A pullback-corrected scalar auxiliary variable optimizer with momentum and adaptive mobility

תקציר מקורי באנגליתarXiv:2609.13569v1 Announce Type: cross Abstract: Objectives in scientific machine learning are often prescribed as a sum of several terms, such as the residual, boundary, initial, and data losses of a physics-informed neural network. In the 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. We carry that correction into an optimizer with momentum and an adaptive mobility, applying it to the gradient and the stored momentum in a single implicit solve. A mobility that is nonincreasing in the Loewner order yields an exact modified energy law, covering Euclidean and AMSGrad-type choices; the corresponding identity for mo