SIAM Student Chapter Seminar: Difference between revisions

From UW-Math Wiki
Jump to navigation Jump to search
No edit summary
 
(132 intermediate revisions by 9 users not shown)
Line 1: Line 1:
__NOTOC__
__NOTOC__


*'''When:''' Mondays at 4 PM
*'''When:''' Fridays at 1 PM unless noted otherwise
*'''Where:''' See list of talks below
*'''Where:''' 9th floor lounge (we will also broadcast the virtual talks on the 9th floor lounge with refreshments)
*'''Organizers:''' [https://sites.google.com/wisc.edu/evan-sorensen Evan Sorensen]
*'''Organizers:''' Yahui Qu, Peiyi Chen and Zaidan Wu
*'''Faculty advisers:''' [http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault], [http://pages.cs.wisc.edu/~swright/ Steve Wright]  
*'''Faculty advisers:''' [http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault], [http://pages.cs.wisc.edu/~swright/ Steve Wright]  
*'''To join the SIAM Chapter mailing list:''' email [mailto:siam-chapter+join@g-groups.wisc.edu siam-chapter+join@g-groups.wisc.edu].
*'''To join the SIAM Chapter mailing list:''' email [mailto:siam-chapter+join@g-groups.wisc.edu siam-chapter+join@g-groups.wisc.edu].
*'''Zoom link:''' https://uwmadison.zoom.us/j/97976615799?pwd=U2xFSERIcnR6M1Y1czRmTjQ1bTFJQT09
*'''Passcode:  281031'''


<br>
== Fall 2024 ==


== Fall 2021  ==
{| class="wikitable"
 
|+
{| cellpadding="8"
!Date
!align="left" | date and time
!Location
!align="left" | location
!Speaker
!align="left" | speaker
!Title
!align="left" | title
|-
|10 AM 10/4
|Birge 346
|Federica Ferrarese (University of Ferrara, Italy)
|Control plasma instabilities via an external magnetic field: deterministic and uncertain approaches
|-
|-
| Sept 20, 4 PM
|11 AM 10/18
| Ingraham 214
|9th floor
| [https://sites.google.com/view/julialindberg/home/ Julia Lindberg] (Electrical and Computer Engineering)
|Martin Guerra (UW-Madison)
|''[[#Sept 20, Julia Lindberg |Polynomial system solving in applications]]''
|Swarm-Based Gradient Descent Meets Simulated Annealing
|-
|-
|12:30 PM 10/31
|VV 901
|Chuanqi Zhang (University of Technology Sydney)
|Faster isomorphism testing of p-groups of Frattini class-2
|-
|-
| Sept 27, 4 PM,
|11/8
| Zoom (refreshments and conference call in 307)
|9th floor
| Wil Cocke (Developer for [https://www.arcyber.army.mil/ ARCYBER])
|Borong Zhang (UW-Madison)
| ''[[#Sept 27, Wil Cocke |Job talk-Software Development/Data Science]]''
|Solving the Inverse Scattering Problem: Leveraging Symmetries for Machine Learning
|
|-
|-
|11/15
|9th floor
(zoom)
|Yantao Wu (Johns Hopkins University)
|Conditional Regression on Nonlinear Variable Model
|-
|-
| Oct 4, '''2:45 PM'''
|
| B119 Van Vleck
|
| [https://sites.google.com/wisc.edu/nair-anjali/home/ Anjali Nair] (Math)
|
| ''[[#Oct 4, Anjali Nair|Reconstruction of Reflection Coefficients Using the Phonon Transport Equation]]''
|
|
|-
|-
|
|
|
|
|-
|-
| Oct 18, 4 PM
| 6104 Social Sciences
| [https://jasonltorchinsky.github.io/ Jason Tochinsky] (Math)
| ''[[#Oct 18, Jason Torchinsky|Improving the Vertical Remapping Algorithm in the Department of Energy’s Energy Exascale Earth Systems Model]]''
|
|
|-
|-
| Oct 25, 4 PM,
| Zoom (refreshments and conference call in 9th floor lounge)
| [https://www.linkedin.com/in/patricktbardsley/ Patrick Bardsley] (Machine Learning Engineer at [https://www.cirrus.com/ Cirrus Logic])
| ''[[#Oct 25, Patrick Bardsley|Job Talk-Machine Learning]]''
|-
|-
| Nov 8, 4 PM,
| Zoom (refreshments and conference call in 9th floor lounge)
| [https://www.linkedin.com/in/libanmohamed496/ Liban Mohammed] (Machine Learning Engineer at [https://www.mitre.org/ MITRE])
|-
|-
| Nov 15, 4 PM,
| Zoom (refreshments and conference call in 9th floor lounge)
| [https://www.linkedin.com/in/kurt-ehlert-320b8397/ Kurt Ehlert] (Trading Strategy Developer at [https://auros.global/about/ Auros])
|-
|-
| Nov 29, 4 PM
| 9th floor lounge
| [https://people.math.wisc.edu/~boakley/ Bryan Oakley] (Math)
| ''[[#Nov 29, Bryan Oakley|Optimal Spatially Dependent Diffusion]]''
|
|
|-
|
|-
|
| Dec 6, 4 PM
| 9th floor lounge
| [https://sites.google.com/view/hongxuchen/ Hongxu Chen] (Math)
|}
|}


