Organizing Committee
Abstract

Information-based complexity (IBC) deals with the computational complexity of continuous problems for which available information is partial, priced and noisy. IBC provides a methodological background for proving the curse of dimensionality as well as provides various ways of vanquishing this curse.

Stochastic computation deals with computational problems that arise in probabilistic models or can be efficiently solved by randomized algorithms. Using IBC background, the complexity of stochastic ordinary (SDE) and partial differential (SPDE) equations have been studied.

Topics covered in the workshop will include: adaptive and nonlinear approximation for SPDEs, infinite-dimensional problems, inverse and ill- posed problems, quasi-Monte Carlo methods, PDEs with random coefficients, sparse/Smolyak grids, stochastic multi-level algorithms, SDEs and SPDEs with nonstandard coefficients, tractability of multivariate problems.

This workshop will bring together researchers from these different fields. The goal is to explore connections, learn and share techniques, and build bridges.

Image for "Information-Based Complexity and Stochastic Computation"
Image courtesy of Dirk Nuyens

Confirmed Speakers & Participants

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Monday, September 15, 2014
TimeEventLocationMaterials
8:30 - 8:55am EDTRegistration11th Floor Collaborative Space 
8:55 - 9:00am EDTWelcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:30am EDTInfinite-dimensional integration by the multivariate decomposition method (MDM) - Ian Sloan, University of New South Wales11th Floor Lecture Hall
9:45 - 10:15am EDTTractability using periodized generalized Faure sequences - Christiane Lemieux, University of Waterloo11th Floor Lecture Hall
10:30 - 11:00am EDTCoffee/Tea Break11th Floor Collaborative Space 
11:00 - 11:30am EDTAdaptive algorithms for stochastic computation - Fred Hickernell, Illinois Institute of Technology11th Floor Lecture Hall
11:45 - 12:15pm EDTConstructive tractability for the Helmholtz equation - Art Werschulz, Fordham University11th Floor Lecture Hall
12:30 - 2:45pm EDTBreak for Lunch  
2:45 - 3:15pm EDTAn upper bound on complexity of optimization for Gaussian random fields - James Calvin, New Jersey Institute of Technology11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:30pm EDTTwo topics in parametric integration applied to stochastic simulation in industrial engineering - Jeremy Staum, Northwestern University11th Floor Lecture Hall
5:00 - 6:30pm EDTWelcome Reception11th Floor Collaborative Space 
Tuesday, September 16, 2014
TimeEventLocationMaterials
9:00 - 9:30am EDTQuadrature for self-similar distributions on R^d - Thomas Müller-Gronbach, Universitat Passau11th Floor Lecture Hall
9:45 - 10:15am EDTRegularity of SDEs with non-globally Lipschitz continuous coefficients - Sonja Cox, Eidgenössische TH Hönggerberg11th Floor Lecture Hall
10:30 - 11:00am EDTCoffee/Tea Break11th Floor Collaborative Space 
11:00 - 11:30am EDTOn a mild Ito formula for stochastic partial differential equations (SPDEs) and on weak convergence rates for SPDEs with nonlinear diffusion coefficients - Arnulf Jentzen, Eidgenössische TH Hönggerberg11th Floor Lecture Hall
11:45 - 12:15pm EDTEmbeddings of Weighted Tensor Product Spaces - Mario Hefter, Universitat Kaiserslautern11th Floor Lecture Hall
12:30 - 2:30pm EDTBreak for Lunch  
2:30 - 3:00pm EDTMultilevel Monte Carlo methods for discontinuous payoffs in the Heston model - Andreas Neuenkirch, Universität Mannheim11th Floor Lecture Hall
3:15 - 3:45pm EDTPreasymptotic estimates for approximation of multivariate Sobolev functions - Thomas Kuhn, Universitat Leipzig11th Floor Lecture Hall
4:00 - 6:00pm EDTPoster Session and Dessert Reception11th Floor Collaborative Space 
Wednesday, September 17, 2014
TimeEventLocationMaterials
