Uncertainty Quantification and Inverse Problems
Levi, Finland, 24–28 March 2024
This event will bring together experts working on various aspects of data assimilation, uncertainty quantification, and inverse problems.
The event will be held on 24–28 March 2024 and it consists of a series of talks in three thematic subcategories: Data Assimilation, Space Physics, and Uncertainty Quantification and Partial Differential Equations
This event is organized by Vesa Kaarnioja, Jana de Wiljes, and Lassi Roininen. Contact person: email@example.com
- 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: Stepwise data absorption combining complementary filtering techniques
Abstract: Data Assimilation serves multiple purposes, including estimating the model state and the initial state of a system for predicting its future state. It combines prior information from numerical model simulations with observed data to produce the most accurate description of a dynamical system and its uncertainty. Here we introduce additional importance sampling steps by splitting the likelihood in order to improve the robustness and accuracy of the estimations. This approach allows us to combine Gaussian approximative filters such as the Ensemble Square Root Filter (ESRF) and consistent filters such as the Ensemble Transform Particle Filter (ETPF). The benefit is that one can exploit the stabilizing properties of ESRF type filters while mimicking the accuracy level of a consistent filter.
- Jana de Wiljes (TU Ilmenau)
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.
- Vesa Kaarnioja (FU Berlin)
Title: Doubling the rate in high-dimensional function approximation with application to numerical integration
Abstract: A recent work , inspired by , considered some general conditions, which ensure that the L2 rate of convergence for function approximation in a Hilbert space H can be doubled for functions belonging to a smoother normed space B, provided that L2, H, and B are suitably related. In this talk, we discuss how these conditions can be used to obtain cubature rules with improved convergence rates for sufficiently smooth integrands. Numerical experiments are presented to support the theoretical results.
This is joint work with Ilja Klebanov (FU Berlin) and Claudia Schillings (FU Berlin).
 I. H. Sloan and V. Kaarnioja. Doubling the rate -- improved error bounds for orthogonal projection in Hilbert spaces. Preprint 2023, arXiv:2308.06052 [math.NA]
 R. Schaback. Improved error bounds for scattered data interpolation by radial basis functions. Math. Comp. 68, 201-216, 1999
- Alejandra Avalos Pacheco (TU Wien)
Title: Efficient Bayesian integrative factor models: Applications from nutritional epidemiology to cancer genomics
Abstract: Data integration of multiple studies can be key to understanding and gaining knowledge in statistical research. Such complex data present artifactual sources of variation, also known as covariate effects, that, if not corrected, could lead to unreliable inference. Traditional multi-study factor analysis (MSFA) have proven to be key for identifying reproducible signal of interest shared by different studies or populations, which traditional factor analysis may miss. Bayesian inference for such models relies on Markov Chain Monte Carlo (MCMC) methods, which scale poorly. Furthermore, MSFA does not include relevant covariates in the model that could bias the results. Both problems are tackled by (i) introducing variational inference algorithms to approximate the posterior distribution of Sparse MSFA, and (ii) presenting novel multi-study factor regression (MSFR) models to jointly learn common and study-specific factors while adjusting for covariate effects. The usefulness of the methods is shown in nutritional epidemiology and cancer genomic applications to (i) obtain dietary patterns, and their association with cardiometabolic disease risk for Hispanic groups and (ii) reveal biological pathways for ovarian cancer datasets using computational resources typically available on a laptop rather than a high-performance computing server.
- Lassi Roininen (LUT University)
Title: Detecting rough features with non-Gaussian models
Abstract: We consider recent advances in using non-Gaussian and hierarchical mixture models for estimating rough features, such as edges, material interfaces, and similar, in Bayesian inverse problems. We go through the recent developments, and papers associated, and also future research directions.