Training material models using gradient descent algorithms. (June 2023) - Chen, Tianju; Messner, Mark C.
Abstract: High temperature design requires accurate constitutive models to describe material inelastic deformation and failure behavior. Oftentimes, calibrating accurate models devolves into the problem of fitting the model parameters against experimental test data. Here, we present the pyopmat package, an open source framework for calibrating constitutive models against experiment data subjected to various loading conditions using machine learning techniques. The package calculates the exact gradient of the model response with respect to the parameters using a combination of automatic differentiation and the adjoint method. Given this exact gradient, we compare the performance of several gradient-based optimization techniques in fitting realistic constitutive models against data. We demonstrate the efficiency and accuracy of our package through example problems using both synthetic data, generated using known parameter sets, under monotonic and cyclic loading conditions and also with an example applying the techniques developed here to actual high temperature creep-fatigue test data. Highlights: Gradient descent optimization of materials constitutive model parameters. Training entire ODE-based models against experiment data based on ML technique. Vectorization allows pyoptmat train and execute models on GPUs. pyoptmat effectively relieves the cost of memory using adjoint method. Accurately evaluate of parameter gradient and efficiently optimize model parameters.