A nonlinear manifold-based reduced order model

A new perspective on model reduction for nonlinear multi-scale analysis of heterogeneous materials. In this work, we seek meaningful low-dimensional structures hidden in high-dimensional multi-scale data. The model relies on a global geometric framework for nonlinear dimensionality reduction (Isomap), and machine learning algorithms. The proposed model provides both homogenization and localization of the multiscale solution in the context of computational homogenization. The manifold-based reduced order model is verified using common principles from the machine-learning community. Both homogenization and localization of the multiscale solution are demonstrated on a large three-dimensional example. This reduced order model can also be used to accelerate fully coupled multiscale computational homogenization simulations.

S. Bhattacharjee and K. Matous, "A Nonlinear Manifold-based Reduced Order Model for Multiscale Analysis of Heterogeneous Hyperelastic Materials", Journal of Computational Physics, 31, 635--653 (2016).