Wed, Jan 22, 2020 @ 03:30 PM - 04:30 PM
Aerospace and Mechanical Engineering
Conferences, Lectures, & Seminars
Speaker: Roger Ghanem, USC
Talk Title: Probabilistic Learning on Manifolds: The Small Data Challenge
Abstract: As the pace of technological innovation and scientific discovery continues to grow, so does the interest in accelerating their integration. We are thus, increasingly, faced with the task of product development without the benefit of hindsight or historical failures. Examples of this evolving paradigm include new materials and novel configurations of complicated systems with complex behavior. This challenge is exacerbated by the growing interactions between technological and socio-economic systems where failure of a technological component can have implications on social trends and public policy, thus highlighting the need to characterize extreme events both for each component and at the system level. The standard paradigm of mapping knowledge into engineered systems where new systems are essentially construed as perturbations of older systems is not equipped for these emerging requirements. Recent approaches under the general heading of Machine Learning (ML) are motivated by the explosion in sensing technologies. Fundamental advances in these ML methods are being realized at the interface of data science and physics constraints.
In this talk I will describe a recent effort within my group along these ML lines. I will focus on one particular approach, the Probabilistic Learning on Manifolds (PMoL), which is relevant under conditions of small data. This approach aims to augment a (small) training dataset with realizations that share with it some key features making these realizations credible surrogates of the original data. These features consist of 1) co-location on a manifold, and 2) statistical consistency. Thus as a first step, we associated a manifold with the training set, that we believe represents all the fundamental constraints (such as physics). We rely on diffusion maps constructs to delineate the manifold. Construed as fluctuating within this manifold, the training dataset is statistically more significant. As a second step, we generate samples on the manifold that have the same probability distribution as the training set. To this end, we construct a projected Ito equation whose invariant measure is that of the training set, and whose samples are constrained to the manifold.
I will show how the above ideas are used as building blocks in a scramjet optimization problem and the design of a digital twin for a structural composite.
Host: AME Department
More Info: https://ame.usc.edu/seminars/
Audiences: Everyone Is Invited
Posted By: Tessa Yao