相关论文: Data Assimilation with Deep Neural Nets Informed b…

Motivated by the gap between theoretical optimal approximation rates of deep neural networks (DNNs) and the accuracy realized in practice, we seek to improve the training of DNNs. The adoption of an adaptive basis viewpoint of DNNs leads to…

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…

This article studies the intimate relationship between two filtering algorithms for continuous data assimilation, the synchronization filter and the nudging filter, in the paradigmatic context of the two-dimensional (2D) Navier-Stokes…

A novel method, based on the combination of data assimilation and machine learning is introduced. The new hybrid approach is designed for a two-fold scope: (i) emulating hidden, possibly chaotic, dynamics and (ii) predicting their future…

Motivated by the challenge of moment recovery in hydrodynamic approximation in kinetic theory, we propose a data-driven approach for the hydrodynamic models. Inspired by continuous data assimilation, our method introduces a relaxation-based…

Deep neural networks (DNN) has received increasing attention in machine learning applications in the last several years. Recently, a non-asymptotic error bound has been developed to measure the performance of the fully connected DNN…

We propose a novel deep neural network (DNN) based approximation architecture to learn estimates of measurements. We detail an algorithm that enables training of the DNN. The DNN estimator only uses measurements, if and when they are…

We present a new method to approximate posterior probabilities of Bayesian Network using Deep Neural Network. Experiment results on several public Bayesian Network datasets shows that Deep Neural Network is capable of learning joint…

In this study, we analyzed a continuous data assimilation scheme applied on a double-diffusive natural convection model. The algorithm is introduced with a first order backward Euler time scheme along with a finite element discretization in…

This report develops several modular, 2-step realizations (inspired by Kalman filter algorithms) of nudging-based data assimilation $$Step \ 1 \quad \frac{\widetilde {v}^{n+1}-v^{n}}{k}+v^{n}\cdot \nabla \widetilde {v}^{n+1}-\nu \triangle…

Deep Learning (DL) models can be used to tackle time series analysis tasks with great success. However, the performance of DL models can degenerate rapidly if the data are not appropriately normalized. This issue is even more apparent when…

Data assimilation is a technique for increasing the accuracy of simulations of solutions to partial differential equations by incorporating observable data into the solution as time evolves. Recently, a promising new algorithm for data…

We formulate a strong equivalence between machine learning, artificial intelligence methods and the formulation of statistical data assimilation as used widely in physical and biological sciences. The correspondence is that layer number in…

We investigate a new sampling scheme aimed at improving the performance of particle filters whenever (a) there is a significant mismatch between the assumed model dynamics and the actual system, or (b) the posterior probability tends to…

Deep metric learning algorithms have been utilized to learn discriminative and generalizable models which are effective for classifying unseen classes. In this paper, a novel noise tolerant deep metric learning algorithm is proposed. The…

Neural machine learning methods, such as deep neural networks (DNN), have achieved remarkable success in a number of complex data processing tasks. These methods have arguably had their strongest impact on tasks such as image and audio…

Errors in the representation of clouds in convection-permitting numerical weather prediction models can be introduced by different sources. These can be the forcing and boundary conditions, the representation of orography, the accuracy of…

In this work, we describe a new approach that uses deep neural networks (DNN) to obtain regularization parameters for solving inverse problems. We consider a supervised learning approach, where a network is trained to approximate the…

Obtaining accurate high-resolution representations of model outputs is essential to describe the system dynamics. In general, however, only spatially- and temporally-coarse observations of the system states are available. These observations…

Continuous data assimilation (CDA) nudges observational data into governing equations to recover the underlying flow and improve predictions. Existing rigorous CDA analyses focus primarily on incompressible flows, yet no physical flow is…