Using Deep Operators to Create Spatio-temporal Surrogates for Dynamical Systems under Uncertainty

Spatio-temporal data, which consists of responses or measurements gathered at different times and positions, is ubiquitous across diverse applications of civil infrastructure. While SciML methods have made significant progress in tackling the issue of response prediction for individual time histories, creating a full spatial-temporal surrogate remains a challenge. This study proposes a novel variant of deep operator networks (DeepONets), namely the full-field Extended DeepONet (FExD), to serve as a spatial-temporal surrogate that provides multi-output response predictions for dynamical systems. The proposed FExD surrogate model effectively learns the full solution operator across multiple degrees of freedom by enhancing the expressiveness of the branch network and expanding the predictive capabilities of the trunk network. The proposed FExD surrogate is deployed to simultaneously capture the dynamics at several sensing locations along a testbed model of a cable-stayed bridge subjected to stochastic ground motions. The ensuing response predictions from the FExD are comprehensively compared against both a vanilla DeepONet and a modified spatio-temporal Extended DeepONet. The results demonstrate the proposed FExD can achieve both superior accuracy and computational efficiency, representing a significant advancement in operator learning for structural dynamics applications.

Transfer Learning as a Method to Reproduce High-Fidelity NLTE Opacities in Simulations

Simulations of high-energy density physics often need non-local thermodynamic equilibrium (NLTE) opacity data. This data, however, is expensive to produce at relatively low-fidelity. It is even more so at high-fidelity such that the opacity calculations can contribute ninety-five percent of the total computation time. This proportion can even reach large proportions. Neural networks can be used to replace the standard calculations of low-fidelity data, and the neural networks can be trained to reproduce artificial, high-fidelity opacity spectra. In this work, it is demonstrated that a novel neural network architecture trained to reproduce high-fidelity krypton spectra through transfer learning can be used in simulations. Further, it is demonstrated that this can be done while achieving a relative percent error of the peak radiative temperature of the hohlraum of approximately 1\% to 4\% while achieving a 19.4x speed up.

Transfer Learning of High-Fidelity Opacity Spectra in Autoencoders and Surrogate Models

Simulations of high energy density physics are expensive, largely in part for the need to produce non-local thermodynamic equilibrium opacities. High-fidelity spectra may reveal new physics in the simulations not seen with low-fidelity spectra, but the cost of these simulations also scale with the level of fidelity of the opacities being used. Neural networks are capable of reproducing these spectra, but neural networks need data to to train them which limits the level of fidelity of the training data. This paper demonstrates that it is possible to reproduce high-fidelity spectra with median errors in the realm of 3\% to 4\% using as few as 50 samples of high-fidelity Krypton data by performing transfer learning on a neural network trained on many times more low-fidelity data.

Neural Network Surrogate Models for Absorptivity and Emissivity Spectra of Multiple Elements

Simulations of high energy density physics are expensive in terms of computational resources. In particular, the computation of opacities of plasmas, which are needed to accurately compute radiation transport in the non-local thermal equilibrium (NLTE) regime, are expensive to the point of easily requiring multiple times the sum-total compute time of all other components of the simulation. As such, there is great interest in finding ways to accelerate NLTE computations. Previous work has demonstrated that a combination of fully-connected autoencoders and a deep jointly-informed neural network (DJINN) can successfully replace the standard NLTE calculations for the opacity of krypton. This work expands this idea to multiple elements in demonstrating that individual surrogate models can be also be generated for other elements with the focus being on creating autoencoders that can accurately encode and decode the absorptivity and emissivity spectra. Furthermore, this work shows that multiple elements across a large range of atomic numbers can be combined into a single autoencoder when using a convolutional autoencoder while maintaining accuracy that is comparable to individual fully-connected autoencoders. Lastly, it is demonstrated that DJINN can effectively learn the latent space of a convolutional autoencoder that can encode multiple elements allowing the combination to effectively function as a surrogate model.