A parallel sampling kernel with splittable random streams, variance reduction, and bitwise replay across worker counts.
A static-and-dynamic analyzer that bounds floating-point expressions with interval and affine arithmetic and searches for unstable regions.
A reproducible planner that selects ordering, preconditioner, and solver parameters from matrix structure under time and memory budgets.
A local checker that compares analytic, automatic, and finite-difference gradients through contact-rich physics simulations.
A typed computation graph that propagates correlated uncertainty using linearization, polynomial chaos, and deterministic sampling.
A local co-simulation kernel that couples independently stepped thermal, electrical, and mechanical models with convergence guarantees.
A trace debugger that attributes numerical divergence to rounding, cancellation, conditioning, and reduction order.
A finite-volume simulator that tracks mass, momentum, and entropy budgets across shocks and adaptive time steps.
A finite-element workbench that refines and coarsens meshes from residual error estimates while preserving reproducible solver traces.
A solver laboratory that exposes identifiability, regularization paths, and uncertainty for ill-posed linear and nonlinear inverse problems.
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