Engineering topics

Jones, Reese E.

Publications and source records attributed to Jones, Reese E..

3 records

DOE OSTI2024

Polyconvex neural network models of thermoelasticity

Machine-learning function representations such as neural networks have proven to be excellent constructs for constitutive modeling due to their flexibility to represent highly nonlinear data and their ability to incorporate constitutive constraints, which also allows them to generalize well to unseen data. Here, in this work, we extend a polyconvex hyperelastic neural network framework to (isotropic) thermo-hyperelasticity by specifying the thermodynamic and material theoretic requirements for an expansion of the Helmholtz free energy expressed in terms of deformation invariants and temperature. Different formulations which a priori ensure polyconvexity with respect to deformation and concavity with respect to temperature are proposed and discussed. The physics-augmented neural networks are furthermore calibrated with a recently proposed sparsification algorithm that not only aims to fit the training data but also penalizes the number of active parameters, which prevents overfitting in the low data regime and promotes generalization. The performance of the proposed framework is demonstrated on synthetic data, which illustrate the expected thermomechanical phenomena, and existing temperature-dependent uniaxial tension and tension-torsion experimental datasets.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Multiscale simulation of spatially correlated microstructure via a latent space representation

When deformation gradients act on the scale of the microstructure of a part due to geometry and loading, spatial correlations and finite-size effects in simulation cells cannot be neglected. We propose a multiscale method that accounts for these effects using a variational autoencoder to encode the structure–property map of the stochastic volume elements making up the statistical description of the part. In this paradigm the autoencoder can be used to directly encode the microstructure or, alternatively, its latent space can be sampled to provide likely realizations. Furthermore, we demonstrate the method on three examples using the common additively manufactured material AlSi10Mg in: (a) a comparison with direct numerical simulation of the part microstructure, (b) a push forward of microstructural uncertainty to performance quantities of interest, and (c) a simulation of functional gradation of a part with stochastic microstructure.

Elastoplasticity↗

DOE OSTI2024

Uncertainty quantification of graph convolution neural network models of evolving processes

The application of neural network models to scientific machine learning tasks has proliferated in recent years. In particular, neural networks have proved to be adept at modeling processes with spatial–temporal complexity. Nevertheless, these highly parameterized models have garnered skepticism in their ability to produce outputs with quantified error bounds over the regimes of interest. Hence there is a need to find uncertainty quantification methods that are suitable for neural networks. In this work we present comparisons of the parametric uncertainty quantification of neural networks modeling complex spatial–temporal processes with Hamiltonian Monte Carlo and Stein variational gradient descent and its projected variant. Specifically we apply these methods to graph convolutional neural network models of evolving systems modeled with recurrent neural network and neural ordinary differential equations architectures. We show that Stein variational inference is a viable alternative to Monte Carlo methods with some clear advantages for complex neural network models. For our exemplars, Stein variational interference gave similar pushed forward uncertainty profiles through time compared to Hamiltonian Monte Carlo, albeit with generally more generous variance. As a result, projected Stein variational gradient descent also produced similar uncertainty profiles to the non-projected counterpart, but large reductions in the active weight space were confounded by the stability of the neural network predictions and the convoluted likelihood landscape.

36 MATERIALS SCIENCE↗