Uncertainty Quantification and Inverse Problems
Levi, Finland, 14 March 2023
This Bayes Comp 2023 satellite event will bring together experts working on various aspects of data assimilation, uncertainty quantification, and inverse problems.
The satellite event will be held on Tuesday 14 March 2023 and it consists of a series of talks separated into three thematic subcategories: Data Assimilation, Space Physics, and Uncertainty Quantification and Partial Differential Equations.
Morning 1: Data Assimilation
- 9.20-9.40: Jouni Susiluoto
- 9.40-10.00: Antti Solonen
Morning 2: Space Physics
- 10.30-10.50: Antti Kero
- 10.50-11.10: Neethal Thomas
- 11.10-11.30: Angelica Maria Castillo Tibocha
- 11.30-11.50: Iris Rammelmüller
Afternoon: Uncertainty Quantification and Partial Differential Equations
- 15.00-15.20: Neil Chada
- 15.20-15.40: Jana de Wiljes
- 15.40-16.00: Andi Wang
- 16.00-16.20: Martin Simon
- 16.20-16.40: Timo Lähivaara
- 16.40-17.00: Alexey Kazarnikov
This satellite event is organized by Andreas Rupp, Vesa Kaarnioja, Jana de Wiljes, and Martin Simon. Contact person: firstname.lastname@example.org
- Angelica Maria Castillo Tibocha (GFZ German Research Centre for Geosciences)
Title: Data assimilation techniques for electron phase space density in the radiation belts
Abstract: Accurate predictions of the effects of hazardous energetic solar plasma events on the near-Earth space environment are invaluable to prepare for and potentially prevent harmful implications to humans and technology in space and on the ground. In order to obtain accurate predictions despite uncertainties in the associated model and the observations, novel data assimilation methods have become increasingly popular. The associated inference problem is particularly challenging when wave activity and mixed diffusion are taken into account, such that the underlying system becomes non-linear. In this case, robust techniques for high dimensional settings are asked for. The class of ensemble Kalman filters has been shown to be one of the most promising filtering tools for non-linear and high dimensional systems in the context of terrestrial weather prediction but has been barely used in the context of electron phase space density for the outer radiation belt. In this study, we adapt traditional ensemble based methods to reduce uncertainties in the estimation of electron phase space density. We use a one-dimensional radial diffusion model, a standard Kalman filter (KF) and synthetic data to setup the framework for one-dimensional ensemble data assimilation. Furthermore, with the split-operator technique, we develop two split-operator Ensemble Kalman filter approaches for electron phase space density in the radiation belts. Validation of the proposed filter approaches is presented against Van Allen Probe and GOES observations and against the 3D split-operator KF.
- Iris Rammelmüller (Universität Klagenfurt)
Title: Computationally efficient air dispersion modelling
Abstract: Air dispersion modelling has become one of the main tools in the study of air quality whereby it is a key element in most environmental impact assessments. Almost every human activity and natural process leads to some form of air pollution. Therefore, air dispersion modelling is a powerful technique to evaluate whether a source creates a problem. Considering climate change, sustainable design and planning of our cities is essential, but alpine regions pose several problems to the correct investigation of air pollutant concentrations.
In general, two different models will be considered, namely the Gaussian Plume Model and the Stochastic Lagrangian Particle Model.
The goal is to extend these models to alpine regions respectively to different source types, deposition and reflection to predict a concentration profile.
- Jana de Wiljes (University of Potsdam)
Title: Projection induced localization for ensemble data-assimilation methods
Abstract: There is a high demand to predict and understand systems where information is available in the form of observations and models, such as those based on first principles. Bayesian sequential learning methods are among the most advanced techniques that can be used in this context. However, the large spatial scale and complexity of these systems still pose significant computational challenges. To address this, many techniques make simplifying assumptions, such as assuming a Gaussian distribution, which can lead to less accurate predictions. However, less restrictive (in the distributional sense) filters tend to suffer more heavily from the curse of dimensionality than their Gaussian approximative filter counterparts. To combat this problem, several numerical improvement tools have been developed over the last two decades. One of the most popular techniques is localization, which leverages the fact that short-range spatial interactions are a key feature of dynamics in many applications. In this context, we introduce an enhanced localisation technique that utilizes prior projection of the state. Consistent filters such as sequential Monte Carlo particularly benefit from this type of localisation.
- Andi Wang (University of Bristol)
Title: Explicit convergence bounds for preconditioned Crank–Nicolson
Abstract: I will derive explicit bounds for the spectral gap and mixing time of the preconditioned Crank—Nicolson algorithm, a popular MCMC scheme within the field of Bayesian inverse problems. The bounds are based on techniques involving isoperimetric and conductance profiles, and under suitable assumptions on the potential are dimension-independent. Furthermore the bounds are computable and applicable for any value of the step-size parameter. Joint work with Christophe Andrieu, Anthony Lee and Sam Power.
- Martin Simon (Frankfurt University of Applied Sciences)
Title: Bayesian uncertainty quantification in climate risk modeling
Abstract: In this talk we discuss an application in the field of quantitative climate risk modeling. We highlight the necessity for uncertainty quantification as well as the theoretical and practical challenges which come along with that. We present a computational framework which addresses some of these challenges and demonstrate the feasibility of practical implementation of this approach. The talk is based on joint work with Heikki Haario, Lassi Roininen and Hendrik Weichel.
- Timo Lähivaara (University of Eastern Finland)
Title: Bayesian inversion for the reconstruction of rough surfaces from acoustic scattering
Abstract: In this work, a framework for reconstructing the elevation profile of a rough surface from acoustic scattering is studied. The acoustic scattering data is measured at a microphone array, while the surface is insonified with a broadband source. In the problem formulation, the forward model is based on the Kirchhoff approximation, which provides reasonable numerical accuracy at high frequencies or in the far field while enabling an efficient exploration of the design space. The inverse problem is formulated in a statistical framework and solved using the Markov chain Monte Carlo method, providing information not only about the point estimates but also an uncertainty envelope. The procedure is demonstrated for a surface with a one-dimensional roughness profile.
- Alexey Kazarnikov (Universität Heidelberg)
Title: Statistical parameter identification by pattern data
Abstract: Understanding the mechanisms of pattern formation is one of the important topics in developmental biology. Mathematical models allow the establishment of a connection between a pattern observed on a macroscopic scale and a hypothetical underlying mechanism. Since the classic work of Alan Turing, reaction-diffusion systems have been the dominant modelling approach. Alternative models combine the dynamics of diffusing molecular signals with tissue mechanics or intracellular feedback. But the quantitative discrimination of competing theories is difficult due to the elusive character of the processes: different mechanisms may result in similar patterns, while patterns obtained with a fixed model and fixed parameter values, but with small random perturbations of initial data, will significantly differ in shape while being of the ''same'' type. In this sense, fixed values of model parameters correspond to a family of patterns, rather than a fixed solution. Additionally, in many experimental situations, only the limiting, stationary regime of the pattern formation process can be observed, without any knowledge of the transient behaviour or the initial state. For this situation, we develop a statistical approach that allows distinguishing the model parameters that correspond to given patterns. The method is tested using different classes of pattern formation models and severely limited data sets.