Related papers: Model Error in Data Assimilation

We identify a strong equivalence between neural network based machine learning (ML) methods and the formulation of statistical data assimilation (DA), known to be a problem in statistical physics. DA, as used widely in physical and…

In machine learning models, the estimation of errors is often complex due to distribution bias, particularly in spatial data such as those found in environmental studies. We introduce an approach based on the ideas of importance sampling to…

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…

Four-dimensional weak-constraint variational data assimilation estimates a state given partial noisy observations and dynamical model by minimizing a cost function that takes into account both discrepancy between the state and observations…

Increasing effort is put into the development of methods for learning mechanistic models from data. This task entails not only the accurate estimation of parameters but also a suitable model structure. Recent work on the discovery of…

Subsampling algorithms for various parametric regression models with massive data have been extensively investigated in recent years. However, all existing studies on subsampling heavily rely on clean massive data. In practical…

Covariance localization is a critical component of ensemble-based data assimilation (DA) and many current localization schemes simply dampen correlations as a function of distance. Increases in computational resources, broadening scope of…

AI and data-driven models have large potential for data assimilation applications by creating fast and accurate forecasts. Their tendency to produce spurious inaccurate, nonphysical results -- hallucination -- however, raises a serious…

In today's modern era of Big data, computationally efficient and scalable methods are needed to support timely insights and informed decision making. One such method is sub-sampling, where a subset of the Big data is analysed and used as…

In this paper, we provide a mathematical framework for improving generalization in a class of learning problems which is related to point estimations for modeling of high-dimensional nonlinear functions. In particular, we consider a…

Data entry constitutes a fundamental component of the machine learning pipeline, yet it frequently results in the introduction of labelling errors. When a model has been trained on a dataset containing such errors its performance is…

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…

Missing data theory deals with the statistical methods in the occurrence of missing data. Missing data occurs when some values are not stored or observed for variables of interest. However, most of the statistical theory assumes that data…

In this article we develop further an algorithm for data assimilation based upon a shadowing refinement technique [de Leeuw et al., SIAM J. Appl. Dyn. Sys., 17 (2018)] to take partial observations into account. Our method is based on…

Parameter estimation in linear errors-in-variables models typically requires that the measurement error distribution be known (or estimable from replicate data). A generalized method of moments approach can be used to estimate model…

This study aims to understand how statistical biases affect the model's ability to generalize to in-distribution and out-of-distribution data on algorithmic tasks. Prior research indicates that transformers may inadvertently learn to rely…

In this article we develop algorithms for data assimilation based upon a computational time dependent stable/unstable splitting. Our particular method is based upon shadowing refinement and synchronization techniques and is motivated by…

In this entry we review the generalization error for classification and single-stage decision problems. We distinguish three alternative definitions of the generalization error which have, at times, been conflated in the statistics…

A common problem in data analysis is that the functional form, as well as the parameter values, of the underlying model which should describe a dataset is not known a priori. In these cases some extra uncertainty must be assigned to the…

Variational data assimilation optimizes for an initial state of a dynamical system such that its evolution fits observational data. The physical model can subsequently be evolved into the future to make predictions. This principle is a…