Events
Department of Mathematics and Statistics
Texas Tech University
Physics-Informed Neural Networks (PINNs) have received much attention recently due to their potential for high-performance computations for complex physical systems, including data-based computing, systems with unknown parameters, and others. The idea of PINNs is to approximate the equations and boundary and initial conditions through a loss function for a neural network. PINNs combine the efficiency of data-based prediction with the accuracy and insights provided by the physical models. However, applications of these methods to predict the long-term evolution of systems with little friction, such as many systems encountered in space exploration, oceanography/climate, and many other fields, need extra care as the errors tend to accumulate, and the results may quickly become unreliable.
We provide a solution to the problem of data-based computation of Hamiltonian systems utilizing symmetry methods. Many Hamiltonian systems with symmetry can be written as a Lie-Poisson system, where the underlying symmetry defines the Poisson bracket. For data-based computing of such systems, we design the Lie-Poisson neural networks (LPNets). We consider the Poisson bracket structure primary and require it to be satisfied exactly, whereas the Hamiltonian, only known from physics, can be satisfied approximately. By design, the method preserves all special integrals of the bracket (Casimirs) to machine precision. LPNets yield an efficient and promising computational method for many particular cases, such as rigid body or satellite motion (the case of SO(3) group), Kirchhoff's equations for an underwater vehicle (SE(3) group), and others.
Joint work with Chris Eldred (Sandia National Lab), Francois Gay-Balmaz (CNRS and ENS, France), and Sophia Huraka (U Alberta). The work was partially supported by an NSERC Discovery grant.
This Departmental Colloquium is sponsored by the Applied Math seminar group.
When: 3:00 pm (Lubbock's local time is GMT -5)
Where: room MATH 011 (basement)
ZOOM details:
- Choice #1: use this link
Direct Link that embeds meeting and ID and passcode.
- Choice #2: join meeting using this link
Join Meeting, then you will have to input the ID and Passcode by hand:
* Meeting ID: 968 6501 7586
* Passcode: Applied
Despite the popularity of classical goodness fit tests such as Pearson’s chi-squared and Kolmogorov-Smirnov, their applicability often faces serious challenges in practical applications. For instance, in a binned data regime, low counts may affect the validity of the asymptotic results. Excessively large bins, on the other hand, may lead to loss of power. In the unbinned data regime, tests such as Kolmogorov-Smirnov and Cramer-von Mises do not enjoy distribution-freeness if the models under study are multivariate and/or involve unknown parameters. As a result, one needs to simulate the distribution of the test statistic on a case-by-case basis. In this talk, I will discuss a testing strategy that allows us to overcome these shortcomings and equips experimentalists with a novel tool to perform goodness-of-fit while reducing substantially the computational costs.
Over the past two decades, significant progress has been made in researching the Kardar-Parisi-Zhang (KPZ) universality class, which is a broad class of phyical and probabilistic models including one-dimensional interface growth processes, interacting particle systems and polymers in random environments, etc. It is broadly believed and partially proved, that all the models share the universal scaling exponents and have the same asymptotic behaviors. The height functions of models in the KPZ universality class are expected to converge to a limiting space-time fluctuation field, the KPZ fixed point. Moreover, there exists a random "directed metric" on the space-time plane that is expected to govern the behavior of all models within the KPZ universality class, referred to as the directed landscape. Remarkably, both the KPZ fixed point and the directed landscape have only been recently constructed in recent research publications [MQR21, DOV18]. These central objects play a crucial role in advancing our understanding of the KPZ universality class.
In this talk, we will discuss some exact formulas of distributions in these two random fields. These exact formulas are given by Fredholm determinant or their analogs. We will show some surprising probabilistic properties of the KPZ fixed point and the directed landscape using the exact formulas. Some of the results are based on joint work with Zhipeng Liu, Ron Nissim, Yizao Wang.
Please attend this week's Statistics seminar at 4 PM (UT-5) Monday the 9th via this Zoom link.
Meeting ID: 926 7350 8524
Passcode: 492943
Abstract. Wave turbulence describes the dynamics of both classical and non-classical nonlinear waves out of thermal equilibrium. In this talk, I will present some of our recent results on wave turbulence theory. In the first part of the talk, I will discuss our rigorous derivation of wave turbulence equations. The second part of the talk is devoted to the analysis of wave turbulence equations as well as some numerical illustrations. The last part concerns some physical applications of wave turbulence theory. The talk is based on my joint work with Gigliola Staffilani (MIT), Avy Soffer (Rutgers), Yves Pomeau (ENS Paris), and Steven Walton (Los Alamos).
When: 4:00 pm (Lubbock's local time is GMT -5)
Where: room MATH 011 (basement)
ZOOM details:
- Choice #1: use this link
Direct Link that embeds meeting and ID and passcode.
- Choice #2: join meeting using this link
Join Meeting, then you will have to input the ID and Passcode by hand:
* Meeting ID: 968 6501 7586
* Passcode: Applied
 | Wednesday
Oct. 11
7 PM
MA 108
|
| Mathematics Education
Math Circle
Miraj Samarakkody
Department of Mathematics and Statistics, Texas Tech University
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Math Circle Fall Poster
abstract noon CDT (UT-5)