Events

May 12 - May 18, 2024

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  Models, Methods, Applications: HPC in Medicine, Science, Engineering, and AI

  Rolf Krause, Professor, Applied Mathematics and Computational Sciences

  May 14, 16:00 - 17:00

  B3 L5 R5209

  machine learning medicine AI

  Abstract The accurate numerical prediction of complex processes in medicine, science, and engineering requires a well balanced interplay of mathematical models, numerical methods, and scientific software. In this talk, we discuss along different examples from engineering, earth-sciences, and medicine the various challenges in building predictive models. Our focus will be on the algorithmic aspects, i.e. on the numerical methods, -may it be finite elements or neural networks in the context of massive parallelism. We will present in particular parallel preconditioners for non-linear problems
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  Towards trustworthy use of scientific machine-learning in large scale numerical simulations

  Alena Kopanicakova, Researcher, Brown University

  May 13, 09:00 - 10:00

  B9 L3 R3128

  numeric simulations

  Recently, scientific machine learning (SciML) has expanded the capabilities of traditional numerical approaches by simplifying computational modeling and providing cost-effective surrogates. However, SciML models suffer from the absence of explicit error control, a computationally intensive training phase, and a lack of reliability in practice. In this talk, we will take the first steps toward addressing these challenges by exploring two different research directions.

May 5 - May 11, 2024

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  Intracellular "in silico microscopes" - Fully 3D Spatio-Temporal Virus Replication Model Simulations

  Gabriel Wittum, Professor, Applied Mathematics and Computational Sciences

  May 9, 12:00 - 13:00

  B9 L2 H2 H2

  Despite being small and simple structured in comparison to their victims, virus particles have the potential to harm severly and even kill highly developed species such as humans. To face upcoming virus pandemics, detailed quantitative biophysical understanding of intracellular virus replication mechanisms is crucial.
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  Optimization for Deep Learning

  Dr. Konstantin Mischenko, Samsung AI Center, Cambridge, UK

  May 7, 16:00 - 17:00

  B5 L5 R5209

  Deep learning mathematical optimization

  Abstract The field of optimization for machine learning has undergone significant changes in recent years with deep learning models increasing in scale and fine-tuning taking a more prominent role. In this presentation, I will share a perspective on the direction of changes in the field and highlight interesting research directions. I will provide real-world examples of what practitioners want from optimization methods to train deep networks at scale. I will then present my recent work on adaptive methods, such as Adam and Adagrad, and explain how we can estimate the learning rate for these
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  Multigrid Monte Carlo Revisited: Theory and Bayesian Inference

  Professor Robert Scheichl, University of Heidelberg

  May 5, 11:00 - 12:00

  B1 L3 R3119

  Multigrid Monte Carlo

  Abstract The fast simulation of Gaussian random fields plays a pivotal role in many research areas such as Uncertainty Quantification, data science and spatial statistics. In theory, it is a well understood and solved problem, but in practice the efficiency and performance of traditional sampling procedures degenerates quickly when the random field is discretised on a grid with spatial resolution going to zero. Most existing algorithms, such as Cholesky factorisation samplers, do not scale well on large-scale parallel computers. On the other hand, stationary, iterative approaches such as the

Apr 28 - May 4, 2024

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  Non-standard Finite Elements for Eigenvalue Problems

  Linda Alzaben, Ph.D. Student, Applied Mathematics and Computational Sciences

  May 2, 14:00 - 15:00

  B1 L2 R2202

  Numerical approximation of partial differential equations involves parameter dependencies from problem formulation and numerical methods. We focus on two areas: least-squares finite element method with linear elasticity, studying its dependence on the Lamé parameter, and the Virtual Element Method, known for handling complex geometries where the stabilization parameter is analyzed.
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  Statistical Deep-Learning for Spatiotemporal Extremes

