| Professor Ioana Dumitriu (University of California, San Diego) | 65 | Professor Ioana Dumitriu (University of California, San Diego) | Zoom | <br>
Title: Spectral gap in random regular hyper/graphs and applications
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Abstract: Random graphs and hypergraphs have been used for decades to model large-scale networks, from biological, to electrical, and to social. Various random graphs (and their not-so-random properties) have been connected to algorithms solving problems from community detection to matrix completion, coding theory, and various other statistics / machine learning fundamental questions; in the past decade, this research area has expanded to include random hypergraphs. One of these special properties is the spectral gap for graph-associated matrices; roughly speaking, it means that the main eigenvalue(s) are well-separated from the bulk and it guarantees strong connectivity properties. This talk will take a look at the spectra of adjacency / Laplacian matrices for some random regular models, explain how we know that the spectral gap is there, and connect spectral properties to the aforementioned applications. It will cover joint work with Gerandy Brito, Kameron Decker Harris, and Yizhe Zhu. | 3/26/2021 7:30:00 PM | 3/26/2021 8:30:00 PM | | |
| Carl Rees Lectures in Mathematical Sciences | 68 | Carl Rees Lectures in Mathematical Sciences | https://udel.zoom.us/j/92058762257 | <br>Speaker: Professor Jan S Hesthaven<br>Professor of Mathematics, Chair of Computational Mathematics and Simulation Science, EPFL, Lausanne, CH <br>
<br>Title: Nonintrusive reduced order models using physics informed neural networks <br>
<br>Abstract: The development of reduced order models for complex applications, offering the promise for rapid and accurate evaluation of the output of complex models under parameterized variation, remains a very active research area. Applications are found in problems which require many evaluations, sampled over a potentially large parameter space, such as in optimization, control, uncertainty quantification, and in applications where a near real-time response is needed. However, many challenges remain unresolved to secure the flexibility, robustness, and efficiency needed for general large-scale applications, in particular for nonlinear and/or time-dependent problems. <br>After giving a brief general introduction to projection based reduced order models, we discuss the use of artificial feedforward neural networks to enable the development of fast and accurate nonintrusive models for complex problems. We demonstrate that this approach offers substantial flexibility and robustness for general nonlinear problems and enables the development of fast reduced order models for complex applications. In the second part of the talk, we discuss how to use residual based neural networks in which knowledge of the governing equations is built into the network and show that this has advantages both for training and for the overall accuracy of the model. Time permitting, we finally discuss the use of reduced order models in the context of prediction, i.e. to estimate solutions in regions of the parameter beyond that of the initial training. With an emphasis on the Mori-Zwansig formulation for time-dependent problems, we discuss how to accurately account for the effect of the unresolved and truncated scales on the long term dynamics and show that accounting for these through a memory term significantly improves the predictive accuracy of the reduced order model. <br> | 11/20/2020 3:00:00 PM | 11/20/2020 4:00:00 PM | | |
| Carl Rees Lectures in Mathematical Sciences | 67 | Carl Rees Lectures in Mathematical Sciences | https://udel.zoom.us/j/92058762257 | <br>Speaker: Professor Jan S Hesthaven<br>Professor of Mathematics, Chair of Computational Mathematics and Simulation Science, EPFL, Lausanne, CH <br>
<br>Title: How to predict a tsunami <br>
<br>Abstract: Computational science and engineering is an essential component of modern science with the goal to model complex systems and develop tools with true predictive qualities. In this talk, we shall discuss this process in the context of tsunami modeling. However, the process, involving model development, verification and validation, is generic for all such activities. During the last decades, earthquake driven tsunamis have impacted the lives of millions and resulted in financial losses in the billions. Some of this devastation could be avoided if one could reliably predict the impact of tsunamis as an integral part of tsunami warning system, giving time to evacuate people and high value asserts as needed. In this talk we go through the steps required to develop, verify and validate a computational models to enable the prediction of tsunami arrival time on a global scale. Working through the computational scheme and key challenges associated with the particular problem, we shall illustrate the challenges associated with solving a problem of realistic complexity. We illustrate the properties of the scheme through a series of simple tests before validating the method for the simulation of large-scale tsunami events on the rotating sphere by performing numerical simulations of several historical large scale events and compare our results to real-world data. By considering both static and dynamic earthquake models, we demonstrate that the model is able to predict arrival times and wave amplitudes accurately, even over long distances but also highlight limitations associated with some of the choices made in the development of the model. This work has been done with in collaboration with B Bonev (EPFL, CH), F. Giraldo (NPS, US), M. Hajihassanpour (Sharif, Iran), and M. A. Kopera (UC Santa Cruz, US). <br>
| 11/19/2020 3:00:00 PM | 11/19/2020 4:00:00 PM | | |
| TBA | 60 | TBA | GORE 116 | TBA | 4/30/2020 7:30:00 PM | 4/30/2020 8:30:00 PM | | |
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