2 papers
math.NA2026
Parametric Sensitivity of POD Reduced-Order Models for Semilinear Evolution Equations with Applications to G-Equations
Shengbo Ma, Luhao Xue, Zhiwen Zhang
Proper Orthogonal Decomposition (POD) provides low-dimensional surrogate models of evolution equations from solution snapshots. In parameterized problems, however, a basis computed…
math.OC2026
Optimization on Affine-Transversal Hilbert Submanifolds: Part I -- Theoretical Foundations
Yongcun Song, Luhao Xue, Xiaoming Yuan +1
In this paper, we establish the theoretical foundations for the generic optimization problem in a Hilbert space whose feasible set is an affine-transversal Hilbert submanifold give…