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Geometry-aware LegONet for PDE Learning on Arbitrary Domains
Jiahao Zhang, Yueqi Wang, Guang Lin
Learned PDE solvers often entangle governing operators with the geometry, boundary conditions, and discretization used for training. This limits reuse when the same physics is pose…
LegONet: Plug-and-Play Structure-Preserving Neural Operator Blocks for Compositional PDE Learning
Jiahao Zhang, Yueqi Wang, Guang Lin
Learned PDE solvers are often trained as monolithic surrogates for a specific equation, boundary condition and discretization. This makes them difficult to reuse when mechanisms ch…
Energy-Dissipative Evolutionary Kolmogorov-Arnold Networks for Complex PDE Systems
Guang Lin, Changhong Mou, Jiahao Zhang
We introduce evolutionary Kolmogorov-Arnold Networks (EvoKAN), a novel framework for solving complex partial differential equations (PDEs). EvoKAN builds on Kolmogorov-Arnold Netwo…
Direct computation of stresses in linear elasticity
Weifeng Qiu, Minglei Wang, Jiahao Zhang
We present a new finite element method based on the formulation introduced by Philippe G.~Ciarlet and Patrick Ciarlet, Jr. in [{\em Math. Models Methods Appl. Sci., 15 (2005), pp.…