  Raphaël Huser, Associate Professor, Statistics

  May 2, 12:00 - 13:00

  B9 L2 H2 H2

  Rare, low-probability events often lead to the biggest impacts. Therefore, the development of statistical approaches for modeling, predicting and quantifying environmental risks associated with natural hazards is of utmost importance. In this seminar, I will show how statistical deep-learning methods can help solve challenges that arise when modeling complex and massive spatiotemporal extremes data.
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  Virtual Element Approximation of Eigenvalue Problems

  Prof. Francesca Gardini, Università di Pavia

  Apr 30, 16:00 - 17:00

  B1 L3 R3119

  Virtual Element Method Elgenvalue FEMSimulation PDE

  We will discuss the solution of eigenvalue problems associated with partial differential equations (PDE)s that can be written in the generalised form Ax = λMx, where the matrices A and/or M may depend on a scalar parameter. Parameter dependent matrices occur frequently when stabilised formulations are used for the numerical approximation of PDEs. With the help of classical numerical examples we will show that the presence of one (or both) parameters can produce unexpected results.
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  A Free Boundary Problem for Accretive Growth

  Katerina Nik, Postdoc, Applied Mathematics and Modelling Group, University of Vienna

  Apr 28, 09:00 - 10:00

  B9 L3 R3128

  Growth is a fundamental process in biological systems and various technological applications, including epitaxial deposition and additive manufacturing. The interaction between growth and mechanics in deformable bodies leads to a wealth of very challenging mathematical questions. I will give a short overview of the key concepts of morphoelasticity, namely, the theory of elastic deformations in growing bodies.

Apr 14 - Apr 20, 2024

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  Traveling wave solutions of Reaction-Diffusion equation in Biological mathematics

  Hoyoun Kim, Postdoctoral Research Fellow, Applied Mathematics and Computational Sciences

  Apr 18, 12:00 - 13:00

  B9 L2 H2 H2

  Traveling wave solutions of reaction-diffusion systems have been studied to explain wave propagation phenomena in biological organisms.
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  Neural Operators: Theory, Architecture, and Applications for PDEs

  Xinliang Liu, Postdoctoral Research Fellow, Applied Mathematics and Computational Sciences

  Apr 16, 16:00 - 17:00

  B1 L3 R3119

  Neural Operator Multigrid

  Abstract Neural operator methods provide a novel approach for solving or learning the complex mappings from parameters to solutions arising from intricate physical systems. In this talk, I will cover the foundational aspects of neural operators, encompassing both theoretical frameworks and algorithmic developments, including some well-known neural operator architectures. Additionally, I will share our recent work on applying the neural operator method to multiscale partial differential equations (PDEs). To tackle the challenges of multiscale PDEs, we have developed a neural operator with a

Mar 31 - Apr 6, 2024

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  A Correlated Three-Dimensional Integral Fractional Ornstein-Uhlenbeck Process Model for Animal Movement

  Jose Hermenegildo Ramirez Gonzalez, Postdoctoral Research Fellow, Statistics

  Apr 4, 12:00 - 13:00

  B9 L2 H2 H2

  Predicting the paths of animals poses a significant challenge, given the intricate nature of their behaviors, the impact of unpredictable environmental elements, individual differences, and the scarcity of precise data on their movements.

Mar 24 - Mar 30, 2024

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  Classification of time series in high dimensions

  Sarbojit Roy, Postdoctoral Research Fellow, Statistics

  Mar 28, 12:00 - 13:00

  B9 L2 H2 H2

  As more and more modern time series data sets are becoming high dimensional, the problem of classification in this context has received increasing attention. We propose a statistical framework for classifying multivariate stationary Gaussian time series where the number of covariates, the length of the series, and the sample size, all grow to infinity.
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  Hessian-dependent Functionals: Mean Field Games, Free Boundaries and Improved Regularity

  Prof. Edgard Pimentel, Department of Mathematics of the University of Coimbra

  Mar 26, 16:00 - 17:00

  B2 L5 R5220

  Hessain-dependent elasticity mean-field games Free Boundaries viscous

  Hessian-dependent functionals play a pivotal role in a wide latitude of problems in mathematics. Arising in the context of differential geometry and probability theory, this class of problems find applications in the mechanics of deformable media (mostly in elasticity theory) and the modelling of slow viscous fluids. We study such functionals from three distinct perspectives.

