Dr.Varvara Roubtsova
​Institut de recherche d'Hydro-Québec

​Friday December 4 2015
10:30am in MC5479

Title: ​SiGran: A 3D virtual laboratory for mechanics of granular media

Abstract: The study of soil stability under water flow is a complex problem in geotechnical field. Phenomena such as liquefaction, internal and external erosion are the result of interaction of soil particles with water flow. A virtual laboratory has been developed to help understand these processes at a micro scale.  Codes for the virtual laboratory are based on coupling of two well-known methods: Discrete Element Method (DEM), which simulates particle movement using Newton’s laws, and Marker-And-Cell (MAC), which models the transient viscous water flows by solving the complete Navier-Stokes equations. 

Special algorithms for 2D and 3D approach were developed in order to create virtual samples of soil with given porosity and particle-size distribution (PSD). The first one is based on a fractal model and the second one  on the real process of particles falling under gravity. A special technique to trace the streamlines was developed to compute the 
tortuosity in porous media. On the other hand, the full equilibrium of internal and external forces in a shear box and the equilibrium of work of external force vs variation of internal energy is presented.

The OpenCL framework was used in order to achieve a high level of data parallelism on NVIDIA Graphics Processing Units (GPU) based Tesla High Performance Computing (HPC) hardware.

Ongoing comparison of results obtained by simulation with theoretical and experimental data was carried out during development of the virtual laboratory. The most interesting results presented include the study of particles interaction in viscous fluids, testing permeability, influence a canal width on particle drag force and others.

Dr. E. Bruce Pitman
State University of New York

E. Bruce Pitman

Friday, November 27, 2015
Location: MC 5417
Time: 3:30 p.m. refreshments, talk starts at 4 p.m.

Title: Where Are You Going To Go When The Volcano Blows?
Abstract: We discuss one approach to determining the hazard threat to a locale due to a large volcanic avalanche. The methodology employed includes large-scale numerical simulations, field data reporting the volume and runout of flow events, and a detailed statistical analysis of uncertainties in the modeling and data. The probability of a catastrophic event impacting a locale is calculated, together with a estimate of the uncertainty in that calculation. By a careful use of simulations, a hazard map for an entire region can be determined.The calculation can be turned around quickly, and the methodology can be applied to other hazard scenarios.

Dr. Jacques Carette
McMaster University

Jacques Carette

Thursday, October 29, 2015
Location: MC 5501
Time: 2:30 p.m. refreshments, talk starts at 3 p.m.

Title: Beyond graphics - more mathematics of building video games

Abstract: As expected, graphics pipelines and physics engines are replete with mathematics. But there is much more applicable mathematics to the building of video games. In this talk, I will outline applications of mathematics to optimal construction of UI layout, analysis of "good game-design principles", shaping sound, and player modelling. If time permits, some soon-to-happen research in my G-ScalE lab will be outlined that finds more applications of mathematics to the construction of video games.

Proximal Thresholds of PLQ Functions

Dr. Warren Hare
University of British Columbia

Warren Hare

Thursday, October 1, 2015
Location: MC 5479
Time: 2:30 p.m. refreshments, talk starts at 3 p.m.

Abstract: Introduced in the 1960s, the Moreau envelope has grown to become a key tool in nonsmooth analysis and optimization. An important aspect in applying the Moreau envelope to nonconvex functions is determining the "prox-threshold'" of the function. In this talk, we seek to understand the prox-thresholds of piecewise linear-quadratic (PLQ) functions (a function made of linear and quadratic pieces). We provide several examples to illustrate the techniques and challenges.

This talk is targeted at a general mathematical audience. A background that includes multivariate calculus (gradients, Hessians) and matrix algebra (determinants, eigenvalues) is all that will be required.

Polynomial equations usually describe nice varieties

Dr. Joachim von zur Gathen
Bonn-Aachen International Center for Information Technology

Joachim von zur Gathen

Thursday, September 10, 2015
Location: MC 5479
Time: 3:30 p.m. refreshments, talk starts at 4 p.m.

Abstract: We consider systems of multivariate polynomials and the variety V that they define.

Fixing the number of variables, the number of polynomials and the sequence of degrees, these systems form a linear space. We ask: when is V nice? Is that usually the case?

"Nice" can refer to various properties:

  • The system is regular, so that no polynomial is a zero divisor modulo the previous ones.
  • V is a set-theoretic complete intersection.
  • V is an ideal-theoretic complete intersection.
  • V is absolutely irreducible.
  • V is nonsingular.
  • V is non-degenerate (not contained in a hyperplane).

All but the last property usually hold. More precisely, for each of them we present a nonzero obstruction polynomial in the coefficients of the system so that the property holds when the obstruction does not vanish.The obstructions come with explicit bounds on their degrees.

If the system is defined over a finite field, this leads to estimates on the probability for the properties to hold. These tend to 1 with growing field size.

Somewhat surprisingly, the last property behaves differently. Fixing the degree of V, most systems (with at least two polynomials) describe varieties that are hypersurfaces in some proper linear subspace.

Joint work with Guillermo Matera.

