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Nonlinear elliptic homogenization with the parametric Deep Ritz method

arXiv · AI, language, vision and robotics · article · Sep 5, 2026 · UTC

Elliptic homogenization is used to determine coarse-grained properties of materials with features on small scales. When these small scale features have rapid, periodic fluctuations, the solution field corresponding to a homogenized constitutive relation closely resembles the true solution based on the heterogeneous material. This homogenized behavior of the material is computed from a cell problem, where a cell is defined to be one period of the fluctuating material. In the context of linear elliptic partial differential equations, the homogenized constitutive relation is defined simply by a c

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