Mar 17 - Mar 23, 2024

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  Tracking rare events within the ensemble Kalman filtering

  Gaukhar Shaimerdenova, Ph.D. Student, Applied Mathematics and Computational Sciences

  Mar 21, 12:00 - 13:00

  B9 L2 H2 H2

  In this work, we employ importance sampling (IS) techniques to track a small over-threshold probability of a running maximum associated with the solution of a stochastic differential equation (SDE) within the framework of ensemble Kalman filtering (EnKF).
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  Crafting Artificial Material Marvels: Innovative Modeling Techniques for Exotic Designs

  Ying Wu, Professor, Applied Mathematics and Computational Sciences

  Mar 19, 16:00 - 17:30

  B9 L2 H2

  Artificial materials represent composite media that can be meticulously engineered to exhibit unique wave propagation behaviors. Our research endeavors are driven by the intriguing principles underlying these materials, such as effective models, and their broad applications, including perfect absorption. In this presentation, I will outline our recent advancements in our innovative design strategies for novel artificial materials from both forward first-principle physics-based modeling and data-driven approaches. Specifically, I will highlight our pioneering work in the designs of double-zero-index materials for both electromagnetic and acoustic waves. Additionally, I will discuss our discovery of the acoustic Purcell effect for enhanced emission, as well as our development of analytic and numerical solutions for space-time modulated wave systems. Furthermore, I will delve into our practical solution for achieving broad frequency cloaking of invisibility. These accomplishments hold significant promise for a wide range of applications spanning sound control, communication, sensing, imaging and more.

Mar 10 - Mar 16, 2024

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  Randomized quasi-Monte Carlo and Owen's boundary growth conditions: A spectral analysis

  Yang Liu , Postdoctoral Research Fellow, Applied Mathematics and Computational Sciences

  Mar 14, 12:00 - 13:00

  B9 L2 H2 H2

  In this work, we analyze the convergence rate of randomized quasi-Monte Carlo (RQMC) methods under Owen's boundary growth condition [Owen, 2006] via spectral analysis.
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  Mathematics and health: a model of the glucose-insulin system for estimating the glycaemic index of food

  Fabio Credali, Postdoc at IMATI, Pavia

  Mar 12, 14:30 - 15:30

  B1 L4 seaside R4214

  In 2019, diabetes caused 1.5 million global deaths, with 48% occurring before age 70. While Type 1 diabetes strongly depends on genetic components and is usually diagnosed in childhood, Type 2 diabetes is primarily caused by long term consumption of high calories foods. Lifestyle choices significantly influence the risk of Type 2 diabetes and obesity, including energy intake, diet composition, physical activity, and smoking.

Mar 3 - Mar 9, 2024

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  Acoustics with a spin: A new paradigm for acoustic metamaterials, scattering, and propagation of sound

  Mohamed D. Farhat, Research Scientist, Waves in Complex Media

  Mar 7, 12:00 - 13:00

  B9 L2 H2 H2

  When pressure acoustic waves interact with rotating scatterers, they undergo peculiar and intriguing characteristics. In this talk, I will discuss our recent findings on the physics of acoustic scattering and propagation in spinning fluids.
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  WAN Approximation of PDEs: Best Approximation, Stabilization and Boundary Conditions

  Prof. Silvia Bertoluzza

  Mar 5, 16:00 - 17:00

  B2 L5 R5209

  WAN PDE approximation Stabilization Boundary Dirichlet

  We present a theoretical analysis of the Weak Adversarial Networks (WAN) method, recently proposed in [1, 2], as a method for approximating the solution of partial differential equations in high dimensions and tested in the framework of inverse problems. In a very general abstract framework.

