Related papers: Topological Approach for Data Assimilation

Topological data analysis refers to approaches for systematically and reliably computing abstract ``shapes'' of complex data sets. There are various applications of topological data analysis in life and data sciences, with growing interest…

We propose a new gradient descent algorithm with added stochastic terms for finding the global optimizers of nonconvex optimization problems. A key component in the algorithm is the adaptive tuning of the randomness based on the value of…

Topology applied to real world data using persistent homology has started to find applications within machine learning, including deep learning. We present a differentiable topology layer that computes persistent homology based on level set…

In this paper, we extend our research concerning the standard and linearized monotonicity methods for the inverse problem of the time harmonic elastic wave equation and introduce the modification of these methods for noisy data. In more…

We describe a new approach allowing for systematic causal attribution of weather and climate-related events, in near-real time. The method is purposely designed to facilitate its implementation at meteorological centers by relying on data…

Abrupt transitions ("tipping") in nonlinear dynamical systems are often accompanied by changes in the geometry of the attracting set, but quantifying such changes from partial and noisy observations in high-dimensional systems remains…

We address data assimilation for linear and nonlinear dynamical systems via the so-called \emph{model reference adaptive system}. Continuing our theoretical developments in \cite{Tram_Kaltenbacher_2021}, we deliver the first practical…

Topological Data Analysis (TDA) has emerged as a powerful framework for extracting robust and interpretable features from noisy high-dimensional data. In the context of Social Choice Theory, where preference profiles and collective…

We conjecture that the inherent difference in generalisation between adaptive and non-adaptive gradient methods in deep learning stems from the increased estimation noise in the flattest directions of the true loss surface. We demonstrate…

Many commercial and defense applications involve multisensor, multitarget tracking, requiring the fusion of information from a set of sensors. An interesting use case occurs when data available at a central node (due to geometric diversity…

We show how the 3DVAR data assimilation methodology can be used in the astrophysical context of a two-dimensional convection flow. We study the way this variational approach finds best estimates of the current state of the flow from a…

Downscaling is a landmark task in climate science and meteorology in which the goal is to use coarse scale, spatio-temporal data to infer values at finer scales. Statistical downscaling aims to approximate this task using statistical…

In this paper we propose a new sequential data assimilation method for non-linear ordinary differential equations with compact state space. The method is designed so that the Lyapunov exponents of the corresponding estimation error dynamics…

In order to handle large data sets omnipresent in modern science, efficient compression algorithms are necessary. Here, a Bayesian data compression (BDC) algorithm that adapts to the specific measurement situation is derived in the context…

Variational data assimilation in continuous time is revisited. The central techniques applied in this paper are in part adopted from the theory of optimal nonlinear control. Alternatively, the investigated approach can be considered as a…

Data rebalancing techniques, including oversampling and undersampling, are a common approach to addressing the challenges of imbalanced data. To tackle unresolved problems related to both oversampling and undersampling, we propose a new…

Finding an optimal parameter of a black-box function is important for searching stable material structures and finding optimal neural network structures, and Bayesian optimization algorithms are widely used for the purpose. However, most of…

Systems exhibiting nonlinear dynamics, including but not limited to chaos, are ubiquitous across Earth Sciences such as Meteorology, Hydrology, Climate and Ecology, as well as Biology such as neural and cardiac processes. However, System…

We provide a clear and concise introduction to the subjects of inverse problems and data assimilation, and their inter-relations. The first part of our notes covers inverse problems; this refers to the study of how to estimate unknown model…

This article develops a novel data assimilation methodology, addressing challenges that are common in real-world settings, such as severe sparsity of observations, lack of reliable models, and non-stationarity of the system dynamics. These…