Tim Sullivan

Junior Professor in Applied Mathematics:
Risk and Uncertainty Quantification

ECMath Colloquium

ECMath Colloquium

Next week's colloquium at the Einstein Center for Mathematics Berlin will be on the topic of Optimisation. The speakers will be:

  • Sebastian Sager (Magdeburg): Mathematical Optimization for Clinical Diagnosis and Decision Support
  • Werner Römisch (HU Berlin): Stochastic Optimization: Complexity and Numerical Methods
  • Karl Kunisch (Graz): Sparsity in PDE-constrained Open and Closed Loop Control

Time and Place. Friday 20 January 2017, 14:00–17:00, Humboldt-Universität zu Berlin, Main Building Room 2.097, Unter den Linden 6, 10099 Berlin

Published on Tuesday 10 January 2017 at 12:00 UTC #event

Jon Cockayne

UQ Talks: Jon Cockayne

Next week Jon Cockayne (University of Warwick) will give a talk on “Probabilistic Numerics for Partial Differential Equations”.

Time and Place. Friday 14 October 2016, 12:00–13:00, ZIB Seminar Room 2006, Zuse Institute Berlin, Takustraße 7, 14195 Berlin

Abstract. Probabilistic numerics is an emerging field which constructs probability measures to capture uncertainty arising from the discretisation which is often necessary to solve complex problems numerically. We explore probabilistic numerical methods for Partial differential equations (PDEs). We phrase solution of PDEs as a statistical inference problem, and construct probability measures which quantify the epistemic uncertainty in the solution resulting from the discretisation [1].

We analyse these probability measures in the context of Bayesian inverse problems, parameter inference problems whose dynamics are often constrained by a system of PDEs. Sampling from parameter posteriors in such problems often involves replacing an exact likelihood with an approximate one, in which a numerical approximation is substituted for the true solution of the PDE. Such approximations have been shown to produce biased and overconfident posteriors when error in the forward solver is not tightly controlled. We show how the uncertainty from a probabilistic forward solver can be propagated into the parameter posteriors, thus permitting the use of coarser discretisations while still producing valid statistical inferences.

[1] Jon Cockayne, Chris Oates, Tim Sullivan, and Mark Girolami. “Probabilistic Meshless Methods for Partial Differential Equations and Bayesian Inverse Problems.” arXiv preprint, 2016. arXiv:1605.07811

Published on Monday 3 October 2016 at 10:00 UTC #event #uq-talk #prob-num

Probabilistic Numerics at MCQMC

There will be a workshop on Probabilistic Numerics at this year's MCQMC conference at Stanford University. The workshop will be held on Thursday, 18 August 2016, 15:50–17:50, at the Li Ka Shing Center on the Stanford University campus. Speakers include:

  • Mark Girolami (University of Warwick & Alan Turing Institute) — Probabilistic Numerical Computation: A New Concept?
  • François-Xavier Briol (University of Warwick & University of Oxford) — Probabilistic Integration: A Role for Statisticians in Numerical Analysis?
  • Chris Oates (University of Technology Sydney) — Probabilistic Integration for Intractable Distributions
  • Jon Cockayne (University of Warwick) — Probabilistic meshless methods for partial differential equations and Bayesian inverse problems

Update, 19 August 2016. The slides from the talks can be found here, on Chris Oates' website.

Published on Sunday 31 July 2016 at 14:00 UTC #prob-num #event

Hans Kersting

UQ Talks: Hans Kersting

Next week Hans Kersting (MPI Tübingen) will give a talk in the UQ research seminar about “UQ in probabilistic ODE solvers”.

Time and Place. Tuesday 14 June 2016, 12:15–13:15, ZIB Seminar Room 2006, Zuse Institute Berlin, Takustraße 7, 14195 Berlin

Abstract. In an ongoing push to construct probabilistic extensions of classic ODE solvers for application in statistics and machine learning, two recent papers have provided distinct methods that return probability measures instead of point estimates, based on sampling and filtering respectively. While both approaches leverage classical numerical analysis, by building on well-studied solutions of existing seminal solvers, the different constructions of probability measures strike a divergent balance between a formal quantification of epistemic uncertainty and a low computational overhead.

On the one hand, Conrad et al. proposed to randomise existing non-probabilistic one-step solvers by adding suitably scaled Gaussian noise after every step and thereby inducing a probability measure over the solution space of the ODE which contracts to a Dirac measure on the true unknown solution in the order of convergence of the underlying classic numerical method. But the computational cost of these methods is significantly above that of classic solvers.

On the other hand, Schober et al. recast the estimation of the solution as state estimation by a Gaussian (Kalman) filter and proved that employing a integrated Wiener process prior returns a posterior Gaussian process whose maximum likelihood (ML) estimate matches the solution of classic Runge–Kutta methods. In an attempt to amend this method's rough uncertainty calibration while sustaining its negligible cost overhead, we propose a novel way to quantify uncertainty in this filtering framework by probing the gradient using Bayesian quadrature.

Published on Monday 6 June 2016 at 10:00 UTC #event #uq-talk #prob-num

Zuse 75

The Digital Future: 75th Anniversary of the Zuse Z3

11 May 2016 marks the seventy-fifth anniversary of the unveiling of Konrad Zuse's Z3 computer. The Z3 was the world's first working programmable, fully automatic digital computer.

In celebration of this landmark achievement in computational science, the Zuse Institute, the Berlin–Brandenburg Academy of Sciences, and Der Tagesspiegel are organising a conference on “The Digital Future: 75 Years Zuse Z3 and the Digital Revolution”. For further information, see www.zib.de/zuse75.

Published on Monday 2 May 2016 at 11:00 UTC #event

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