3 papers
math.NA2026
Evo-GTransNet for Parabolic PDEs: A Fixed-Feature Galerkin Method of Lines with Quadrature-Mass Orthonormalization
Lili Ju, Jin Zhao
In this paper, we develop an evolutionary generalized transferable neural network (Evo-GTransNet) solver for parabolic partial differential equations, formulated as a retained-spac…
stat.ML2026
Guided Flow Matching for Forward and Inverse PDE Problems with Sparse Observations: Algorithm and Theory
Xifeng Zhang, Jin Zhao
Reconstructing PDE solutions from sparse observations is a core challenge in scientific computing. We present FM4PDE, a flow-matching generative framework that learns the joint dis…
math.NA2026
Shifted Matrix-Sign Reflectors for Prescribed-Index Eigenspace Reflection
Jin Zhao
Spectral projectors and the reflectors derived from them are basic objects in numerical linear algebra. This paper studies the prescribed-index reflector I-2P_k, where P_k is the s…