Using Neural Physics for Constructing Finite Element Solution Methods: NN4FEM
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We present NN4FEM, a compact Neural Physics explicit finite element framework implemented in Python using tensor products. The framework models finite-strain solid mechanics with linear tetrahedra and a compressible (or nearly incompressible) neo-Hookean constitutive model augmented by an optional viscous regularisation term. To map efficiently to GPUs or AI processors, NN4FEM avoids global sparse-matrix assembly and instead evaluates deformation gradients, Cauchy stresses, and internal nodal forces using batched element-wise operations followed by scatter-add assembly. [1] We test the implementation on three benchmarks: (i) a homogeneous-deformation manufactured solution on tetrahedral cube meshes, (ii) a pressurised thick-walled spherical shell, and (iii) a pressurised thick-walled cylindrical tube with prescribed axial stretch, both compared against analytical closed-form solutions for hyper elastic shells and tubes. [2]
