{"ID":2841776,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.11388","arxiv_id":"2511.11388","title":"Robust inverse material design with physical guarantees using the Voigt-Reuss Net","abstract":"We propose a spectrally normalized surrogate for forward and inverse mechanical homogenization with hard physical guarantees. Leveraging the Voigt-Reuss bounds, we factor their difference via a Cholesky-like operator and learn a dimensionless, symmetric positive semi-definite representation with eigenvalues in $[0,1]$; the inverse map returns symmetric positive-definite predictions that lie between the bounds in the Löwner sense. In 3D linear elasticity on an open dataset of stochastic biphasic microstructures, a fully connected Voigt-Reuss net trained on $\u003e\\!7.5\\times 10^{5}$ FFT-based labels with 236 isotropy-invariant descriptors and three contrast parameters recovers the isotropic projection with near-perfect fidelity (isotropy-related entries: $R^2 \\ge 0.998$), while anisotropy-revealing couplings are unidentifiable from $SO(3)$-invariant inputs. Tensor-level relative Frobenius errors have median $\\approx 1.7\\%$ and mean $\\approx 3.4\\%$ across splits. For 2D plane strain on thresholded trigonometric microstructures, coupling spectral normalization with a differentiable renderer and a CNN yields $R^2\u003e0.99$ on all components, subpercent normalized losses, accurate tracking of percolation-induced eigenvalue jumps, and robust generalization to out-of-distribution images. Treating the parametric microstructure as design variables, batched first-order optimization with a single surrogate matches target tensors within a few percent and returns diverse near-optimal designs. Overall, the Voigt-Reuss net unifies accurate, physically admissible forward prediction with large-batch, constraint-consistent inverse design, and is generic to elliptic operators and coupled-physics settings.","short_abstract":"We propose a spectrally normalized surrogate for forward and inverse mechanical homogenization with hard physical guarantees. Leveraging the Voigt-Reuss bounds, we factor their difference via a Cholesky-like operator and learn a dimensionless, symmetric positive semi-definite representation with eigenvalues in $[0,1]$;...","url_abs":"https://arxiv.org/abs/2511.11388","url_pdf":"https://arxiv.org/pdf/2511.11388v2","authors":"[\"Sanath Keshav\",\"Felix Fritzen\"]","published":"2025-11-14T15:17:37Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[\"Convolutional Neural Network\"]","has_code":false}