Feb 25 - Mar 2, 2024

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  Quadratic Forms in Gaussian Random Variables: A Survey of Theoretical Results and Applications

  Mohanad Ahmed, Research Specialist, Information Science Lab

  Feb 29, 12:00 - 13:00

  B9 L2 H2 H2

  Quadratic Forms in Gaussian Random Variables (QFGRV) appear in a wide variety of applications in signal processing, communications, performance and reliability engineering, genetics, etc.
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  Critical Phenomena in Financial Markets and Social Networks

  Prof. Christof Schmidhuber, ZHAW School of Engineering

  Feb 27, 16:00 - 17:00

  B9 L2 R2322

  Financial Market Social Network Analysis Critical Phenomena Arbitrageurs

  Analogies between financial markets and critical phenomena have long been observed empirically. So far, no convincing theory has emerged that can explain these empirical observations. Here, we take a step towards such a theory by modeling financial markets as a lattice gas.

Feb 11 - Feb 17, 2024

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  Fuzzy clustering of circular time series based on a new distance with applications to wind data

  Ángel López Oriona, Postdoctoral Research Fellow, Statistics

  Feb 15, 12:00 - 13:00

  B9 L2 H2 H2

  Time series clustering is an essential machine learning task with applications in many disciplines. While the majority of the methods focus on time series taking values on the real line, very few works consider time series defined on the unit circle, although the latter objects frequently arise in many applications. In this talk, the problem of clustering circular time series is discussed.
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  Local flex markets from theory to practice: the UK landscape and international experiences

  Jason Avramidis, Director of Innovation and International Flexibility Markets for OakTree Power, UK

  Feb 13, 12:00 - 13:00

  B1 L4 R4214

  Until very recently, distribution-led local flexibility markets were exclusively an academic endeavor, with few practical applications, mostly limited to small-scale innovation projects. However, with European regulation finally catching up with the realities of modern distribution networks, local flexibility markets are slowly becoming a reality - new ones popping up across the continent, or some even becoming a BAU option in the most advanced countries.
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  Model hierarchies in semiclassical semi-relativistic quantum models: From Dirac-Maxwell to Euler-Poisson

  Professor Norbert J Mauser, Mathematics, University of Vienna

  Feb 11, 16:00 - 17:00

  B1 L3 R3119

  The Pauli-Poisswell equation models fast-moving charges in semiclassical semi-relativistic quantum dynamics. It is at the center of a hierarchy of models from the Dirac-Maxwell equation to the Euler-Poisson equation that is linked by asymptotic analysis of small parameters such as the Planck constant or inverse speed of light. We discuss the models and their application in plasma and accelerator physics as well as the many mathematical problems they pose

Feb 4 - Feb 10, 2024

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  Dependence and Causality in Functional Brain Networks

  Hernando Ombao, Professor, Statistics

  Feb 8, 12:00 - 13:10

  B9 L2 H2 H2

  Brain activity over the entire network is complex. A full understanding of brain activity requires careful study of its multi-scale spatial-temporal organization. Motivated by these challenges, we will explore some characterizations of dependence between components of a multivariate time series and then apply these to the study of brain functional connectivity.
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  Matrix-free Monolithic Multigrid Methods for Stokes and Generalized Stokes Problems

  Prof. Ulrich Langer, Institute of Numerical Mathematics, Johannes Kepler University, Linz

  Feb 7, 16:00 - 17:00

  B2 L5 R5209

  stokes equation

  We consider the widely used continuous $Q_{k+1}-Q_k$ quadrilateral or hexahedral Taylor-Hood elements for the finite element discretization of the Stokes and generalized Stokes systems in two and three spatial dimensions.
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  Fast Solution Methods for Wave Propagation Problems: From Classical Domain Decomposition Solvers to Learning