== Abstracts ==
==Abstracts==
 
'''October 4th, Federica Ferrarese (University of Ferrara, Italy)''': The study of the problem of plasma confinement in huge devices, such as for example Tokamaks and Stellarators, has attracted a lot of attention in recent years. Strong magnetic fields in these systems can lead to instabilities, resulting in vortex formation. Due to the extremely high temperatures in plasma fusion, physical materials cannot be used for confinement, necessitating the use of external magnetic fields to control plasma density. This approach involves studying the evolution of plasma, made up of numerous particles, using the Vlasov-Poisson equations. In the first part of the talk, the case without uncertainty is explored. Particle dynamics are simulated using the Particle-in-Cell (PIC) method, known for its ability to capture kinetic effects and self-consistent interactions. The goal is to derive an instantaneous feedback control that forces the plasma density to achieve a desired distribution. Various numerical experiments are presented to validate the results. In the second part, uncertainty is introduced into the system, leading to the development of a different control strategy. This method is designed to steer the plasma towards a desired configuration even in the presence of uncertainty. The presentation concludes with a comparison of the two control strategies, supported by various numerical experiments.
=== Sept 20, Julia Lindberg===
Polynomial systems arise naturally in many applications in engineering and the sciences. This talk will outline classes of homotopy continuation algorithms used to solve them. I will then describe ways in which structures such as irreducibility, symmetry and sparsity can be used to improve computational speed. The efficacy of these algorithms will be demonstrated on systems in power systems engineering, statistics and optimization
 
 
=== Sept 27, Wil Cocke ===
I mostly work as a software developer with an emphasis on data science projects dealing with various Command specific projects. The data science life-cycle is fairly consistent across industries: collect, clean, explore, model, interpret, and repeat with a goal of providing insight to the organization. During my talk, I will share some lessons learned for mathematicians interested in transitioning to software development/ data science.
 
 
=== Oct 4, Anjali Nair ===
The phonon transport equation is used to model heat conduction in solid materials. I will talk about how we use it to solve an inverse problem to reconstruct the thermal reflection coefficient at an interface. This takes the framework of a PDE constrained optimization problem, and I will also mention the stochastic methods used to solve it.
 
=== Oct 18, Jason Torchinsky ===
A vertical Lagrangian coordinate has been used in global climate models for nearly two decades and has several advantages over other discretizations, including reducing the dimensionality of the physical problem. As the Lagrangian surfaces deform over time, it is necessary to accurately and conservatively remap the vertical Lagrangian coordinate back to a fixed Eulerian coordinate. A popular choice of remapping algorithm is the piecewise parabolic method, a modified version of which is used in the atmospheric component of the Department of Energy's Energy Exascale Earth System Model. However, this version of the remapping algorithm creates unwanted noise at the model top and planetary surface for several standard test cases. We explore four alternative modifications to the algorithm and show that the most accurate of these eliminates this noise.
 
