Science patterns enabled by Jaxstro

Modules remain the durable technical units of this site. This page takes the other route: start with a research question, then find its equation, primitive, transform boundary, evidence, and owner. Use every pattern with How to learn with Jaxstro: predict, compute, audit. Signatures live in API reference, and claims resolve to Validation.

Locate an event or equilibrium¶

Question. Where does a signed physical residual cross zero?

Equation. $G(x;\theta)=0$.

Primitive. Root-finding uses safeguarded_bracketed_root for an auditable value and trace.

Transform boundary. Scalar jit; value/shape vmap; physical-cost lax.map.

Failure evidence. Missing brackets, nonfinite evaluations, exhaustion, and exact roots have distinct statuses.

Ownership. Jaxstro owns scalar numerical evidence; the downstream project owns the physical residual and accepted state.

Differentiate a certified equilibrium¶

Question. How does a unique smooth equilibrium move with a model parameter?

Equation. $dx^\star/d\theta=-(\partial_\theta G)/(\partial_x G)$.

Primitive. Root-finding provides implicit_bracketed_root separately from the value solver.

Transform boundary. The implicit derivative requires uniqueness and smoothness assertions plus convergence, finiteness, residual, width, and slope gates.

Failure evidence. Rejection returns NaN for the derivative-facing value and attempted gradient while retaining primal diagnostics.

Ownership. Jaxstro checks local numerical evidence; the scientist owns the global branch claim.

Accumulate a conserved or integrated quantity¶

Question. What total follows from a sampled density, rate, or source term?

Equation. $Q=\int_a^b q(x)\,dx$.

Primitive. Newton–Cotes integration, Fixed-node quadrature, and Structured 1D meshes cover sampled, fixed-node, and conservative accumulation.

Transform boundary. Fixed shapes compose with JAX; node choice and discretization error remain distinct from pathwise derivatives.

Failure evidence. Exactness, convergence, conservation, and FD comparisons support different claims.

Ownership. Jaxstro owns accumulation rules; applications own the integrand and resolution study.

Interpolate a tabulated physical model¶

Question. How can an expensive table be evaluated between samples without inventing unsupported behavior?

Equation. $y(x)$ is reconstructed locally from values, slopes, or grid stencils.

Primitive. Cubic interpolation, Regular-grid interpolation, and B-splines.

Transform boundary. Prepared fixed-rank evaluation is JAX-native; topology and policy selection stay discrete.

Failure evidence. Boundary policy, monotonicity, support, affine recovery, and holdouts are separate checks.

Ownership. Jaxstro owns interpolation mechanics; source adapters own coordinate semantics and policy evidence.

Cross a limiting distribution parameter smoothly¶

Question. Can a normalized distribution remain differentiable where its closed form has a removable singularity?

Equation. A finite power law approaches a logarithmic form as $\alpha\rightarrow-1$.

Primitive. Distribution kernels uses smooth kernels in powerlaw_logpdf, powerlaw_cdf, and powerlaw_ppf.

Transform boundary. Interior parameter derivatives are smooth through the limit; support boundaries remain explicit.

Failure evidence. Normalization, round trips, analytic limits, and central FD versus AD are checked.

Ownership. Jaxstro owns finite kernels, not population semantics or probabilistic programming.

Transform coordinates, units, and spectra¶

Question. How can an observable change representation without changing physical meaning?

Equation. Rotations, dimensional conversions, and density Jacobians preserve named invariants.

Primitive. Quantities, units, and dimensional boundaries, Geometry helpers, and Spectra data architecture.

Transform boundary. Smooth transforms support AD away from singularities; parsing and data preparation stay host-side.

Failure evidence. Round trips, conventions, dimensional errors, singular contracts, and product identities are tested.

Ownership. Jaxstro owns representation mechanics; domain packages own observational interpretation.

Find local spatial interactions¶

Question. Which objects can interact within a cutoff, and was allocation sufficient?

Equation. Candidate gathering precedes $\lVert x_i-x_j\rVert\le r$.

Primitive. Spatial indexing and neighbor contracts separates conservative recall from exact fixed-radius pairs.

Transform boundary. Topology is discrete; fixed-shape pair payloads feed JAX kernels.

Failure evidence. Recall, symmetry, cutoff, capacity, and overflow are distinct contracts.

Ownership. Jaxstro owns indexing and filtering; consumers own interaction physics and overflow policy.

Connect model PyTrees to inference parameters¶

Question. How can a structured model expose selected leaves to inference?

Equation. Bijections map unconstrained vectors to constrained parameters with log-Jacobian terms.

Primitive. The parameter bridge in Astro-first, science-general vision connects PyTrees, vectors, and transforms.

Transform boundary. Selected inexact leaves transform; reconstruction and cached-derived values require explicit ownership.

Failure evidence. Round trips, transform identities, log determinants, and recovery tests bound the claim.

Ownership. Jaxstro owns parameter mechanics, not an optimizer, sampler, likelihood, or model.

Preserve provenance from artifact to claim¶

Question. Can a result be traced to source data, method, environment, and validation?

Equation. Provenance is a graph of artifacts, transformations, assertions, and evidence.

Primitive. Provenance architecture covers runtime manifests and provenance cards.

Transform boundary. Hashing and registry resolution are host-side; identifiers travel beside JAX computations.

Failure evidence. Missing artifacts, stale generated pages, unresolved tests, and changed hashes fail explicit gates.

Ownership. Jaxstro owns reusable records and routing; scientists own source adequacy and the scientific claim.