  Prof. Dr. Victorita Dolean, Mathematics and Computer Science, Scientific Computing, TU Eindhoven

  Feb 6, 16:00 - 17:00

  B2 L5 R5220

  wave propagation numerical methods

  Wave propagation and scattering problems are of huge importance in many applications in science and engineering - e.g., in seismic and medical imaging and more generally in acoustics and electromagnetics.
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  Diffusion with Heterogeneous Persistence and Permeability

  Prof. Yong-Jung Kim, KAIST, Korea

  Feb 6, 14:00 - 15:30

  B2 L5 R5209

  A subtle difference in a diffusion model can lead to an opposite conclusion. We need to understand how each component involved in the diffusion phenomenon contributes to the diffusion model. In this talk, we will discuss how nonconstant persistence and permeability play a role in the diffusion phenomenon.
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  Recent advances in doubly nonlinear equations

  Professor Vincenzo Vespri, of Mathematics Department at the University of Florence, Italy

  Feb 5, 16:00 - 17:00

  B1 L3 R3119

  The term doubly nonlinear refers to the fact that the diffusion part depends nonlinearly both on the gradient and the solution itself. Such equations describe several physical phenomena and were introduced by Lions and Kalashnikov. These equations have an intrinsic mathematical interest because they represent a natural bridge between the more natural generalizations of the heat equation: the p-Laplacian and the porous medium equation.

Jan 28 - Feb 3, 2024

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  Think globally, act locally: from domain decomposition to nonlinear model order reduction

  Prof. Charbel Farhat

  Jan 30, 14:00 - 15:00

  KAUST Auditorium R2030

  Abstract The Finite Element Tearing and Interconnecting (FETI) methodology is a family of domain decomposition (DD)-based iterative methods for the fast solution on massively parallel processors of large-scale systems of equations arising from finite element (FE) spatial approximations. Developed in its basic form in 1991, it has been extended and refined during 18 years to enable ever faster and more accurate analyses of a broad range of engineering and pathfinder systems such as re-entry vehicles, modern aircraft, advanced Formula 1 cars, aircraft carriers, underwater systems, electronic

Jan 21 - Jan 27, 2024

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  On space-time models: models and applications

  Elias Teixeira Krainski, Postdoctoral Research Fellow, Statistics

  Jan 25, 12:00 - 13:00

  B9 L2 H2 H2

  Partial differential equations are a mathematical tool widely used to model phenomena in several different fields. A stochastic partial differential equation (SPDE) introduces random forcing to take the nature of real-world observations.
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  A Posteriori Error Estimation and Adaptivity for Elliptic Interface Problems

  Prof. Zhiming Chen, Academy of mathematics and Systems Science, Chinese Academy of Sciences

  Jan 24, 14:30 - 16:00

  B4 L5 R5220

  adaptive methods linear elliptic equations

  In this short course, we will introduce some elements in deriving the hp a posteriori error estimate for a high-order unfitted finite element method for elliptic interface problems. The key ingredient is an hp domain inverse estimate, which allows us to prove a sharp lower bound of the hp a posteriori error estimator.
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  Arbitrarily High-order Finite Element Methods for Arbitrarily Shaped Domains with Automatic Mesh Generation

  Prof. Zhiming Chen, Academy of Mathematics and Systems Science, Chinese Academy of Sciences

  Jan 23, 16:00 - 17:00

  B2 L5 R5220

  High-order FEM adaptive methods

  Coffee time: 15:30–16:00. We consider high-order unfitted finite element methods on Cartesian meshes with hanging nodes for elliptic interface problems, which release the work of body-fitted mesh generation and allow us to design adaptive finite element methods for solving curved geometric singularities.
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  Scalable demand response of decentralised assets: A perspective on reinforcement learning as a control paradigm

  Prof. Bert Claessens, Ghent University, Belgium

  Jan 22, 13:00 - 14:00

  B3 L5 R5209

  In the last decade reinforcement learning has demonstrated tremendous progress in terms of being a model-free control paradigm for decision making in complex systems with uncertainty and partial observability, thus making it a candidate technology for demand response with a promise of true scalability.

