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A pullback-corrected scalar auxiliary variable (PB--SAV) method, one scalar tracks the shifted objective while the component gradients build a positive semidefinite curvature correction of rank at most the number of components, reducing to a dense system whose order is the number of components.
Geometry-aware LegONet (gLegONet), a boundary-manifold extension of Lego-like operator learning, is introduced, a boundary-manifold extension of Lego-like operator learning that converts arbitrary-domain PDE learning from geometry-specific retraining or soft penalty enforcement into boundary-guaranteed assembly of reus...
Numerical experiments demonstrate that LR-EDNN substantially reduces computational cost while maintaining the accuracy and qualitative fidelity of the full EDNN solver when the rank is chosen adequately.
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