=== Oct 25, Patrick Bardsley ===
During the course of a PhD, students typically enter a proverbial `coal mine’ to extract new information about one or more problems, and in the process become a domain expert in a small niche of the technical and scientific world. Upon leaving the academy, unless one lands a job in their niche domain, much of their problem- and domain-specific knowledge is no longer essential. However, mathematics is broad and general, arguably the most general of all scientific disciplines. This fact alone is a mathematician’s greatest asset and ‘leg-up’ when entering the industrial workforce. In this talk, I will discuss some details of my work, both inside and outside of the academy, with the goal of highlighting the skills and concepts that have been the most general and transferable for me. For example, my academic work on hyperbolic inverse problems helped me learn signal processing concepts I now use daily, while my studies on polycrystalline grain growth pushed me to learn thermodynamics, which translated well to the information theory concepts I now utilize. I will also give you some idea of my current day-to-day responsibilities, and close with my thoughts and suggestions on job searches.
 


=== Nov 29, Bryan Oakley ===
'''October 18th, Martin Guerra (UW-Madison)''': In generic non-convex optimization, one needs to be able to pull samples out of local optimal points to achieve global optimization. Two common strategies are deployed: adding stochasticity to samples such as Brownian motion, as is done in simulated annealing (SA), and employing a swarm of samples to explore the whole landscape, as is done in Swarm-Based Gradient Descent (SBGD). The two strategies have severe drawbacks but complement each other on their strengths. SA fails in the accuracy sense, i.e., finding the exact optimal point, but succeeds in always being able to get close, while SBGD fails in the probability sense, i.e., it has non-trivial probability to fail, but if succeeds, can find the exact optimal point. We propose to combine the strength of the two and develop a swarm-based stochastic gradient method with samples automatically adjusting their annealing. Using mean-field analysis and long-time behavior PDE tools, we can prove the method to succeed in both the accuracy sense and the probability sense. Numerical examples verify these theoretical findings.
The solution to the diffusion equation is known to converge exponentially to its steady state, and the rate is given by the spectral gap of the elliptic operator. Using variational techniques, we will maximize the spectral gap over choices of spatially dependent diffusion functions. Using this characterization, we can obtain bounds on the optimal rate of convergence.


'''October 31st, Chuanqi Zhang''' (University of Technology Sydney): The finite group isomorphism problem asks to decide whether two finite groups of order N are isomorphic. Improving the classical $N^{O(\log N)}$-time algorithm for group isomorphism is a long-standing open problem. It is generally regarded that p-groups of class 2 and exponent p form a bottleneck case for group isomorphism in general. The recent breakthrough by Sun (STOC '23) presents an $N^{O((\log N)^{5/6})}$-time algorithm for this group class. Our work sharpens the key technical ingredients in Sun's algorithm and further improves Sun's result by presenting an $N^{\tilde O((\log N)^{1/2})}$-time algorithm for this group class. Besides, we also extend the result to the more general p-groups of Frattini class-2, which includes non-abelian 2-groups. In this talk, I will present the problem background and our main algorithm in detail, and introduce some connections with other research topics. For example, one intriguing connection is with the maximal and non-commutative ranks of matrix spaces, which have recently received considerable attention in algebraic complexity and computational invariant theory. Results from the theory of Tensor Isomorphism complexity class (Grochow--Qiao, SIAM J. Comput. '23) are utilized to simplify the algorithm and achieve the extension to p-groups of Frattini class-2.


'''November 8th, Borong Zhang''' (UW-Madison): The inverse scattering problem—reconstructing the properties of an unknown medium by probing it with waves and measuring the medium's response at the boundary—is fundamental in physics and engineering. This talk will focus on how leveraging the symmetries inherent in this problem can significantly enhance machine learning methods for its solution. By incorporating these symmetries into both deterministic neural network architectures and probabilistic frameworks like diffusion models, we achieve more accurate and computationally efficient reconstructions. This symmetry-driven approach reduces the complexity of the models and improves their performance, illustrating how physical principles can inform and strengthen machine learning techniques. Applications demonstrating these benefits will be briefly discussed.


