Distance-Weighted Gradient Integration
DWGI is an experimental global-integration sibling of Interlinear / DWGN. It starts from a finite discrete design lattice and an initial set of adjacent sampled gradients, but replaces generational nearest-neighbour propagation with a simultaneous global reconstruction.
For each adjacent lattice edge, DWGI estimates a desired scalar increment from the original sampled gradients. Reconstructed DWGI values do not themselves generate new gradients.
Global weighted least squares
The missing scalar values are solved together by minimizing the disagreement between lattice-edge differences and transported sampled gradients. Sampled values remain fixed exactly.
The normal equations form a sparse weighted graph Laplacian. The current implementation solves this system by Jacobi-preconditioned conjugate gradients.
Gradient transport
An exact factor and exact adjacent level pair are preferred when such evidence exists. If that pair was not sampled, DWGI can fall back to original gradients for the same factor. If an active factor has no original adjacent gradient evidence at all, the reconstruction stops rather than inventing variation that is not identifiable from the sample.
Controls and interface
The public interface mirrors Interlinear. The principal controls include distance weighting, conjugate-gradient tolerance, iteration limit and verbosity. The Sim::OPT metamodel bridge can select DWGI explicitly; DWGN remains the default reconstruction method and no OPTcue installation is required for DWGI itself.
Qualification
DWGI has reproduced linear and separable quadratic synthetic fields to numerical precision or tight tolerance in small qualification problems, while interaction fields show the expected approximation error. Larger synthetic tests have also been used to exercise sparse-system construction and the iterative solver.
DWGI should presently be regarded as a research method to be compared with DWGN, not as its production replacement. A useful scientific comparison should examine reconstructed landscapes, holdout error, rankings or incumbents, wall-clock cost, memory and solver residuals on the same prepared sparse lattice.