[00965] New mathematical trends in weather prediction and inverse problems
Session Date & Time :
00965 (1/2) : 5C (Aug.25, 13:20-15:00)
00965 (2/2) : 5D (Aug.25, 15:30-17:10)
Type : Proposal of Minisymposium
Abstract : In applied mathematics including inverse problems, problems are often ill-posed and/or data are limited. Such difficulties have been treated in different subfields of science: medical imaging, data assimilation in numerical weather prediction, etc. In this minisymposium, researchers from data assimilation and inverse problems will gather and discuss different tools and ideas in applied mathematics to handle complicated problems and incomplete data.
Steve Penny (National Oceanic and Atmospheric Administration)
Mao Ouyang (Chiba University)
John C. Schotland (Yale University)
Subhadip Mukherjee (University of Bath)
Marcello Carioni (University of Twente)
Zakhar Shumaylov (University of Cambridge)
Talks in Minisymposium :
[03741] Gaussian Assimilation of non-Gaussian Image Data via Pre-Processing by Variational Auto-Encoder (VAE)
Author(s) :
Daisuke Hotta (Meteorological Research Institute, Japan Meteorological Agency)
Abstract : Assimilation of image data such as satellite images with conventional data assimilation methods is challenging due to non-Gaussian error distribution, dimensional redundancy, and strong inter-pixel correlations. While several techniques have been proposed to address each of these issues, no single method can simultaneously handle them all. Here we propose to use a Variational AutoEncoder to resolve all three difficulties. A preliminary assessment with a toy model shows promising results.
[04216] Implementing local ensemble transform Kalman filter to reservoir computing for improving weather forecast
Author(s) :
Mao Ouyang (Chiba University)
Shunji Kotsuki (Chiba University)
Abstract : Data assimilation (DA) improves the numerical weather prediction (NWP) by combining the model forecast and observational data. The forecasts were usually obtained from a physical-based model, but recent studies reported that the reservoir computing (RC) could be implemented to surrogate both the small- and intermediate-scale physical models. This study implemented the DA, i.e., local ensemble transform Kalman filter, in both the physic-based and RC-surrogated models and compared their performances in the improvement of forecasts.
[04315] Sparse optimization of inverse problems regularized with infimal-convolution-type functionals
Author(s) :
Marcello Carioni (University of Twente)
Abstract : The infimal convolution of functionals is a convex-preserving operation that have been used to construct regularizers for inverse problems by optimally combining features of two or more functionals. In this talk, we analyze the infimal convolution regularization from a sparse optimization point of view. First, we discuss optimal transport-type energies. Then, we consider the infimal convolution of a parametrized family of functionals and we develop optimization methods taking advantage of the sparsity in the parameters.
[04562] Efficient data-driven regularization for ill-posed inverse problems in imaging
Author(s) :
Subhadip Mukherjee (University of Bath, UK)
Marcello Carioni (University of Twente)
Ozan Öktem (KTH Royal Institute of Technology)
Carola-Bibiane Schönlieb (University of Cambridge)
Abstract : In recent years, data-driven regularization has led to impressive performance for image reconstruction problems in various scientific applications, e.g., medical imaging. We propose a new adversarial learning approach for imaging inverse problems by combining an iteratively unrolled network with a deep regularizer using ideas from optimal transport. The resulting unrolled adversarial regularization approach is shown to be provably stable, efficient in terms of image reconstruction time, and competitive with supervised methods in empirical performance.
[05386] Inverse problems for nonlocal PDEs with applications to quantum optics
Author(s) :
John Schotland (Yale University)
Abstract : I will discuss recent work with Jeremy Hoskins and Howard Levinson on reconstruction methods for inverse problems for nonlocal PDEs. Applications to quantum optics will be discussed.
