# A DNN Framework for Learning Lagrangian Drift With Uncertainty

arXiv: https://arxiv.org/abs/2204.05891 · HTML: https://mlsanity.com/paper/2204.05891/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 38 references that are in the map.
- First posted on arXiv 12 Apr 2022.

## Builds on (most cited first, 11 of 11)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Rethinking Atrous Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1706.05587/) (2017)
- [Mixed Precision Training](https://mlsanity.com/paper/1710.03740/) (2017)
- [Stable ResNet](https://mlsanity.com/paper/2010.12859/) (2020)
- [On the adequacy of untuned warmup for adaptive optimization](https://mlsanity.com/paper/1910.04209/) (2019)
- [Exploratory Lagrangian-Based Particle Tracing Using Deep Learning](https://mlsanity.com/paper/2110.08338/) (2021)

## Built on by (most cited first, 3 of 3)

- [Deep learning for Lagrangian drift simulation at the sea surface](https://mlsanity.com/paper/2211.09818/) (2022)
- [Multi-Modal Drift Forecasting of Leeway Objects via Navier-Stokes-Guided CNN and Sequence-to-Sequence Attention-Based Models](https://mlsanity.com/paper/2508.18284/) (2025)
- [Impact of geophysical fields on Deep Learning-based Lagrangian drift simulations](https://mlsanity.com/paper/2604.03292/) (2026)

## Abstract (arXiv)

Reconstructions of Lagrangian drift, for example for objects lost at sea, are often uncertain due to unresolved physical phenomena within the data. Uncertainty is usually overcome by introducing stochasticity into the drift, but this approach requires specific assumptions for modelling uncertainty. We remove this constraint by presenting a purely data-driven framework for modelling probabilistic drift in flexible environments. Using ocean circulation model simulations, we generate probabilistic trajectories of object location by simulating uncertainty in the initial object position. We train an emulator of probabilistic drift over one day given perfectly known velocities and observe good agreement with numerical simulations. Several loss functions are tested. Then, we strain our framework by training models where the input information is imperfect. On these harder scenarios, we observe reasonable predictions although the effects of data drift become noticeable when evaluating the models against unseen flow scenarios.