Manifold embedding data-driven mechanics

This article introduces a new data-driven approach that leverages manifold embedding generated by the invertible neural network to improve robustness, efficiency, and accuracy of constitutive-law-free simulations with limited data. We achieve this training deep globally map data from constitutive onto lower-dimensional Euclidean vector space. As such, we establish relation between norm mapped space metric lead more physically consistent notion distance for material treatment in return allows us bypass expensive combinatorial optimization, which may significantly speed up model-free when are abundant high dimensions. Meanwhile, learning also improves robustness algorithm is sparse or distributed unevenly parametric Numerical experiments provided demonstrate measure performance technique under different circumstances. Results obtained proposed method those via classical energy norms compared.