Sent on behalf of the CMAI Colloquium. ------------------------------------------------------------------------------------------------------------ Dear All, The next CMAI Colloquium<https://cmai.gmu.edu/index.php/events/#colloquium> will be on Date: Friday February 05, 2021 at 10:00 am (Eastern Time) Speaker: Prof. Georg Stadler<https://secure-web.cisco.com/12FcBqa1o3OKceIQVEd_KdjZEPDe7O3rZ6m9jt2COw7TX9KYIGyghmlNVX5Tn2uPMEvwx6a1FtUNW33bNl26vAnfvDdCEq8zrJS34JmLQXv9CwLTUBcDs4wqeI-n_NREx1T3zb4n40GXtik3MbVW6Zn4IdHCF7-EqL1x55eFCadP9k56bKTvK_xuUlS-lIDN6KWGBzgv0InSSGVKzhNkOgBzM2istbbnERGrsu02vfH4P7LQCHQOLG_Zht0XeCUCq-N8UMlXdPC5Ld5xIgvQAhjtgu302k4tu9AMQ-9CVb9ZejXSZrWqop5h7bEpDGQNSG_D2r3BwGFYa_qQpAvWwzHVxe8pPgxSIFRnyIwKuCFkzfUXRQpq7x5jKKRCooMxr5nlRymI-hb6XOWaS-GgA0qxj215IpCUFy88zl9Xa90e-WcmTNKQ4ZP0-UmlUzW135-UOBQnb2eJjYXAZrckcYw/https%3A%2F%2Fmath.nyu.edu%2F%7Estadler%2Findex.html> Courant Institute of Mathematical Sciences, New York University Title: Estimation of extreme event probabilities in systems governed by PDEs Zoom Link: Join Zoom Meeting<https://secure-web.cisco.com/1YKACvIA2YdXokMtDI6vFCHde5TL19rv8B2WvK3B02B-DBPqcjBiXPG88dHVhFkRXhfHIWP1G7hLcLGoHQMr2n7Kwe2QbPr49lVYv3Qnb6lvJ8s8WX2audvZlGfx3OQO__l6prpm9fqc5kjFxKH9RNOz6qzLusfaLIlMA5ySl2-9fq9BvNn49lFHRjEnrUqM8fLBv5WRSsimVzkS3T_KZSthR38cJA0HOH5o24sRJcvH4HNTHRj9R2VXVZHIqrx-R4BUyNAJ10mzO7lyvRHOIs-xKfhKo_t568B4GGFvwCpbv3ZBZcdtbzl6rPsYNmLUC0kLHEYNnar5Mf1jb2EllHKs1zEci07oxcSOzo2acJmDianS3uCsyxH0g2BPROSr_puWMMLLQYwbX99rzoBueC_wz_4qEK0qHpoIy3OGDox0ieB6xbc13K6cInJ5JKkQb99pmC3wVku1EYcX52xsg5Q/https%3A%2F%2Fgmu.zoom.us%2Fj%2F95486569124%3Fpwd%3DRGJDTDNIRnd4WFVEbXhaTE9UcGJudz09> Abstract: We propose methods for the estimation of extreme event probabilities in complex systems governed by PDEs. Our approach is guided by ideas from large deviation theory (LDT) and borrows methods from PDE-constrained optimization. The systems under consideration involve random parameters and we are interested in quantifying the probability that a scalar function of the system state is at or above a threshold. The proposed methods initially solve an optimization problem over the set of parameters leading to events above a threshold. Based on solutions of this PDE-constrained optimization problem, we propose (1) an importance sampling method and (2) a method that uses curvature information of the extreme event boundary to estimate small probabilities. We illustrate the application of our approach to quantify the probability of extreme tsunami events on shore. Tsunamis are typically caused by a sudden, unpredictable change of the ocean floor elevation during an earthquake. We model this change as random process and use the one-dimensional shallow water equation to model tsunamis. The PDE-constrained optimization problem arising in this application is governed by the shallow water equation. This is joint work with Shanyin Tong and Eric Vanden-Eijnden from NYU. Best, CMAI Team ================================================================== Harbir Antil Director, Center for Mathematics and Artificial Intelligence (CMAI) Associate Professor, Mathematical Sciences George Mason University Fairfax, VA 22030 Phone: (703) 993-5086 Fax: (703) 993-1491 http://math.gmu.edu/~hantil/ https://cmai.gmu.edu/
