Hyperreduction speeds up discovering neural materials from experiments
Hyperreduction accelerates finite element model updating for the discovery of neural materials
Computational Engineering, Finance, and ScienceArtificial Intelligence
Summary
Finding how materials behave by simulating their structure can take a lot of time because it involves complex calculations at many steps. The authors introduce a way to simplify these calculations by focusing on the most important parts of the model, making the process much faster. They use special mathematical techniques and neural networks designed to always behave physically and safely. Their method worked well on real and simulated examples, cutting down training time from hours to minutes without losing accuracy.
What this means in practice
- •For structural engineers: Efficiently identify accurate material models from experimental data to improve structural simulations with less computation time.
- •For manufacturing simulation teams: Rapidly calibrate neural material models for complex parts to speed up virtual testing and reduce physical prototyping.
Authors
Hagen Holthusen, Matthias Knipper, Kevin Linka
Abstract
Finite element model updating is among the most general approaches to discover constitutive models from structural experiments: since the displacement field is computed rather than measured, it accommodates arbitrary geometries, boundary conditions, and sparse or noisy data. However, every loss evaluation requires a nonlinear finite element solve per load step, and training neural materials requires many such evaluations. Intrusive model order reduction lowers this cost while retaining boundary conditions and variational structure. How can a reduced model remain accurate while the network weights change at every training step? We combine proper orthogonal decomposition and energy-conserving sampling and weighting with adjoint sensitivities of the reduced model, and adapt both the trial space and the sampled elements along the optimization path. The constitutive law is a polyconvex neural network: a logarithmic normalization term, together with a zero-anchored input convex architecture and a growth term, renders the energy polyconvex, coercive, and non-negative by construction, independent of the trained weights. We demonstrate the approach on two experimental datasets and one synthetic three-dimensional example. For a two-phase specimen, training time decreases from nine hours to 41 minutes compared with a full-order identification, without loss of accuracy. In the three-dimensional example, six modes replace 48 672 degrees of freedom, 116 of 15 625 elements suffice to evaluate the internal forces, and training takes 13 minutes. In all cases, the identified material reproduces the measured reaction force and predicts the displacement field from the force alone. Hyperreduction makes the discovery of neural materials from structural data affordable while retaining the advantages of finite element model updating.