ABSTRACT: This talk surveys a few computational questions related to climate action that fall within the purview of the ACDL. The selected questions are of broad scope and are meant as focal points for determining the right, specific questions that would benefit from taking the theoretical direction of our current research, or using the software we have developed. In the first question, we revisit Prof. Qiqi Wang's recent results (and talk) on subtle perturbations provoking a significant change in the statistical behavior of a chaotic system. This observation sets the stage to ask how best to construct data-driven parameterized models of chaotic processes that mimic the observed measurements of statistics, as opposed to mimicking individual trajectories for a length of time.
BIO: Nisha is a PhD student working with Qiqi Wang. She has enjoyed working on sensitivity computation in chaotic systems with her adviser. She hopes to, in the near future, take the dynamical systems approach for solving problems relevant to climate studies.
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ABSTRACT: The efficient discretization of chaotic systems, particularly large eddy simulation (LES), remains one of the key research objectives of the CFD community. A wide class of applications of LES seeks to capture meaningful averages of unpredictable, aperiodic signals in the system's outputs of interest. In other words, we seek to capture finite-time discrete estimates of infinite-time integrals of the true system. In this talk, we consider the question of how to optimally use computational resources to estimate the long-term output of chaotic systems. First, we will explore the balance between statistical and discretization error for the Lorenz system, a simple chaotic ODE system. Next, we will explore how this cost balance is amortized in a highly parallel computing environment. Finally, we will explore some more recent results that show some promise for targeting an optimal balance of statistical and discretization error in practice, when our a priori knowledge of a system's convergence features is, at best, endowed with considerable uncertainty.
BIO: Cory Frontin is a 6th year PhD student studying under Prof. David Darmofal, studying discretization methods for chaotic systems. His research interests are in numerical methods and their application to complex and uncertain systems, ranging from aerodynamics to climate and even sports. After work (during quarantine, at least), he can be most frequently found listening to jazz, funk, and soul and trying to learn how to play them with instruments.