Efficient material model parameter optimization in finite element analysis with differentiable physics

Abstract

In this study, an efficient finite element model parameter optimization method is proposed by integrating differentiable physics into an optimization scheme for faster convergence with fewer function evaluations than finite difference (FD) gradient–based and gradient–free methods. The method is demonstrated using constitutive material model calibration and stress-field homogenization problems. The method leverages the efficiency of commercial finite element solvers by integrating them into a differentiable programming framework and applying automatic differentiation (AD) to the stress return-mapping algorithm, enabling the direct computation of loss function gradients. This approach circumvents the need for finite differences in gradient-based methods, while outperforming gradient-free methods. The performances of AD-enhanced and gradient-free methods are compared across problems ranging in dimensionality from 1-D to 24-D. In a 3-D problem, Bayesian optimization and Nelder-Mead required over 50 additional objective function evaluations on average and took ∼ 13 times longer in wall-clock time to converge than the AD-enhanced methods. For the 24-D problem, it took FD over 15 times longer to compute gradients than AD. AD-enhanced methods maintained their efficiency with increasing dimensionality, making them especially powerful for complex materials problems with high dimensional parameter spaces.