Applied Mathematics and Machine Learning
Department of Mathematics and Statistics
Texas Tech University
The Applied Math seminar group recommends people attend the Colloquium given on the 10th in Experimental Sciences Building 1, room 120.
Abstract: Rooted in Approximation Theory, Optimal Recovery can be viewed as a trustworthy learning theory focusing on the worst case. Regrettably, compared to more popular Machine Learning alternatives, the classical theory of Optimal Recovery overlooked the computational aspect, with a few exceptions, e.g., the development of spline functions. Nowadays, modern optimization techniques facilitate advances — even theoretical ones — on the minimax problems that abound in the field. I will illustrate this point by selecting a few snippets from my recent work.
KEY WORDS/RELATED TOPICS: Prediction of (multivalued) functions based on merely convex models; Estimation of linear functionals in the space of continuous functions; Full Recovery from deterministically inaccurate data in Hilbert spaces; Estimation of linear functionals from stochastically inaccurate data; Prediction of the maxima of Lipschitz functions from inaccurate point values
When: 3:00 pm (Lubbock's local time is GMT -5)
Where: room Math 011 (Math Basement)
ZOOM details:
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* Meeting ID: 915 2866 2672
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Abstract. Convergent of a finite element discretization of Chorin's projection method for the incompressible Navier-Stokes equations to Leray-Hopf solutions
Abstract: We consider Chorin's projection method combined with a finite element spatial discretization for the time-dependent incompressible Navier-Stokes equations. The projection method advances the solution in two steps: A prediction step which computes an intermediate velocity field that is generally not divergence-free, and a projection step which enforces (approximate) incompressibility by projecting this velocity onto the (approximately) divergence-free subspace. We establish convergence, up to a subsequence, of the numerical approximations generated by the projection method with finite element spatial discretization to a Leray-Hopf solution of the incompressible Navier-Stokes equations, without any additional regularity assumptions beyond square-integrable initial data and square-integrable forcing. A discrete energy inequality yields a priori estimates, which we combine with a new compactness result to prove precompactness of the approximations in $L^2([0,T]\times\Omega)$, where $[0,T]$ is the time interval and $\Omega$ is the spatial domain. Passing to the limit as the discretization parameters vanish, we obtain a weak solution of the Navier–Stokes equations. A central difficulty is that different a priori bounds are available for the intermediate and projected velocity fields; our compactness argument carefully integrates these estimates to complete the convergence proof.
When: 4:00 pm (Lubbock's local time is GMT -5)
Where: room Math 011 (Math Basement)
ZOOM details:
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* Meeting ID: 915 2866 2672
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Abstract Motivated by nonlinear approximation results for classes of parametric partial differential equations (PDEs), we seek to better understand so-called library approximations to analytic functions of countably infinite number of variables. Rather than approximating a function of interest by a single space, a library approximation uses a collection of spaces and the best space may be chosen for any point in the domain. In the setting of this paper, we use a specific library which consists of local Taylor approximations on sufficiently small rectangular subdomains of the (rescaled) parameter domain Y := [−1, 1]^N. When the function of interest is the solution of a certain type of parametric PDE, recent results prove an upper bound on the number of spaces required to achieve a desired target accuracy. In this talk, we discuss a similar result for a more general class of functions with anisotropic analyticity. In this way we show both where the previous theory depends on being in the setting of parametric PDEs with affine diffusion coefficients, and prove a more general result outside of this setting.
When: 4:00 pm (Lubbock's local time is GMT -5)
Where: room Math 011 (Math Basement)
ZOOM details:
- Choice #1: use this
Direct Link that embeds meeting ID and passcode
or
- Choice #2: Log into zoom, then join by manually inputting the meeting ID and passcode ...