Deep Learning and its Challenges for Technical Computing

By Graham Taylor, Assistant Professor at School of Engineering and Leader of the Machine Learning Research Group at University of Guelph

Graham Taylor

Tuesday, April 7, 2015
Location: DC 1304
Time: 3:30 - 4:30 p.m.

Abstract: A central challenge in visual reasoning is that of untangling the many factors of variation that explain an image or video. Photometric and geometric "nuisance" factors are intertwined with the variables of interest, for example, object identity in recognition tasks. To date, the dominant methodology for addressing this challenge has been to engineer a feature extraction pipeline, usually containing multiple stages of processing. An alternative approach is "Representation Learning": relying on the data, instead of feature engineering to learn representations that are invariant to nuisance factors. Techniques that learn multiple layers of representation, which are referred to as "Deep Learning", have demonstrated not only impressive success in recent benchmarks and competitions but applicability to multiple domains. In this talk, I will review the foundations of Deep Learning with an emphasis on computer vision applications. I will also highlight the challenges the field brings to technical computing and the opportunities that may be afforded by parallelization and hardware acceleration. I will also review several open source tools and libraries developed by the community.

Modeling Multi-Scale Processes in Hydraulic Fracture Propagation Using the Implicit Level set Algorithm (ILSA)

By Anthony Peirce, Professor, Department of Mathematics at University of British Columbia

Thursday, March 26, 2015
Location: CPH 4333
Time: 2:30 - 3:30 p.m.
Anthony Peirce's talk of the video

Anthony Peirce

Abstract: In this talk I describe an implicit level set algorithm (ILSA) suitable for modeling multi-scale behavior in planar hydraulic fractures propagating in three dimensional elastic media. The novel ILSA scheme (Peirce 2015) is able to represent the required multi-scale behavior on a relatively coarse rectangular mesh. This is achieved by using the local front velocity to construct, for each point of a set of control points, a mapping that adaptively identifies the dominant length scale at which the appropriate multi-scale universal asymptotic solution needs to be sampled. Finer-scale behavior is captured in a weak sense by integrating the universal asymptotic solution for the fracture width over partially filled tip elements and using these integrals to set the average values of the widths in all tip elements. The ILSA solution shows good agreement with a multi-scale reference solution comprising a radial solution that transitions from viscosity to toughness dominated propagation regimes. The ILSA scheme is also used to model blade-like hydraulic fractures that break through stress barriers located symmetrically with respect to the injection point. For the zero toughness case, the ILSA solution shows close agreement to experimental results. The multi-scale ILSA scheme is also used to provide results when the material toughness KIc is non-zero. In this case, different parts of the fracture-free-boundary can be propagating in different regimes. I demonstrate how we have used these reference solutions to construct reduced order models that can execute in a fraction of the original computational time. I also provide examples in which this methodology is used to model multiple hydraulic fractures that propagate simultaneously in parallel planes. These multi-fracture models highlight surprising dynamics between the interacting fractures that indicate significant potential for using numerical design to improve production.

Exploiting Symmetries to Construct Efficient MCMC Alforithms with an Application to SLAM

By Csaba Szepesvari, Professor of Computer Science at University of Alberta and Principal Investigator of the Alberta Innovates Center for Machine Learning

Wednesday, March 18, 2015
Location: DC 1304
Time: 11 a.m.

Csaba Szepesvari

Abstract: Sampling from a given target probability distribution is a key problem in many different disciplines, including probabilistic inference. In many problems, the probability distribution, or its factors are known to be invariant under some transformations of the underlying space. How can this knowledge be exploited in designing efficient sampling algorithms? In this work we explore how to use the Metropolis-Hastings (MH) algorithm in this setting, to take advantage of this knowledge. The unique feature of our method is that it uses (mathematical) groups to capture and exploit invariances. This is in contrast to essentially all previous works, where invariances were exploited by collapsing the equivalence classes to reduce the space that sampling was performed on. While this previous approach works well when the whole target distribution is invariant under the considered transformations, it fails when the invariance concerns only individual factors, or is only "approximately" true. To illustrate the impact of exploiting symmetries, the new approach is applied to the simultaneous localization and mapping (SLAM) problem in robotics, where symmetries come from elementary geometrical and physical considerations. New experimental evidence using real-world benchmark data shows that this general method performs competitively with special-purpose algorithms in the challenging range-only SLAM problem.

This is joint work with Roshan Shariff and Andras Gyorgy. The talk is based on the following paper, to appear at AISTAT 2015.

Parallel and other simulations in R made easy: An end-to-end study

By Marius Hofert, Assistant Professor of Statistics and Actuarial Science at University of Waterloo

Monday, January 12, 2015
Location: DC 1304
Time: 3:30 - 4:30 p.m.

 Marius Hofert

Abstract: After a short introduction to stochastic dependence modeling with copulas, a practical problem in Quantitative Risk Management will serve as motivation for the development of the R package "simsalapar" for conducting large-scale simulation studies in R. This package aims at simplifying statistical simulation studies and carefully deals with important tasks such as parallel computing, seeding, catching of warnings and errors, and measuring run time. The approaches taken by "simsalapar" and presented in this talk may be of interest to students, researchers and practitioners as a how-to for conduction realistic, large-scale simulation studies.

Past CM Colloquiums