Events
Department of Mathematics and Statistics
Texas Tech University
The Vlasov system is known as a fundamental model in plasma physics which describes the dynamics of dilute charged particles due to self-induced electrostatic forces. The main numerical challenges lie in the high dimensionality of the phase space, multi-scale feature, and the inherent conservation property of the solutions. In this talk, we introduce a conservative adaptive low-rank tensor method. The approach takes advantage of the fact that the differential operators in the Vlasov equation are tensor friendly, based on which we propose to build up the low-rank solution basis dynamically and adaptively by exploring the intrinsic low-rank structure of Vlasov dynamics. We further develop a novel low-rank scheme with local mass, momentum, and energy conservation by considering the corresponding macroscopic equations. The mass and momentum conservation are achieved by a conservative low-rank truncation, while the energy conservation is achieved by replacing the energy component of the Vlasov solution by the one obtained from a conservative scheme for the macroscopic energy equation. The algorithm is extended to high-dimensional problems with the hierarchical Tucker tensor decomposition of Vlasov solutions, overcoming the curse of dimensionality. An extensive set of nonlinear Vlasov examples are performed to demonstrate the effectiveness and conservation property of the proposed conservative low-rank tensor approach.
Dr. Wei Guo's Tenure and Promotion Colloquium has been archived in the Mediasite catalog.
In the past few years, I am interested in recurrent diseases and multiple disease outcomes shown in pathogen-immune interaction models. The crucial role of the immune system is to eliminate foreign pathogens and cancerous cells, simultaneously, preserving self-tolerance. The failure of complete elimination leads to persistent antigens and chronic inflammation, which in turn actives immune tolerance and inhibits immune functions. Through applied bifurcation theory, my work reveals the causal mathematical mechanisms for "slow-fast" motions in recurrent diseases and identifies the key parameter determining multiple disease outcomes. The mathematical results lead to a better understanding of the underlining biological mechanisms, which will shed new light to improve immunotherapy.
Dr. Wenjing Zhang's Tenure and Promotion Colloquium has been archived in the Mediasite catalog.
Simulation of phenomena in nature requires a faithful model, an accurate discretization method, an efficient solution algorithm, and software that is both efficient and adaptable. Use of simulation in real-world decision making requires an understanding of the uncertainties in the model data and their propagation through the simulation. Through the course of my career I’ve worked on all of those aspects of applied scientific computing. Here I concentrate on three problems: (1) quantifying the effect of parametric uncertainties in medical infrared thermography, (2) a method to measure model uncertainty in nonlinear dynamics, and (3) a family of preconditioners for implicit Runge-Kutta timesteppers applicable to a large family of hyperbolic and parabolic partial differential equations.
Dr. Katharine Long's Tenure and Promotion Colloquium has been archived in the Mediasite catalog.
No abstract.
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Lifting theory of modules was studied intensively by Auslander, Ding,
and Solberg. This notion is tightly connected to the deformation
theory of modules and has important applications in the theory of
maximal Cohen-Macaulay approximations. Later, Yoshino generalized the
lifting results for modules to the case of complexes. Further
generalization was given by Nasseh and Sather-Wagstaff for DG modules
(a notion from rational homotopy theory) in order to obtain a clearer
insight on a conjecture of Vasconcelos in commutative algebra.
In this talk, I will survey recent developments on lifting theory of
DG modules and describe the relationship between this notion and
another conjecture in commutative algebra, namely, the
Auslander-Reiten conjecture. The talk is based on several joint works
with Maiko Ono and Yuji Yoshino.
Join Zoom Meeting https://texastech.zoom.us/j/91729629174?pwd=TFJHbDk1ZS9KeTBRaldNL1hUbVNlQT09
Meeting ID: 971 2962 9174
Passcode: 914040
Deep Learning (DL) methods have been transforming computer vision with innovative adaptations
to other domains including climate change.
For DL to pervade Science and Engineering (S&E) applications where risk management is a core component,
well-characterized uncertainty estimates must accompany predictions.
However, S&E observations and model-simulations often follow heavily skewed distributions and
are not well modeled with DL approaches, since they usually optimize a Gaussian, or Euclidean,
likelihood loss. Recent developments in Bayesian Deep Learning (BDL), which attempts to capture
uncertainties from noisy observations, aleatoric, and from unknown model parameters, epistemic,
provide us a foundation. Here we present a discrete-continuous BDL model with Gaussian and lognormal
ikelihoods for uncertainty quantification (UQ).
We demonstrate the approach by developing UQ estimates on `DeepSD', a super-resolution based
DL model for Statistical Downscaling (SD) in climate applied to precipitation, which follows an
extremely skewed distribution.
We find that the discrete-continuous models outperform a basic Gaussian distribution in terms
of predictive accuracy and uncertainty calibration.
Furthermore, we find that the lognormal distribution, which can handle skewed distributions,
produces quality uncertainty estimates at the extremes.
Such results may be important across S&E, as well as other domains such as finance and economics,
where extremes are often of significant interest.
Furthermore, to our knowledge, this is the first UQ model in SD where both aleatoric and epistemic
uncertainties are characterized.