Learning reduced models from data in a nonintrusive fashion is an important problem in science and engineering [1, 2, 3]. A typical approach is to first learn an encoder-decoder pair, embed the training snapshot trajectories with the learned encoder, and then fit a reduced dynamical-system model to the embedded trajectories. However, the decomposition of the training process into first learning an encoder-decoder pair for the embedding and only sub-sequentially learning a model of the dynamics typically means that the encoder-decoder pair are trained with the objective of accurately approximating the training data, rather than taking the reduced-model prediction error into account. Thus, the encoder-decoder pair can overfit to achieving a low reconstruction error on the training data by learning embeddings of the snapshot trajectories that are non-smooth, which means that learning a reduced model can become challenging. Correspondingly, it has been observed that learning embeddings and models together can be beneficial; see, e.g., [4, 5, 6, 7]. In the context of intrusive model reduction with linear approximations, there is work that optimizes the reduced basis with respect to the model prediction error [8], quantities of interest [9], and to achieve stability [10]; however, we focus here on the setting of nonintrusive model reduction and nonlinear approximations.

A recent alternative for hydrogen transportation as a mixture with natural gas is blending it into natural gas pipelines. However, hydrogen embrittlement of material is a major concern for scientists and gas installation designers to avoid process failures. In this paper, we propose a physics-informed machine learning model to predict the gas pressure on the pipes' inner wall. Despite its high-fidelity results, the current PDE-based simulators are time- and computationally-demanding. Using simulation data, we train an ML model to predict the pressure on the pipelines' inner walls, which is a first step for pipeline system surveillance. We found that the physics-based method outperformed the purely data-driven method and satisfy the physical constraints of the gas flow system.

A parametric adaptive greedy Latent Space Dynamics Identification (gLaSDI) framework is developed for accurate, efficient, and certified data-driven physics-informed greedy auto-encoder simulators of high-dimensional nonlinear dynamical systems. In the proposed framework, an auto-encoder and dynamics identification models are trained interactively to discover intrinsic and simple latent-space dynamics. To effectively explore the parameter space for optimal model performance, an adaptive greedy sampling algorithm integrated with a physics-informed error indicator is introduced to search for optimal training samples on the fly, outperforming the conventional predefined uniform sampling. Further, an efficient k-nearest neighbor convex interpolation scheme is employed to exploit local latent-space dynamics for improved predictability. Numerical results demonstrate that the proposed method achieves 121 to 2,658x speed-up with 1 to 5% relative errors for radial advection and 2D Burgers dynamical problems.

Neil Savage is a science and technology writer based in Lowell, MA, USA.

"It's not rocket science" may be a tired cliché, but that doesn't mean designing rockets is any less complicated. Time, cost and safety prohibit testing the stability of a test rocket using a physical build "trial and error" approach. But even computational simulations are extremely time consuming. A single analysis of an entire SpaceX Merlin rocket engine, for example, could take weeks, even months, for a supercomputer to provide satisfactory predictions. One group of researchers at The University of Texas at Austin is developing new "scientific machine learning" methods to address this challenge.

In the not too distant future, we can expect to see our skies filled with unmanned aerial vehicles (UAVs) delivering packages, maybe even people, from location to location. In such a world, there will also be a digital twin for each UAV in the fleet: a virtual model that will follow the UAV through its existence, evolving with time. "It's essential that UAVs monitor their structural health," said Karen Willcox, director of the Oden Institute for Computational Engineering and Sciences at The University of Texas at Austin (UT Austin) and an expert in computational aerospace engineering. "And it's essential that they make good decisions that result in good behavior." An invited speaker at the 2019 International Conference for High Performance Computing, Networking, Storage and Analysis (SC19), Willcox shared the details of a project--supported primarily by the U.S. Air Force program in Dynamic Data-Driven Application Systems (DDDAS)--to develop a predictive digital twin for a custom-built UAV.