Dec 3 - Dec 9, 2023

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  Multilevel Monte Carlo for a class of Partially Observed Processes in Neuroscience

  Dec 7, 12:00 - 13:00

  B9 L2 H2

  In this talk, we consider Bayesian parameter inference associated to a class of partially observed stochastic differential equations (SDE) driven by jump processes. Such type of models can be routinely found in applications, of which we focus on the case of neuroscience.
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  A Brief History of Artificial Intelligence: Its Past and Its Future

  Dr. Jeffrey M. Bradshaw, Institute for Human and Machine Cognition (IHMC), Florida, USA

  Dec 6, 14:00 - 15:00

  B1 L4 R4102

  Over the past decades, Jeff has been lucky enough to follow some of these developments from a front-row seat. He will share selected perspectives on current and past research including the various pendulum swings over the years between extremes, such as expertise-based knowledge engineering vs. data-centric machine learning, autonomous vs. mixed-initiative systems, publicly available chatbot capabilities vs. personalized, policy-governed multi-agent systems. In this talk, I will show what past research in AI has to teach us about the future.
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  Nonlinear energy stability for phase-field models: Numerics and analysis

  Prof. Tao Tang

  Dec 5, 16:00 - 17:00

  B5 L5 R5209

  phase-field models

  Coffee Time: 15:30 - 16:00. The phase-field model, a powerful modeling tool for dealing with interface problems, has been widely used in various fields such as computational physics, computational biology, materials engineering, and even image processing. The dissipation of free energy is an important and fundamental property of the phase-field model.
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  Error Estimates for Deep Learning Methods in Fluid Dynamics

  Professor, Suleyman Ulusoy, School of Arts and Sciences, American University of Ras Al Khaimah

  Dec 5, 14:30 - 15:30

  B1 L4 R4214

  We provide error estimates and stability analysis of deep learning techniques for certain partial differential equations including the incompressible Navier-Stokes equations. In particular, we obtain explicit error estimates (in suitable norms) for the solution computed by optimizing a loss function in a Deep Neural Network approximation of the solution, with a fixed complexity. This is a joint work with A. Biswas and J. Tian.
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  Gradient Estimates for weak solutions of Elliptic PDE's - Seminar

  Giuseppe Di Fazio, Professor, Mathematics and Computer Sciences, University of Catania, Italy

  Dec 5, 13:00 - 14:00

  B1 L4 R4214

  Let us consider an elliptic equation of second order in variational form i.e. div(A(x)∇u) = divf in a bounded domain Ω ⊂ Rn where the function f belongs to some suitable function space.
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  Nonlinear stability of splitting methods for Cahn-Hilliard equations

  Prof. Tao Tang's personal website

  Dec 4, 15:30 - 17:00

  B3 L5 R5220

  nonlinear stability splitting methods Cahn-Hilliard equations

  Splitting methods have been shown to a useful tool in solving phase field equations. However, rigorous nonlinear stability analysis has not been available. In this short course, we will discuss some recent development in this direction.
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  Splitting methods: merits and pitfalls

  Prof. Alexander Ostermann

  Dec 3, 16:00 - 17:00

  B2 L5 R5220

  splitting methods numerical integration computational efficiency pitfalls

  Coffee Time: 15:30 - 16:00. Splitting methods are a well-established tool for numerically integrating time-dependent partial differential equations. These methods split the vector field into disjoint components, which are integrated separately using an appropriate time step. The individual flows are then combined to obtain the desired numerical approximation.

