ADR 0005: Add Taylor as the built-in nominal backend

• Status: accepted
• Date: 2026-07-28
• Supersedes: ADR 0004’s default for built-in nominal dynamics; DOP853 remains the general backend

Context

ADR 0004 selected DOP853 because it supplied final state, dense output, events, and direct variational equations behind a small pure-Rust dependency. The same evidence showed a nominal high-accuracy performance gap relative to the upstream warmed heyoka implementation.

The eleven pykep dynamics types come from only nine fixed equation families. They do not require arbitrary symbolic expressions, LLVM, events in Taylor mode, heyoka batch mode, or arbitrary precision. A disposable eccentric Kepler prototype passed a predeclared matched-error gate at tight tolerances.

Decision

Add a private fixed-capacity Taylor-series engine inside pykep-core. Implement coefficient kernels only for the built-in models. Publish Taylor, IntegrationMethod, and AdaptiveIntegrator, but keep the coefficient trait private until a real third-party system requires it.

Make Taylor the default of AdaptiveIntegrator and of the nominal Kepler/CR3BP/BCP convenience methods. This follows upstream pykep, where these TA-derived equation families are exposed as heyoka Taylor-adaptive integrators. Keep direct Dop853 calls, generic user dynamics, event location, and the existing direct-variational sensitivity convenience methods on DOP853. Add explicit *_with_method variants for built-in dynamics and ZOH schedules.

Use tolerance-selected order 8–24 and component-scaled step selection from the final two coefficients. Preserve an optimized Kepler recurrence where full-series generic evaluation would erase the measured crossover.

For the first release, dense grids clip Taylor steps at sample times and seeded sensitivities use centered complete propagations. Document their cost instead of claiming the not-yet-implemented polynomial interpolation and direct Taylor variational optimizations.

Consequences

• No C/C++ runtime, LLVM, JIT latency, or new runtime dependency is added.
• At 1e-14 and machine epsilon the representative Kepler solve is faster and more accurate than DOP853; at 1e-9 it is slower.
• Built-in nominal dynamics default to the algorithm family used by upstream pykep; callers can still request DOP853 explicitly.
• User-defined DynamicsModel implementations continue to use DOP853.
• Wide STMs and event-driven problems should continue to use DOP853.
• Equation duplication between evaluated and coefficient kernels is accepted as localized technical debt, protected by upstream, DOP853, and official-heyoka cross-validation.

The raw measurements and validation boundaries are recorded in High-accuracy Taylor integration.