scholarly journals Neural networks as smooth priors for inverse problems for PDEs

2021 ◽  
pp. 100008
Author(s):  
Jens Berg ◽  
Kaj Nyström
Keyword(s):  
Neural Networks ◽  
Inverse Problems

Jointly learning variational data assimilation models and solvers for geophysical dynamics

2021 ◽  
Author(s):  
Ronan Fablet ◽  
Bertrand Chapron ◽  
Lucas Drumetz ◽  
Etienne Memin ◽  
Olivier Pannekoucke ◽  
...  
Keyword(s):  
Neural Networks ◽  
Data Assimilation ◽  
Inverse Problems ◽  
Automatic Differentiation ◽  
Variational Data Assimilation ◽  
Point Of View ◽  
Variational Model ◽  
Short Term ◽  
End To End ◽  
Short Term Forecasting

<p>This paper addresses representation learning for the resolution of inverse problems  with geophysical dynamics. Among others, examples of inverse problems of interest include space-time interpolation, short-term forecasting, conditional simulation w.r.t. available observations, downscaling problems… From a methodological point of view, we rely on a variational data assimilation framework. Data assimilation (DA) aims to reconstruct the time evolution of some state given a series of  observations, possibly noisy and irregularly-sampled. Here, we investigate DA from a machine learning point of view backed by an underlying variational representation.  Using automatic differentiation tools embedded in deep learning frameworks, we introduce end-to-end neural network architectures for variational data assimilation. It comprises two key components: a variational model and a gradient-based solver both implemented as neural networks. A key feature of the proposed end-to-end learning architecture is that we may train the neural networks models using both supervised and unsupervised strategies. We first illustrate applications to the reconstruction of Lorenz-63 and Lorenz-96 systems from partial and noisy observations. Whereas the gain issued from the supervised learning setting emphasizes the relevance of groundtruthed observation dataset for real-world case-studies, these results also suggest new means to design data assimilation models from data. Especially, they suggest that learning task-oriented representations of the underlying dynamics may be beneficial. We further discuss applications to short-term forecasting and sampling design along with preliminary results for the reconstruction of sea surface currents from satellite altimetry data. </p><p>This abstract is supported by a preprint available online: https://arxiv.org/abs/2007.12941</p>

scholarly journals Neural networks with excitatory and inhibitory components: Direct and inverse problems by a mean-field approach

2016 ◽  
Vol 93 (1) ◽  
Author(s):  
Matteo di Volo ◽  
Raffaella Burioni ◽  
Mario Casartelli ◽  
Roberto Livi ◽  
Alessandro Vezzani
Keyword(s):  
Neural Networks ◽  
Inverse Problems ◽  
Mean Field ◽  
Direct And Inverse Problems ◽  
Field Approach ◽  
Inhibitory Components
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