* Meeting ID: 915 2866 2672
* Passcode: applied
Abstract. An amazing property of Hermite interpolation is that it is a projection
in a Sobolev seminorm. As a result, in constrast with the usual Lagrange
interpolant, Hermite interpolation has a smoothing effect. We show how to
exploit this projection property to develop Hermite-based solvers for differen-
tial equations with novel properties. For hyperbolic pdes, Hermite methods
admit order-independent time steps and highly localized evolution processes
which can be exploited on modern computer architectures. For initial value
problems one can develop implicit schemes of arbitrary order for which the
system size is also order-independent.
When: 4:00 pm (Lubbock's local time is GMT -5)
Where: room Math 011 (Math Basement)
ZOOM details:
- Choice #1: use this link
Direct Link that embeds meeting and ID and passcode.
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Join Meeting, then you will have to input the ID and Passcode by hand:
* Meeting ID: 915 2866 2672
* Passcode: applied
Abstract. This research focuses on the interface reactions in composite energetic materials involving TiO2 polymorphs and γ-Al2O3 surface, investigated through experimental and theoretical approaches. Using density functional theory (DFT), we examined the adsorption and decomposition of ammonium perchlorate (NH4ClO4) on rutile (110, 100, 001) and anatase (101, 001) TiO2 surfaces, revealing highly stable complexes stabilized by covalent and hydrogen bonds. Our calculations showed that adsorption energies range from -120 to -302. kJ/mol, with subsequent decomposition reactions being highly exergonic (ΔEdec ranging from -199 to -381. kJ/mol) and exothermic, releasing significant heat aligned with experimental observations. Notably, the anatase (101) surface exhibits greater reactivity than the rutile (110), an insight supported by experimental validation. The activation mechanisms are primarily entropy-driven across the TiO2 phases. Additionally, the study investigated alumina (Al2O3) passivation shells on aluminum particles and their reactions with halogenated species. DFT calculations demonstrated that iodine species (HI and I-) exhibit nearly triple the adsorption energies compared to fluorinated fragments, with energetically favorable adsorption but unfavorable exchange reactions with alumina. Differential scanning calorimetry (DSC) experiments confirmed the higher energy release during iodine-related reactions, highlighting potential pathways for alumina modification. These insights open avenues for tailoring surface chemistries to enhance energetic material performance.
When: 4:00 pm (Lubbock's local time is GMT -5)
Where: room Math 011 (Math Basement)
ZOOM details:
- Choice #1: use this link
Direct Link that embeds meeting and ID and passcode.
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Join Meeting, then you will have to input the ID and Passcode by hand:
* Meeting ID: 915 2866 2672
* Passcode: applied
 | Wednesday
Oct. 22
4 PM
Math 011
|
| TBA
Andreas Mang
Department of Mathematics, University of Houston
|
Abstract. TBA.
When: 4:00 pm (Lubbock's local time is GMT -5)
Where: room Math 011 (Math 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: 915 2866 2672
* Passcode: applied
 | Wednesday
Oct. 29
4 PM
Math 011
|
| TBA
Christopher Rycroft
Department of Mathematics, University of Wisconsin–Madison
|
Abstract. TBA.
When: 4:00 pm (Lubbock's local time is GMT -5)
Where: room Math 011 (Math 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: 915 2866 2672
* Passcode: applied
Abstract. TBA.
When: 4:00 pm (Lubbock's local time is GMT -5)
Where: room Math 011 (Math 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: 915 2866 2672
* Passcode: applied
 | Wednesday
Nov. 12
4 PM
Math 011
|
| TBA
Laurent Jay
Department of Mathematics, The University of Iowa
|
Abstract. TBA.
When: 4:00 pm (Lubbock's local time is GMT -5)
Where: room Math 011 (Math 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: 915 2866 2672
* Passcode: applied
 | Wednesday
Nov. 19
4 PM
Math 011
|
| TBA
Anh-Khoi Vo
Department of Mathematics, University of Houston
|
Abstract. TBA.
When: 4:00 pm (Lubbock's local time is GMT -5)
Where: room Math 011 (Math 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: 915 2866 2672
* Passcode: applied