Speaker
Description
Numerical-relativity data are not generic arrays to be enhanced, but
discretized geometric fields constrained by the Einstein equations. We
introduce AI(\times)NR-Pathfinder, a constraint-aware learning framework
that applies small, stencil-consistent correction operators to
(3+1) numerical-relativity slices while preserving the algebraic
structure of the conformal variables. The framework is designed not as a
replacement for elliptic initial-data solvers, but as a controlled method
for moving an existing numerical-relativity state toward a nearby
lower-constraint configuration within a restricted correction subspace. We
first establish the method in the instance-adapted limit, where a single
binary boson-star slice is optimized to convergence and used to construct
a corrected numerical-relativity state. In this setting, the corrected
state reduces Hamiltonian- and momentum-constraint residuals by
(82)--(93\%) on the evaluated physical domain, remains well behaved
under short-time evolution, and preserves the relevant field-level
structure.
The central nontrivial result emerges from a core-localized comparison
with two directly generated fine-grid reference states: a plain
superposition construction and a physics-motivated remedy designed to
reduce superposition-induced core distortions. The model is not trained
to match either reference state. Nevertheless, the corrected state
suppresses the core-localized constraint residuals to levels substantially
below both fine-grid references in all reported core-window diagnostics.
This demonstrates that the learned update is capable of correcting the
most physically critical regions of the initial data: the boson-star
cores, where superposition artefacts are expected to have the largest
dynamical impact. The result is therefore not merely a reduction of a
domain-averaged loss, but a targeted improvement in the regions most
relevant to the subsequent evolution.
We then train the same correction framework on a family of binary
boson-star configurations and test it on held-out configurations, finding
systematic reductions of both Hamiltonian- and momentum-constraint
residuals across the test set. A preliminary vacuum-GR check on perturbed
Bowen--York data further suggests that the same correction framework is
not tied to the binary boson-star setting, but can also be applied to
vacuum initial data. Together, these results demonstrate that
constraint-aware learning can identify physically meaningful correction
directions in constrained geometric data. AI(\times)NR-Pathfinder
therefore provides a concrete step toward physically grounded
machine-learning assistance for Einstein-constraint control in numerical
relativity.