# A DNN Framework for Learning Lagrangian Drift With Uncertainty

**Authors:** Joseph Jenkins, Adeline Paiement, Yann Ourmières, Julien Le Sommer, Jacques Verron, Clément Ubelmann, Hervé Glotin  
**arXiv:** [2204.05891](https://arxiv.org/abs/2204.05891)  
**Date:** 2022-04-12  
**Summary page:** https://www.summarizepaper.com/en/paper/2204.05891v2/

## Key points

- New approach to modelling Lagrangian drift with uncertainty using deep learning
- Data-driven framework that can model probabilistic drift in flexible environments without specific assumptions
- Generation of probabilistic trajectories by simulating uncertainty in initial object position using ocean circulation model simulations
- Training of emulator of probabilistic drift over one day using perfectly known velocities and good agreement with numerical simulations observed
- Testing of several loss functions to optimize model performance
- Robustness evaluation with imperfect input information still resulting in reasonable predictions
- Contributions include proposing a novel data-driven approach applicable to any source or measure of uncertainty, introducing a new statistical representation of particle location for uncertain drift modelling, and improving performance by aligning learning criteria with problem setting
- Review of previous works on uncertain drift and trajectory modelling, dataset and methodology introduction, and presentation of experimental results provided
- Promising results offered with potential for improving Lagrangian drift reconstructions in various applications such as tracking lost objects at sea.

## Summary

This manuscript presents a new approach to modelling Lagrangian drift with uncertainty using deep learning. The proposed framework is purely data-driven and can model probabilistic drift in flexible environments without the need for specific assumptions. The authors generate probabilistic trajectories of object locations by simulating uncertainty in the initial object position using ocean circulation model simulations. They train an emulator of probabilistic drift over one day using perfectly known velocities and observe good agreement with numerical simulations. Several loss functions are tested to optimize the performance of the model. To further evaluate the framework's robustness, models are trained where the input information is imperfect but reasonable predictions are still observed. The contributions of this work include proposing a novel data-driven approach to modelling Lagrangian drift with uncertainty that can be applied to any source or measure of uncertainty. Additionally, they introduce a new statistical representation of particle location for modelling uncertain drift which has not been done in previous frameworks and demonstrate that performance can be improved by aligning the learning criteria with the problem setting. The rest of the article provides a review of previous works on uncertain drift and trajectory modelling, introduces their dataset and methodology, and presents experimental results. Overall, this manuscript offers promising results and opens up possibilities for improving Lagrangian drift reconstructions in various applications such as tracking objects lost at sea.