Abstract Modeling the localized intensive deformation in a damaged solid requires highly refined discretization for accurate prediction, which significantly increases computational cost. Although adaptive model refinement can be employed enhanced effectiveness, it is cumbersome traditional mesh‐based methods to perform while modeling evolving localizations. In this work, neural network‐enhanced...

We develop an extension of the sliced inverse regression (SIR) framework for dimension reduction using kernel models and Tikhonov regularization. The result is a numerically stable nonlinear dimension reduction method. We prove consistency of the method under weak conditions even when the reproducing kernel Hilbert space induced by the kernel is infinite dimensional. We illustrate the utility o...