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Two neural network models are proposed which learn the spectrum directly from the geometry of the domain and can be used to optimize the domain from one or more eigenvalues, and which produce accurate differentiable estimates of eigenvalues, which can be used in shape optimization problems involving spectral quantities...
We study torsional rigidity as a function of the labeled vertices of a convex polygon. Starting from the distributed second shape derivative, we derive the Hessian with respect to vertex coordinates. At a regular polygon, dihedral symmetry makes this matrix block circulant in radial-tangential coordinates, reducing its...
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