Nov 26 - Dec 2, 2023

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  Discretization and Optimization in Applied Geometry

  Nov 30, 12:00 - 13:00

  B9 L2 H2

  Many problems in applied geometry amount to the solution of a typically nonlinear partial differential equation. We will discuss why it may not be a good idea to discretize the equation, but to take the viewpoint of discrete differential geometry and discretize the theory.
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  Symmetry and Beyond

  Prof. Jiping Zhang

  Nov 29, 15:00 - 16:00

  B3 L5 R5220

  symmetry groups symmetric polynomials monstrous moonshine

  A fascination with symmetric forms seems to be an innate feature of human perception and for millennia it has influenced art and natural philosophy. The concept of symmetry is one of the very few on which mathematicians and physicists agree, namely that Symmetry ≡ Groups. We describe some special symmetries and related problems including symmetric polynomials and monstrous moonshine.
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  Basic Algebraic Structures

  Prof. Efim Zelmanov

  Nov 29, 14:00 - 15:00

  B3 L5 R5220

  Structures Galois

  We will give an overview of the development of Abstract Algebra from Galois to our time. The talk will be accessible to general audience with basic mathematical background.
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  Numerical approximation of PDEs on complex geometries: fluid-structure interaction problems and virtual element methods

  Fabio Credali, Postdoctoral Research Fellow, Applied Mathematics and Computational Sciences

  Nov 28, 16:30 - 18:30

  KAUST

  The studies in numerical approximation of partial differential equations are characterized by the necessity of managing complex geometries and their discretization. We focus our attention on two different fields where complex geometries are very common: the mathematical modeling of fluid-structure interaction problems and the family of virtual element methods.

Nov 19 - Nov 25, 2023

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  Efficient Inference for Joint Models of Multivariate Longitudinal and Survival Data Using INLAjoint

  Denis Rustand, Postdoctoral Research Fellow, Statistics

  Nov 23, 12:00 - 13:00

  B9 L2 H2

  Clinical research often requires the simultaneous study of longitudinal repeated measurements and time-to-event (i.e., survival) data. Joint models, which can combine these two types of data, are invaluable tools in this context.

Nov 12 - Nov 18, 2023

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  Multiscale Learning of High-dimensional Cell Fate

  Prof. Qing Nie, Department of Mathematics, Department of Developmental and Cell Biology, NSF-Simons Center for Multiscale Cell Fate Research, University of California, Irvine

  Nov 16, 15:30 - 17:00

  B9 L4 R4225

  Abstract Cells make fate decisions in response to dynamic environments, and multicellular structures emerge from multiscale interplays among cells and genes in space and time. The recent single-cell genomics technology provides an unprecedented opportunity to profile cells for all their genes. While those measurements provide high-dimensional gene expression profiles for all cells, it requires fixing individual cells that lose many important spatiotemporal information. Is it possible to infer temporal relationships among cells from single or multiple snapshots? How to recover spatial
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  How do periodic structures affect nonlinear waves?

  David Ketcheson, Professor, Applied Mathematics and Computational Sciences

  Nov 16, 12:00 - 13:00

  B9 L2 H2

  We are all familiar with the tendency of water waves to break in shallow water, for instance at the beach. Indeed, breaking is a universal behavior of solutions to first-order nonlinear hyperbolic PDEs, and manifests itself in phenomena ranging from traffic jams to shock waves.
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  Tensor-train Methods for Partial Differential Equations and its application to a Neutron Transport Problem

  Daniele Boffi, Associate Dean for Faculty, Computer, Electrical and Mathematical Sciences and Engineering

  Nov 14, 15:30 - 17:00

  B9 L4 R4225

  Partial Differential Equations

  Tensor network techniques are known for their ability to approximate low-rank structures and beat the curse of dimensionality. They are also increasingly acknowledged as fundamental mathematical tools for efficiently solving high-dimensional Partial Differential Equations (PDEs). In this talk, we present a novel method that incorporates the Tensor Train (TT) and Quantized Tensor Train (QTT) formats for the computational resolution of time-independent Boltzmann Neutron Transport equations (BNTEs) in Cartesian coordinates.