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math.NA2025
Learning Singularity-Encoded Green's Functions with Application to Iterative Methods
Qi Sun, Shengyan Li, Bowen Zheng +2
Green's function provides an inherent connection between theoretical analysis and numerical methods for elliptic partial differential equations, and general absence of its closed-f…
math.NA2024
Lift-and-Embed Learning Methods for Solving Scalar Hyperbolic Equations with Discontinuous Solutions
Qi Sun, Zhenjiang Liu, Lili Ju +1
Deep learning methods, which exploit auto-differentiation to compute derivatives without dispersion or dissipation errors, have recently emerged as a compelling alternative to clas…
math.NA2024
Neural Green's Function Accelerated Iterative Methods for Solving Indefinite Boundary Value Problems
Shengyan Li, Qi Sun, Xuejun Xu +1
Neural operators, which learn mappings between the function spaces, have been applied to solve boundary value problems in various ways, including learning mappings from the space o…