<br>
'''November 15th, Yantao Wu''' (Johns Hopkins): We consider the problem of estimating the intrinsic structure of composite functions of the type $\mathbb{E} [Y|X] = f(\Pi_\gamma X) $ where $\Pi_\gamma:\mathbb{R}^d\to\mathbb{R}^1$ is the closest point projection operator onto some unknown smooth curve $\gamma: [0, L]\to \mathbb{R}^d$ and  $f: \mathbb{R}^1\to \mathbb{R}^1$ is some unknown  {\it link} function. This model is the generalization of the single-index model where $\mathbb{E}[Y|X]=f(\langle v, X\rangle)$ for some unknown {\it index} vector $v\in\mathbb{S}^{d-1}$. On the other hand, this model is a particular case of function composition model where $\mathbb{E}[Y|X] = f(g(x))$ for some unknown multivariate function $g:\mathbb{R}^d\to\mathbb{R}$. In this paper, we propose an algorithm based on conditional regression and show that under some assumptions restricting the complexity of curve $\gamma$, our algorithm can achieve the one-dimensional optimal minimax rate, plus a curve approximation error bounded by $\mathcal{O}(\sigma_\zeta^2)$. We also perform numerical tests to verify that our algorithm is robust, in the sense that even without some assumptions, the mean squared error can still achieve $\mathcal{O}(\sigma_\zeta^2)$.


== Past Semesters ==
==Past Semesters==
*[https://wiki.math.wisc.edu/index.php/SIAM_Spring_2024 Spring 2024]
*[[SIAM Fall 2023|Fall 2023]]
*[[SIAM Spring 2023|Spring 2023]]
*[[SIAM Seminar Fall 2022|Fall 2022]]
*[[Spring 2022 SIAM|Spring 2022]]
*[[SIAM Student Chapter Seminar/Fall2021|Fall 2021]]
*[[SIAM_Student_Chapter_Seminar/Fall2020|Fall 2020]]
*[[SIAM_Student_Chapter_Seminar/Fall2020|Fall 2020]]
*[[SIAM_Student_Chapter_Seminar/Spring2020|Spring 2020]]
*[[SIAM_Student_Chapter_Seminar/Spring2020|Spring 2020]]

Latest revision as of 22:40, 13 November 2024


Fall 2024

Date Location Speaker Title
10 AM 10/4 Birge 346 Federica Ferrarese (University of Ferrara, Italy) Control plasma instabilities via an external magnetic field: deterministic and uncertain approaches
11 AM 10/18 9th floor Martin Guerra (UW-Madison) Swarm-Based Gradient Descent Meets Simulated Annealing
12:30 PM 10/31 VV 901 Chuanqi Zhang (University of Technology Sydney) Faster isomorphism testing of p-groups of Frattini class-2
11/8 9th floor Borong Zhang (UW-Madison) Solving the Inverse Scattering Problem: Leveraging Symmetries for Machine Learning
11/15 9th floor

(zoom)

Yantao Wu (Johns Hopkins University) Conditional Regression on Nonlinear Variable Model

Abstracts

October 4th, Federica Ferrarese (University of Ferrara, Italy): The study of the problem of plasma confinement in huge devices, such as for example Tokamaks and Stellarators, has attracted a lot of attention in recent years. Strong magnetic fields in these systems can lead to instabilities, resulting in vortex formation. Due to the extremely high temperatures in plasma fusion, physical materials cannot be used for confinement, necessitating the use of external magnetic fields to control plasma density. This approach involves studying the evolution of plasma, made up of numerous particles, using the Vlasov-Poisson equations. In the first part of the talk, the case without uncertainty is explored. Particle dynamics are simulated using the Particle-in-Cell (PIC) method, known for its ability to capture kinetic effects and self-consistent interactions. The goal is to derive an instantaneous feedback control that forces the plasma density to achieve a desired distribution. Various numerical experiments are presented to validate the results. In the second part, uncertainty is introduced into the system, leading to the development of a different control strategy. This method is designed to steer the plasma towards a desired configuration even in the presence of uncertainty. The presentation concludes with a comparison of the two control strategies, supported by various numerical experiments.

