Our next seminar will be held on Friday the 30th of September 2022, at 14h30 ECT, at the Pierre et Marie Curie campus of Sorbonne Université, in seminar room 105 of LiP6, located on the first floor of the corridor 25/26 (easier access through tower 26).

The seminar can also be followed remotely through zoom here: https://zoom.us/j/94432755467

You can ask questions during and after the talk, in the slack channel.

Arthur Filoche’s talk is entitled:

« Variational data assimilation with deep prior »

Data Assimilation remains the operational choice when it comes to

forecast and estimate Earth’s dynamical systems, and proposes a large panel of methods to optimally combine a dynamical model and observations

allowing to predict, filter, or smooth system state trajectory.

The classical variational assimilation cost function is derived from

modelling errors prior with uncorrelated in times Gaussian distribution.

The optimization then relies on errors covariance matrices as

hyperparameters.

But such statistics can be hard to estimate particularly for background

and model errors. In this work, we propose to replace the Gaussian prior

with a deep convolutional prior circumventing the use of background

error covariances.

To do so, we reshape the optimization so that the initial condition to

be estimated is generated by a deep architecture. The neural network is

optimized on a single observational window, no learning is involved as

in a classical variational inversion.

The bias induced by the chosen architecture regularizes the proposed

solution with the convolution operators imposing locality.

From a computational perspective, control parameters have simply been

organized differently and are optimized using only the observational

loss function corresponding to a maximum-likelihood estimation.

We propose several experiments highlighting the regularizing effect of

deep convolutional prior. First, we show that such prior can replace

background regularization in a strong-constraints 4DVar using a shallow

water model. We extend the idea in a 3DVar set-up using spatio-temporal

convolutional architecture to interpolate sea surface satellite tracks

and obtain results on par with optimal interpolation with fine-tuned

background matrix. Finally, we give perspective toward applying the same

method in weak-constrained 4DVar removing the need for model-errors

covariances but still enforcing correlation in space and time of model

errors.

Biographic notice:

Arthur Filoche is a Ph.D. student at the LiP6 of Sorbonne Université in France, under the supervision of Dominique Béréziat, Julien Brajard, and Anastase Charantonis. His research interests lie in combining deep learning and data assimilation