Improved surrogates in inertial confinement fusion with manifold and cycle consistencies.

Neural networks have become the method of choice 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 1) consistent with the physical manifold, resulting in physically meaningful predictions, and 2) cyclically consistent with a jointly trained inverse model; i.e., backmapping predictions through the inverse results in the original input parameters. We find that these two consistencies lead to surrogates that are superior in terms of predictive performance, are 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 one-dimensional semianalytic numerical simulator and demonstrate the effectiveness of our approach.

Scalable Topological Data Analysis and Visualization for Evaluating Data-Driven Models in Scientific Applications.

With the rapid adoption of machine learning techniques for large-scale applications in science and engineering comes the convergence of two grand challenges in visualization. First, the utilization of black box models (e.g., deep neural networks) calls for advanced techniques in exploring and interpreting model behaviors. Second, the rapid growth in computing has produced enormous datasets that require techniques that can handle millions or more samples. Although some solutions to these interpretability challenges have been proposed, they typically do not scale beyond thousands of samples, nor do they provide the high-level intuition scientists are looking for. Here, we present the first scalable solution to explore and analyze high-dimensional functions often encountered in the scientific data analysis pipeline. By combining a new streaming neighborhood graph construction, the corresponding topology computation, and a novel data aggregation scheme, namely topology aware datacubes, we enable interactive exploration of both the topological and the geometric aspect of high-dimensional data. Following two use cases from high-energy-density (HED) physics and computational biology, we demonstrate how these capabilities have led to crucial new insights in both applications.

A new route to chaos: sequences of topological torus bifurcations.

We consider a sequence of topological torus bifurcations (TTBs) in a nonlinear, quasiperiodic Mathieu equation. The sequence of TTBs and an ensuing transition to chaos are observed by computing the principal Lyapunov exponent over a range of the bifurcation parameter. We also consider the effect of the sequence on the power spectrum before and after the transition to chaos. We then describe the topology of the set of knotted tori that are present before the transition to chaos. Following the transition, solutions evolve on strange attractors that have the topology of fractal braids in Poincare sections. We examine the topology of fractal braids and the dynamics of solutions that evolve on them. We end with a brief discussion of the number of TTBs in the cascade that leads to chaos.