Embedded Files
Dr. Sui Tang is an Associate Professor of Mathematics at the University of California, Santa Barbara. She earned her Ph.D. in Mathematics from Vanderbilt University under the supervision of Akram Aldroubi and was previously an Assistant Research Professor at Johns Hopkins University, where she was mentored by Mauro Maggioni. Her research centers on the mathematical foundations of data science, with interests in statistical learning theory, inverse problems, and harmonic analysis, with a particular emphasis on the recovery of governing laws from complex, high-dimensional dynamical systems. She is a recipient of the NSF CAREER Award and a Hellman Faculty Fellowship.
Title: Data-Driven Discovery of Interaction Kernels in Particle-Based Systems and Their Mean-Field Limits
Title: Data-Driven Discovery of Interaction Kernels in Particle-Based Systems and Their Mean-Field Limits
Abstract: We study the problem of inferring interaction kernels from observed behaviors in particle and agent-based systems, which arise in fields ranging from physics to the social sciences. We first consider stochastic systems whose interaction kernels depend on pairwise distances, and introduce a nonparametric inference framework based on a regularized maximum likelihood estimator. This approach enables the estimation of distance-based interaction kernels with consistency and a near-optimal convergence rate that is independent of the dimension of the state space. We also analyze the error induced by discrete-time observations and demonstrate the effectiveness of the method through numerical experiments on models such as stochastic opinion dynamics and the Lennard–Jones system. Finally, we extend the analysis to the identification of nonlocal interaction potentials in aggregation–diffusion equations from noisy data using sparsity-promoting methods. This talk is based on joint work with Fei Lu, Mauro Maggioni, José A. Carrillo, Gissell Estrada-Rodriguez, and László Miklós.
Professor Mezić works in the field dynamical systems, control theory and applications in
artificial intelligence. He did his Ph. D. in Dynamical Systems at the California Institute of
Technology. Dr. Mezic was a postdoctoral researcher at the Mathematics Institute,
University of Warwick, UK in 1994-95. From 1995 to 1999 he was a member of College of Engineering at the University of California, Santa Barbara where he is currently a Mosher Endowed Chair in Mechanical Engineering-Dynamical Systems and a Distinguished Professor. In 2000-2001 he has worked as an Associate Professor at Harvard University in the Division of Engineering and Applied Sciences. He won the Alfred P. Sloan Fellowship in Mathematics, NSF CAREER Award from the National Science Foundation and the George S. Axelby Outstanding Paper Award from IEEE. He also won the United Technologies Senior Vice President for Science and Technology Special Achievement Prize in 2007. For his work on analysis and control of complex systems, he was named Fellow of the American Physical Society, Fellow of the Society for Industrial and Applied Mathematics and Fellow of the Institute of Electrical and Electronics Engineers. He is the recipient of the 2021 J. D. Crawford SIAM Prize, awarded once in two years to a researcher in Dynamical Systems.
Title: Koopman Operator and Learning of Dynamical Systems and Beyond
Title: Koopman Operator and Learning of Dynamical Systems and Beyond
Abstract: Many approaches to machine learning have struggled with applications that possess complex process dynamics. I will describe an approach to machine learning of dynamical systems based on Koopman Operator Theory (KOT) that produces generative, predictive, context-aware models amenable to (feedback) control applications. KOT has deep mathematical roots and I will discuss its basic tenets. Its first applications were in fluid mechanics and a number of these will be showcased a number of these, but a number of other examples will be discussed, including use in soft robotics.
Acknowledgement: Support from ARO, AFOSR, DARPA, NSF and ONR is gratefully acknowledged.
Dr. Ben Fitzpatrick is an applied mathematician and statistician with over 40 years of experience collaborating with engineers, biologists, public health scientists, social scientists, and policy makers on quantitative analyses. His work experience is a blend of academic research and industrial practice. Dr. Fitzpatrick recently retired from the Clarence J. Wallen, S.J., endowed chair in the Department of Mathematics, Statistics and Data Science at Loyola Marymount University, where he taught a variety of applied mathematics and statistics courses, worked with colleagues in biology, computer science, and psychology, and oversaw the biomathematics individualized studies program. He has directed and co-directed many undergraduate research projects in biomathematics, biostatistics, and dynamic modeling of social interactions and obtained grants from the Air Force, the National Institute for Alcoholism and Alcohol Abuse, and the National Science Foundation. Dr. Fitzpatrick also serves as President of Tempest Technologies, managing projects that bring computational, mathematical, and statistical technologies to bear in engineering and public health arenas. He has provided consulting advice to government and private industry clients on modeling, statistical algorithms, data analysis, and dynamic optimization of engineering and social systems. He has successfully delivered a number of special-purpose software and software/hardware products to government and government-contractor clients.
Title: Modeling the Crisis of Reproducibility
Title: Modeling the Crisis of Reproducibility
Abstract: One of the most important aspects of mathematical modeling is the ability to examine counterfactual circumstances. Social science and public policy are fields where counterfactual analysis can be especially important. In this presentation, we focus on one particular social and policy challenge: the so-called crisis of reproducibility. We aim to show that mathematical simulation modeling can provide insights into interventions proposed to improve reproducibility in life and social science research.
Experimental design and statistical data analysis are thought to be major contributors to reproducibility problems, particularly practices such as P-hacking to produce results below this threshold, selective reporting of positive studies, and designing studies with too few subjects. A number of interventions have been proposed, ranging from insisting on culture change to registered reporting to reducing the threshold of significance. In this talk, we use an evolutionary agent-based model comprised of researchers who test hypotheses and strive to increase their publication rates. Properties like effort, effect size, number of hypotheses tested, and registered reporting varied across researchers, with evolution driven by total publication value. We see that reducing the signficance threshold does not necessarily reduce P-hacking but that it may improve the false positive rate in the literature. Likewise, registered reporting shows promise in reducing false positives but may require changes in the academic incentive system for widespread adoption.
Dr. Hayden Schaeffer is the Director of Applied Mathematics and a Professor of Mathematics at the University of California, Los Angeles. His research is in mathematical and scientific machine learning, differential equations, randomization, and modeling. He has received an NSF CAREER award and an AFOSR Young Investigator Award. Previously, he was an NSF Mathematical Sciences Postdoctoral Research Fellow, a von Karman Instructor at Caltech, a UC President’s Postdoctoral Fellow at UC Irvine, an NDSEG Fellow, and a Collegium of University Teaching Fellow at UCLA.
Page updated
Google Sites
Report abuse