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The aim of these notes is to demonstrate the potential for ideas in machine learning to impact on the fields of inverse problems and data assimilation. The perspective is one that is primarily aimed at researchers from inverse problems and/or data as
Externí odkaz:
http://arxiv.org/abs/2410.10523
The filtering distribution captures the statistics of the state of a dynamical system from partial and noisy observations. Classical particle filters provably approximate this distribution in quite general settings; however they behave poorly for hig
Externí odkaz:
http://arxiv.org/abs/2409.09800
Autor:
Nelsen, Nicholas H., Stuart, Andrew M.
Publikováno v:
SIAM Review Vol. 66 No. 3 (2024) pp. 535-571
Supervised operator learning centers on the use of training data, in the form of input-output pairs, to estimate maps between infinite-dimensional spaces. It is emerging as a powerful tool to complement traditional scientific computing, which may oft
Externí odkaz:
http://arxiv.org/abs/2408.06526
Autoencoders have found widespread application, in both their original deterministic form and in their variational formulation (VAEs). In scientific applications it is often of interest to consider data that are comprised of functions; the same persp
Externí odkaz:
http://arxiv.org/abs/2408.01362
Autor:
Karlbauer, Matthias, Maddix, Danielle C., Ansari, Abdul Fatir, Han, Boran, Gupta, Gaurav, Wang, Yuyang, Stuart, Andrew, Mahoney, Michael W.
Remarkable progress in the development of Deep Learning Weather Prediction (DLWP) models positions them to become competitive with traditional numerical weather prediction (NWP) models. Indeed, a wide number of DLWP architectures -- based on various
Externí odkaz:
http://arxiv.org/abs/2407.14129
Filtering - the task of estimating the conditional distribution of states of a dynamical system given partial, noisy, observations - is important in many areas of science and engineering, including weather and climate prediction. However, the filteri
Externí odkaz:
http://arxiv.org/abs/2406.18066
In this paper, we study efficient approximate sampling for probability distributions known up to normalization constants. We specifically focus on a problem class arising in Bayesian inference for large-scale inverse problems in science and engineeri
Externí odkaz:
http://arxiv.org/abs/2406.17263
Transformers, and the attention mechanism in particular, have become ubiquitous in machine learning. Their success in modeling nonlocal, long-range correlations has led to their widespread adoption in natural language processing, computer vision, and
Externí odkaz:
http://arxiv.org/abs/2406.06486
Bayesian inversion is central to the quantification of uncertainty within problems arising from numerous applications in science and engineering. To formulate the approach, four ingredients are required: a forward model mapping the unknown parameter
Externí odkaz:
http://arxiv.org/abs/2405.17955
Gaussian Measures Conditioned on Nonlinear Observations: Consistency, MAP Estimators, and Simulation
The article presents a systematic study of the problem of conditioning a Gaussian random variable $\xi$ on nonlinear observations of the form $F \circ \phi(\xi)$ where $\phi: \mathcal{X} \to \mathbb{R}^N$ is a bounded linear operator and $F$ is nonli
Externí odkaz:
http://arxiv.org/abs/2405.13149