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math.NA2026
A Geometry-Aware Operator Learning Framework for Interface Problems on Varying Domains
Shanshan Xiao, Ye Li, Zhongyi Huang +1
Solving Partial Differential Equation (PDE) interface problems on varying domains is a critical task in design and optimization, yet it remains computationally prohibitive for trad…
math.NA2024
A deformation-based framework for learning solution mappings of PDEs defined on varying domains
Shanshan Xiao, Pengzhan Jin, Yifa Tang
In this work, we establish a deformation-based framework for learning solution mappings of PDEs defined on varying domains. The union of functions defined on varying domains can be…