Clarkson University
Guangming Yao
Division of Math and CS
Clarkson University
Office: SC 363
Office Phone: (315)268-6496
About Me Teaching Publications Research Interests Activities Students Useful Links
Stochastic Differential Equations(May 31, 2021--July 23, 2021)
Reading:
1. Introduction to Stochastic Processes by Gregory Lawler
2. An Introduction to Stochastic Differential Equations by LC Evans
4. Numerical treatment of stochastic differential equations, SIAM Journal on Numerical Analysis
5. Snifferes, buzzers, toggles and blinkersL dynamics of regulatory and signaling pathways in the cell, Current Opinion
Week 1, May 31 -- June 4
Responsible Conduct of Research Training (CITI)
Disbursement Order Form
Small group zoom meeting @10am daily
Big group zoom meeting @1pm on Tuesday
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Review Paper #8, here is the published version of paper #8
Good reference on stocahstic calculus: Book #2
Good reference on stocahstic calculus: Module 1 (~50 min), Course on Asset Pricing , Prof. John H Cochrane, Stanford University
Good reference on stocahstic process: MIT Open Courseware: Advanced Stochastic Processes , Prof. David Gamarnik, MIT
NSF REU on HPC in Engineering Weekly Group Meeting: Intro. to research process Friday, 1PM--3PM
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Weekly Seminar @ 11am on Thursday: Jonathan Doane, Binghamton University (Graduate Student, REU Alumnus, 2013), Studying algebra via logic
Abstract: Universal algebra is the study of sets equipped with finitary operations; these are called ``algebras.'' E.g., a group is (G;*,-1,1) with binary multiplication, unary inversion, and nullary identity. But wait, groups are required to satisfy certain axioms, right? As it turns out, classes of algebras which are closed under homomorphisms, subalgebras, and products, correspond with classes of algebras given by an axiomatization. Through this correspondence, we can study algebraic classes by instead studying their axiomatizations! In this talk, we will work through a specific, unusual example.
Week 2, June 7 -- June 11
Small group zoom meeting @10am daily
Big group presentation @1pm on Friday
How to install missing modules automatically on PyCharm Preferences-->Show Import Popup-->show import opup
Presentation by Dr. Han on May 9, 2018
Game Night with HPC Group,, Wednesday, 7PM--9PM, Organizer: 2021 NSF REU on HPC in Engineering
Weekly Seminar @ 10am on Tuesday: Dr. Jiequn Han, Instructor, Dept. of Math, Princeton University
Title: Deep BSDE Method for High-Dimensional PDEs & Games
Abstract: Developing algorithms for solving high-dimensional partial differential equations, controls, and games has been an exceedingly difficult task for a long time, due to the notorious "curse of dimensionality". In this talk, I will introduce the Deep BSDE method for solving high-dimensional parabolic PDEs. The algorithm builds on the reformulation of backward stochastic differential equations and utilizes deep neural networks as efficient approximators to unknown high-dimensional components. Numerical results of various examples, including multi-agent games, demonstrate the efficiency and accuracy of the proposed algorithms in high-dimensions. If time permits, I will introduce some convergence analysis of the Deep BSDE method in terms of a posteriori error estimation and an upper bound for the minimized objective function.
Dr. Jiequn Han is an Instructor at the Department of Mathematics, Princeton University. His research draws inspiration from various disciplines of science and is devoted to solving high-dimensional problems arising from scientific computing. His current research interests mainly focus on solving high-dimensional partial differential equations and machine learning based-multiscale modeling.
Weekly Seminar @ 11am on Thursday: Dr. Chunlei Liang, Professor, Mechanical & Aeronautical Eng, Clakrson Universoity
Title: When the Navier-Stokes Equations Meet Complex Geometries
Abstract: When the Navier-Stokes equations meet complex geometries, they can reveal complex flow physics happening in real life. Professor Liang develops computational methods to solve the Navier-Stokes equations iteratively on parallel computers and simulate many complex physical phenomena. These computer solutions can simulate unsteady flows around flapping wings, turbulence around wind turbines, and interior hydrodynamics in the sun. Professor’s research aims to help engineering design and advance predictive science to better understand nature.
Professor Chunlei Liang joined Clarkson University in 2019. He received his PhD from University of London. His research interests include computational fluid dynamics, computational heat transfer, and computational magnetohydrodynamics. He received an ONR Young Investigator Program award in 2014, an NSF CAREER Award in 2016, and a PECASE award in 2019. He is an associate editor of the ASME Journal of Fluids Engineering and an editorial board member of Computers & Fluids, an Elsevier journal.
