Sui Tang – “Learning interaction kernels in agent-based systems”

/ September 18, 2019/

When:
October 15, 2019 @ 12:00 pm – 1:30 pm
2019-10-15T12:00:00-04:00
2019-10-15T13:30:00-04:00
Where:
Clark 316

Abstract: Interacting agent-based systems are ubiquitous in science, from the modeling of particles in Physics to prey-predator in Biology, to opinion dynamics in economics and social sciences, where the interaction law between agents yields a rich variety of collective dynamics. Inferring the interaction laws between agents from observational trajectory data is a fundamental task for modeling and prediction, yet challenging due to the implicit nonlinear forward map of the system and high dimensionality of the state space. Consequently, the learning algorithms often offer no guarantees and the resulting discoveries of interaction laws need external human validation.

Given abundant data sampled from multiple trajectories, we use tools from statistical/machine learning to construct estimators for interaction kernels with provably good statistical and computational properties, under the minimal assumptions that the interaction kernels only depend on pairwise distance. In particular, we show that despite the high-dimensionality of the systems, optimal learning rates can still be achieved, equal to that of a one-dimensional regression problem. Numerical simulations on a variety of examples suggest the learnability of kernels in models used in practice, and that our estimators are robust to noise, and produced accurate predictions of collective dynamics in relative large time intervals, even when they are learned from data collected in short time intervals. This talk is based on the joint work with Mauro Maggioni, Fei Lu and Ming Zhong.

Bio: Dr. Sui Tang is a Postdoc Fellow in the Department of Mathematics at Johns Hopkins University working with Mauro Maggioni and Fei Lu. She did her Ph.D. in mathematics at Vanderbilt University advised by Akram Aldroubi, 2016. She is interested in solving problems in the mathematical foundations of Data Science, mainly used tools from statistical learning, harmonic analysis, and approximation theory. Her research is related to exploiting dynamical data sets in physical systems to perform inference with statistical guarantees and build generalizable, interpretable predictive models.

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