Learning effective Sargassum transport dynamics from limited drifter observations
Authors: F. J. Beron-VEra, M. J. Olascoaga, J. Morell, E. Cruz
Organizations: Department of Atmospheric Sciences Rosenstiel School of Marine, Atmospheric, and Earth Science University of Miami Miami, Florida, USA · Department of Ocean Sciences Rosenstiel School of Marine, Atmospheric, and Earth Science University of Miami Miami, Florida, USA · Department of Marine Sciences University of Puerto Rico Mayagüez, Puerto Rico
Floating-material transport is influenced by unresolved processes that are often absent from available circulation products. We develop a data-driven transport-learning framework for learning effective transport corrections from limited Lagrangian observations using physically motivated ocean--atmosphere diagnostics and finite-memory representations motivated in part by inertial-particle memory effects. The diagnostic representation is analyzed through predictive and sparse symbolic-discovery approaches under leave-one-trajectory-out validation. Applications to Sargassum-following drifters in the Puerto Rico region and the Gulf Stream show that the diagnostics contain transport-relevant information beyond the baseline circulation products. Multilayer perceptron (MLP) ensembles provide flexible predictive trajectory corrections, while Sparse Identification of Nonlinear Dynamics (SINDy) tests whether instantaneous or delayed sparse symbolic transport structure can be extracted from the diagnostics. The results differ across flow regimes: (i) in Puerto Rico, delayed sparse symbolic corrections provide modest but systematic improvement; (ii) in the Gulf Stream application, dynamically useful sparse symbolic corrections remain primarily instantaneous even though delayed predictive information persists. These results support finite-memory transport effects in coarse-grained floating-material transport while also illustrating the difficulty of obtaining stable delayed sparse symbolic closures.
The North Pacific Subtropical Gyre (NPSG) is a major accumulation zone for floating plastic debris, resulting from basin-scale convergent ocean circulation. Effective cleanup strategies in this region rely on accurate forecasts of Lagrangian particle drift. Here, we introduce Drift Field Net (DFN), a deep neural network that predicts ocean surface flow fields from operational satellite observations. DFN is trained using a novel two-stage strategy that combines pretraining on simulated data with Lagrangian fine-tuning based on an advection-consistent loss function. This physics-informed optimization directly improves the accuracy of particle trajectory predictions. We evaluate DFN against an operational physics-based forecasting system and demonstrate the potential of deep learning for ocean surface flow prediction. On in situ drifter trajectories, DFN reduces the mean positioning error by 20 km after a 7-day forecast compared with the operational model. Furthermore, Lagrangian fine-tuning with the proposed advection loss further reduces the positioning error by 10 km, highlighting the benefits of incorporating Lagrangian constraints into the training process.
This work addresses the problem of learning the dynamics of high-dimensional probability densities over time using unlabeled samples, without assuming access to trajectory information. We introduce two-parameter flows that learn only sampling-time transports from a base distribution to each marginal and then extract a physics-time velocity by regressing on coupled synthetic trajectories. We prove that the resulting physics-time dynamics are unique and inherit regularity from the sampling-time transports. Because we can build on standard, well-developed conditional flow matching techniques for learning the base-to-marginal transports, our approach scales to high dimensions and avoids per-step optimal-transport couplings, while allowing admissible non-gradient dynamics that can naturally explain rotational or circulating physics phenomena.
Paul Schwerdtner, Tobias Blickhan, Benjamin Peherstorfer
Flow matching (FM) has emerged as a powerful framework for learning dynamic transport maps between two empirical distributions. However, less explored is the setting with intermediate observed marginals that can help constrain the flows between the endpoints. This "multimarginal" regime is central to modeling temporal evolution in dynamical systems in many scientific domains that can sample sequential distributions. We tackle this problem with a novel approach that leverages the connection between FM and dynamic optimal transport (OT), softly steering the flow towards the intermediate marginals through potential terms in the dynamic OT action. By extending the conditional FM learning target to incorporate these potentials, we derive an efficient, simulation-free algorithm for multimarginal FM that offers considerable flexibility in the spatiotemporal dynamics of the learned flows. We demonstrate state-of-the-art performance and training efficiency of OT-potential FM (OTP-FM) on diverse single-cell RNA sequencing, oceanographic, and meteorological datasets. Our code is available at https://github.com/Bexorg-Inc/OTP-FM.