9:00 - 9:30am EDTOptimal quasi-Monte Carlo rules on higher order digital nets for numerical integration of multivariate periodic functions - Aicke Hinrichs, Universität Rostock11th Floor Lecture Hall
9:45 - 10:15am EDTApproximation of additive random fields - Marguerite Zani, Université d'Orléans11th Floor Lecture Hall
10:30 - 11:00am EDTCoffee/Tea Break11th Floor Collaborative Space 
11:00 - 11:30am EDTOptimal algorithms for doubly weighted approximation of smooth functions - Leszek Plaskota, University of Warsaw11th Floor Lecture Hall
11:45 - 12:15pm EDTGeneralized multilevel methods for accelerating hierarchical stochastic collocation approximations of PDEs with random input data - Clayton Webster, Oak Ridge National Laboratory11th Floor Lecture Hall
12:15 - 12:20pm EDTWorkshop Group Photo  
12:30 - 2:15pm EDTBreak for Lunch  
2:15 - 2:45pm EDTTractability of multivariate integration in Hermite spaces - Friedrich Pillichshammer, Johannes Kepler Universität Linz11th Floor Lecture Hall
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
3:30 - 4:00pm EDTA dynamic near-optimal algorithm for online linear programming - Yinyu Ye, Stanford University11th Floor Lecture Hall
4:15 - 4:45pm EDTComplexity of Banach Space Valued and Parametric Stochastic Ito Integration - Thomas Daun, Universitat Kaiserslautern11th Floor Lecture Hall
Thursday, September 18, 2014
TimeEventLocationMaterials
9:00 - 9:30am EDTOn the complexity of first order PDEs - Stefan Heinrich, Universität Kaiserslautern11th Floor Lecture Hall
9:45 - 10:15am EDTDeterministic quadrature rules for marginals of SDEs based on weak Ito-Taylor steps - Larisa Yaroslavtseva, Universität Passau11th Floor Lecture Hall
10:30 - 11:00am EDTCoffee/Tea Break11th Floor Collaborative Space 
11:00 - 11:30am EDTOptimal approximation of Sobolev functions in the L2 and in the supremum norm - Winfried Sickel, Friedrich-Schiller-Universität11th Floor Lecture Hall
11:45 - 12:15pm EDTA reduced fast component-by-component construction of (polynomial) lattice points - Peter Kritzer, Johannes Kepler Universität Linz11th Floor Lecture Hall
12:30 - 2:45pm EDTBreak for Lunch  
2:45 - 3:15pm EDTA refined classification of problems with (sub)exponential information-based complexity - Pawel Siedlecki, University of Warsaw11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:30pm EDTRandomized algorithms on the approximation of rank one tensors - Daniel Rudolf, Friedrich-Schiller-Universität11th Floor Lecture Hall
Friday, September 19, 2014
TimeEventLocationMaterials
9:00 - 9:30am EDTError analysis for multivariate and infinite-dimensional integration with respect to different underlying norms - Michael Gnewuch, Christian-Albrechts Universität Kiel11th Floor Lecture Hall
9:45 - 10:15am EDTHigh-dimensional and infinite-dimensional hyperbolic crosses and their applications in approximation and uncertainty quantification - Dinh Dung, Vietnam National University11th Floor Lecture Hall
10:30 - 11:00am EDTCoffee/Tea Break11th Floor Collaborative Space 
11:00 - 11:30am EDTApproximation in cosine space using tent-transformed lattice rules - Dirk Nuyens, Katholieke Universiteit Leuven11th Floor Lecture Hall
11:45 - 12:15pm EDTConstructing quasi-Monte Carlo methods for high dimensional integrals over the Euclidean space and applications - Frances Kuo, University of New South Wales11th Floor Lecture Hall
12:30 - 5:00pm EDTAfternoon open for collaboration  

Associated Semester Workshops

High-dimensional Approximation
Image for "High-dimensional Approximation"
Approximation, Integration, and Optimization
Image for "Approximation, Integration, and Optimization"
Discrepancy Theory
Image for "Discrepancy Theory"

Research Cluster

Lecture Videos

Tractability of multivariate integration in Hermite spaces

Friedrich Pillichshammer
Johannes Kepler Universität Linz
September 17, 2014

Adaptive algorithms for stochastic computation

Fred Hickernell
Illinois Institute of Technology
September 15, 2014