Physics-informed UNets for Discovering Hidden Elasticity in Heterogeneous Materials

Soft biological tissues often have complex mechanical properties due to variation in structural components. In this paper, we develop a novel UNet-based neural network model for inversion in elasticity (El-UNet) to infer the spatial distributions of mechanical parameters from strain maps as input images, normal stress boundary conditions, and domain physics information. We show superior performance, both in terms of accuracy and computational cost, by El-UNet compared to fully-connected physics-informed neural networks in estimating unknown parameters and stress distributions for isotropic linear elasticity. We characterize different variations of El-UNet and propose a self-adaptive spatial loss weighting approach. To validate our inversion models, we performed various finite-element simulations of isotropic domains with heterogenous distributions of material parameters to generate synthetic data. El-UNet is faster and more accurate than the fully-connected physics-informed implementation in resolving the distribution of unknown fields. Among the tested models, the self-adaptive spatially weighted models had the most accurate reconstructions in equal computation times. The learned spatial weighting distribution visibly corresponded to regions that the unweighted models were resolving inaccurately. Our work demonstrates a computationally efficient inversion algorithm for elasticity imaging using convolutional neural networks and presents a potential fast framework for three-dimensional inverse elasticity problems that have proven unachievable through previously proposed methods.Comment: 25 pages, 9 figure

GAN for time series prediction, data assimilation and uncertainty quantification

We propose a new method in which a generative adversarial network (GAN) is used to quantify the uncertainty of forward simulations in the presence of observed data. Previously, a method has been developed which enables GANs to make time series predictions and data assimilation by training a GAN with unconditional simulations of a high-fidelity numerical model. After training, the GAN can be used to predict the evolution of the spatial distribution of the simulation states and observed data is assimilated. In this paper, we describe the process required in order to quantify uncertainty, during which no additional simulations of the high-fidelity numerical model are required. These methods take advantage of the adjoint-like capabilities of generative models and the ability to simulate forwards and backwards in time. Set within a reduced-order model framework for efficiency, we apply these methods to a compartmental model in epidemiology to predict the spread of COVID-19 in an idealised town. The results show that the proposed method can efficiently quantify uncertainty in the presence of measurements using only unconditional simulations of the high-fidelity numerical model.Comment: arXiv admin note: text overlap with arXiv:2105.0772

An evolve-then-correct reduced order model for hidden fluid dynamics

In this paper, we put forth an evolve-then-correct reduced order modeling approach that combines intrusive and nonintrusive models to take hidden physical processes into account. Specifically, we split the underlying dynamics into known and unknown components. In the known part, we first utilize an intrusive Galerkin method projected on a set of basis functions obtained by proper orthogonal decomposition. We then formulate a recurrent neural network emulator based on the assumption that observed data is a manifestation of all relevant processes. We further enhance our approach by using an orthonormality conforming basis interpolation approach on a Grassmannian manifold to address off-design conditions. The proposed framework is illustrated here with the application of two-dimensional co-rotating vortex simulations under modeling uncertainty. The results demonstrate highly accurate predictions underlining the effectiveness of the evolve-then-correct approach toward realtime simulations, where the full process model is not known a priori

Improved Surrogates in Inertial Confinement Fusion with Manifold and Cycle Consistencies

Neural networks have become very popular in surrogate modeling because of their ability to characterize arbitrary, high dimensional functions in a data driven fashion. This paper advocates for the training of surrogates that are consistent with the physical manifold -- i.e., predictions are always physically meaningful, and are cyclically consistent -- i.e., when the predictions of the surrogate, when passed through an independently trained inverse model give back the original input parameters. We find that these two consistencies lead to surrogates that are superior in terms of predictive performance, more resilient to sampling artifacts, and tend to be more data efficient. Using Inertial Confinement Fusion (ICF) as a test bed problem, we model a 1D semi-analytic numerical simulator and demonstrate the effectiveness of our approach. Code and data are available at https://github.com/rushilanirudh/macc/Comment: 10 pages, 6 figure