Week 3, June 14 -- June 18
Goal of this week
A more theoretical paper on BSDE--Parabolic PDE STRONG-VISCOSITY SOLUTIONS: CLASSICAL AND PATH-DEPENDENT PDEs
A reference on BSDE--Nonlinear Parabolic PDE from 1997 Probabilistic interpretation AIHPB_1997
A reference on semilinear Parabolic PDE Semilinear parabolic problems
4. Game Night with HPC Group,, Wednesday, 7PM--9PM, Organizer: 2021 NSF REU on HPC in Engineering
5. Weekly Seminar @ 11am on Thursday: Dr. John Maharry (graph theory), Professor, Ohio State University
Title: Flexibility of Embeddings on Surfaces using Graph Structures
Abstract: There are many natural questions about graphs and how they embed on various surfaces. Does a graph embed on a given surface? Is that embedding 'unique'? If not, how are distinct embeddings related? What surface operations can reembed a graph? Many of these questions are still wide open, but the theorems that are known depend strongly of various 'structures' within the graphs. These concepts include ideas of connectivity, minor containment, and face-width. We will give some examples and main ideas of how these structures can be used to describe the flexibility of graph embeddings on surfaces like the plane, the projective plane, the Torus and the Klein bottle.
6. Math Jeopardy! (Trivia Game) 6PM--7Pm on Thursday
Week 4, June 21 -- June 25
Goal of this week
0. A good reference on SDE and parabolic PDE: Pardoux, Etienne, and Shanjian Tang. "Forward-backward stochastic differential equations and quasilinear parabolic PDEs." Probability Theory and Related Fields 114.2 (1999): 123-150.
1. Keep reading the reference on Machine Learning #3 from last week
2. Keep adding examples to the BSDE solver.
3. Prepare for group talk at 11AM on Friday, join the meeting here.
4. Deep Learning and Reinforcement Learning Summer School, Toronto 2017
5. Monte Carlo Methods for Solving the Boltzman Ttransport Equations
6. Seminar on Thursday @11am by Dr. Brandt Kronholm on Partition Theory, Join the seminar here, Abstract
Week 5, June 28 -- July 2
3. Modify the code so it works for 1D
4. Modify the code so it works for estimations in a region
5. Weekly Seminar @ 11am on Tuesday: Rachael Poyar (NSA)
Title: The Secret Lives of Mathematicians
Abstract: Mathematics can be more than just a subject in school; it can be a career. The government is the number one single employer of mathematicians in the country. Many of those mathematicians end up at the National Security Agency (NSA), where they find careers in research, cybersecurity, and cryptanalysis. This talk will be an introduction to the roles of mathematicians at NSA, as well as basics of cryptography.
Bio: Rachael Poyar: Rachael is a team lead in Cryptographic Algorithm Evaluation at the National Security Agency. In her job, she works with mathematicians, computer scientists, and men and women of many talents to analyze and improve the security of the nation through understanding and evaluating cryptography. Rachael has worked at the NSA since 2012, beginning her career in the Cryptanalysis Development Program, gaining experience in signals analysis, reverse engineering, data analysis, and programming. She has taught short courses at the agency in Voice over Internet Protocol technologies and cryptographic hashes. She has also served in officer roles in the Women in Mathematics Society, a group at NSA committed to enhancing the agency as a workplace that is welcoming to a diverse group of mathematicians, and she helps with recruitment and interviewing. Rachael has a Bachelor's degree in Mathematics and Religion from Moravian College, a M.S. in Mathematics from the University of Delaware, and a M.Ed. from the University of Delaware in Education.
6. Weekly Seminar @ 11am on Thursday: Emily Stark, Wesleyan University
Title: The space at infinity
Abstract: Understanding the relationship between a space's geometry and its symmetries is a natural, foundational mathematical aim. The geometry and symmetries of the Euclidean plane are very familiar to us: the interior angles of every triangle add to 180 degrees; two lines that start parallel to each other remain parallel forever; polygons with four right angles exist; there are translations in every direction, and so on. However, not every geometry behaves in this way. For example, the geometry of a sphere is quite different. This talk will be an introduction to the vast universe of non-Euclidean geometries and one important tool used to study them: the boundary at infinity.
Week 6, July 5 -- July 9
4. Try to solve Equation (69) on page 544
6. Weekly Seminar on Thursday, Dr. Edward Kansa, Convergent Solutions
Title: An overview of meshless radial basis functions and their applications
Abstract: Early analog and digital computers were extremely limited in available memory computational speed. Therefore, numerical algorithms to solve ordinary differential equations (ODEs), partial differential equations (PDEs) as well as integral equations (IEs) were quite primitive. These algorithms were the finite difference, finite element, and finite volume methods that were founded on low order polynomial methods to avoid higher order polynomial snaking. Although there were theorems proven that in the limit,1` these local methods converge to the exact problem, the main conundrum is that one cannot go to the limit on existing computers. These primitive methods contaminate the numerical results unphysical. In contracts, there are higher order continuously differential basis functions such as sine functions or rational polynomials that can duplication sophisticated structures such as finite discontinuities. Not all basis functions can replicate a test function with a minimal number of basis functions. Continuously differentiable radial basis functions that are exponentially or spectrally convergent, do not require a mesh, can approximate functions in n-dimensional space (ℜn), and are pre-wavelets (non-orthonormalized), converge faster when the space dimension increases. By solving for the expansion coefficients, from a small number of samplings, a wide variety of approximation, interpolation, ODEs, PDEs, and IEs are solved numerically with great accuracy. Because these basis functions are so flexible, there are thousands of journal articles published l=illustrating their power.
Week 7, July 12 -- July 16
Week 8, July 19 -- July 23