October 18th, Martin Guerra (UW-Madison): In generic non-convex optimization, one needs to be able to pull samples out of local optimal points to achieve global optimization. Two common strategies are deployed: adding stochasticity to samples such as Brownian motion, as is done in simulated annealing (SA), and employing a swarm of samples to explore the whole landscape, as is done in Swarm-Based Gradient Descent (SBGD). The two strategies have severe drawbacks but complement each other on their strengths. SA fails in the accuracy sense, i.e., finding the exact optimal point, but succeeds in always being able to get close, while SBGD fails in the probability sense, i.e., it has non-trivial probability to fail, but if succeeds, can find the exact optimal point. We propose to combine the strength of the two and develop a swarm-based stochastic gradient method with samples automatically adjusting their annealing. Using mean-field analysis and long-time behavior PDE tools, we can prove the method to succeed in both the accuracy sense and the probability sense. Numerical examples verify these theoretical findings.

October 31st, Chuanqi Zhang (University of Technology Sydney): The finite group isomorphism problem asks to decide whether two finite groups of order N are isomorphic. Improving the classical $N^{O(\log N)}$-time algorithm for group isomorphism is a long-standing open problem. It is generally regarded that p-groups of class 2 and exponent p form a bottleneck case for group isomorphism in general. The recent breakthrough by Sun (STOC '23) presents an $N^{O((\log N)^{5/6})}$-time algorithm for this group class. Our work sharpens the key technical ingredients in Sun's algorithm and further improves Sun's result by presenting an $N^{\tilde O((\log N)^{1/2})}$-time algorithm for this group class. Besides, we also extend the result to the more general p-groups of Frattini class-2, which includes non-abelian 2-groups. In this talk, I will present the problem background and our main algorithm in detail, and introduce some connections with other research topics. For example, one intriguing connection is with the maximal and non-commutative ranks of matrix spaces, which have recently received considerable attention in algebraic complexity and computational invariant theory. Results from the theory of Tensor Isomorphism complexity class (Grochow--Qiao, SIAM J. Comput. '23) are utilized to simplify the algorithm and achieve the extension to p-groups of Frattini class-2.

November 8th, Borong Zhang (UW-Madison): The inverse scattering problem—reconstructing the properties of an unknown medium by probing it with waves and measuring the medium's response at the boundary—is fundamental in physics and engineering. This talk will focus on how leveraging the symmetries inherent in this problem can significantly enhance machine learning methods for its solution. By incorporating these symmetries into both deterministic neural network architectures and probabilistic frameworks like diffusion models, we achieve more accurate and computationally efficient reconstructions. This symmetry-driven approach reduces the complexity of the models and improves their performance, illustrating how physical principles can inform and strengthen machine learning techniques. Applications demonstrating these benefits will be briefly discussed.

November 15th, Yantao Wu (Johns Hopkins): We consider the problem of estimating the intrinsic structure of composite functions of the type $\mathbb{E} [Y|X] = f(\Pi_\gamma X) $ where $\Pi_\gamma:\mathbb{R}^d\to\mathbb{R}^1$ is the closest point projection operator onto some unknown smooth curve $\gamma: [0, L]\to \mathbb{R}^d$ and  $f: \mathbb{R}^1\to \mathbb{R}^1$ is some unknown  {\it link} function. This model is the generalization of the single-index model where $\mathbb{E}[Y|X]=f(\langle v, X\rangle)$ for some unknown {\it index} vector $v\in\mathbb{S}^{d-1}$. On the other hand, this model is a particular case of function composition model where $\mathbb{E}[Y|X] = f(g(x))$ for some unknown multivariate function $g:\mathbb{R}^d\to\mathbb{R}$. In this paper, we propose an algorithm based on conditional regression and show that under some assumptions restricting the complexity of curve $\gamma$, our algorithm can achieve the one-dimensional optimal minimax rate, plus a curve approximation error bounded by $\mathcal{O}(\sigma_\zeta^2)$. We also perform numerical tests to verify that our algorithm is robust, in the sense that even without some assumptions, the mean squared error can still achieve $\mathcal{O}(\sigma_\zeta^2)$.

Past Semesters