria for users. Implementation order, file ownership, and pull-request acceptance gates are tracked in a private planning document.

Current Foundation

NTX provides a JAX-native local monoenergetic solver with:

• analytic, DKES-style, VMEC, and Boozer geometry paths;

• prepared CPU/GPU scans and bounded batching;

• differentiable coefficient and profile workflows;

• NEOPAX-compatible database export and bootstrap-current workflows;

• analytical, convergence, imported-reference, and derivative physics gates;

• machine-readable benchmark and publication-artifact manifests.

Promoted claims and current numerical thresholds are listed in the benchmark matrix. A completed diagnostic is not automatically a validated research claim: promotion requires independent physics evidence, convergence, reusable inputs, tests, and documented provenance.

Research Directions

Direction	Current supported scope	Promotion requirement
Optimization-grade derivatives	Direct AD, prepared adjoints, geometry controls, and explicit-relaxed boundary sensitivities	AD, centered finite difference, and prepared-adjoint agreement on reusable geometry families with bounded memory
Implicit-equilibrium derivatives	Non-shipping diagnostic	Contracted equilibrium residual plus Boozer and NTX transport tangent agreement, not equilibrium-volume agreement alone
Profile, UQ, and design workflows	Differentiable reduced profile/current examples	Broader profile bases, uncertainty models, robust objectives, and independent physics checks before stellarator-design claims
Geometry-family validation	Owned analytic, finite-beta, QA/QH, and selected file-backed stress families	Production radial, electric-field, collisionality, angular, and Legendre ladders with independent references
Bootstrap-current closure	Scoped fixed-field total-current stress comparison and integrated transfer workflow	Physics-derived species-resolved closure that improves broader QA/QH cases without regressing integrated transfer; no fitted bridge constants
Production throughput	Prepared reuse, CPU batching, device parallelism, and measured crossover artifacts	Reproducible production-grid runtime and memory maps on named CPU and GPU hardware
Physics expansion	Local monoenergetic Lorentz model	A separately derived, tested, and literature-anchored model; do not silently broaden the current solver’s claims

Validation Standard

A research result is eligible for promotion only when it has:

1. a stated physical model, ordering, normalization, and validity boundary;

2. an owned or permanently accessible input with provenance;

3. angular, Legendre, radial, and parameter convergence appropriate to the observable;

4. analytical or independent numerical evidence with aligned physics settings;

5. residual, symmetry, conservation, and positivity checks where applicable;

6. direct tests of coordinate and normalization mappings;

7. autodiff agreement with centered finite differences for derivative claims;

8. runtime and memory measurements for performance claims;

9. a reusable script, regression test, machine-readable artifact, and publication-ready figure.

Stress diagnostics that miss one of these requirements remain useful, but their scope must be explicit in the validation page and benchmark matrix.

Numerical Priorities

Near-term numerical work should preserve the current physical operator while improving evidence and ownership:

• converge variable-coefficient Fourier collocation with measured angular oversampling and successive refinement;

• keep true full-system and reduced Schur residuals distinct;

• reuse prepared geometry, lowered programs, and compiled closures across scans;

• avoid vectorization that increases memory without measured throughput benefit;

• specialize adjoints only when primal and tangent regression gates remain unchanged;

• split large modules along stable public ownership boundaries, not by moving complexity into untested helpers.

The numerics, convergence, autodiff, and performance pages define the current implementation contracts.

Physics Basis

The forward formulation follows the Legendre-space monoenergetic treatment in Javier Escoto’s thesis, arXiv:2510.27513. Research directions are also informed by:

• neoclassical adjoint optimization, arXiv:1904.06430;

• differentiable plasma workflows, arXiv:2410.11161;

• direct neoclassical ion-transport optimization, arXiv:2406.04147;

• near-axis quasi-isodynamic verification, JPP 2025;

• zero-bootstrap-current piecewise omnigenity, arXiv:2505.02546;

• hidden-symmetry optimization, arXiv:2502.09350.

The expanded bibliography and the exact role of each source are maintained in Literature.

Source Ownership

Concern	Primary package area
Operator and source assembly	ntx.operators
Preparation, solve, and scans	ntx.solver
Geometry evaluation and imports	ntx.geometry
Stable input/output contracts	ntx.io and ntx.inputfiles
Profile and current workflows	ntx.profiles
NEOPAX bridge	ntx.neopax
Physics gates and artifacts	ntx.validation

See the source-code map before changing ownership. Public APIs should remain stable while internal modules are reduced to coherent, testable areas.

Next Milestone

The next milestone is not a single larger claim. It is a sequence of bounded pull requests from the private plan: finish user-facing documentation hygiene, continue stable source ownership, strengthen reusable geometry and profile derivative families, and promote only the independent geometry/current comparisons that pass their full convergence gates.