The research, led by Tianrui Zhou of Fujian Chuanzheng Communications College together with Jinggai Wang of Jimei University and Hao Li of the Shanghai Aids to Navigation Department of Donghai Navigation Safety, tackles a problem that has long divided the maritime-forecasting community. Physics-based drift models, such as Monte Carlo simulations and ocean-circulation models like FVCOM, describe the forces acting on a floating object and solve the equations of motion. They are interpretable, but they demand accurate hydrodynamic coefficients, high-resolution environmental inputs and often heavy computation. State-estimation tools such as Kalman filters are fast, but they stumble when buoy motion is highly nonlinear or when observations are gappy and irregular. Data-driven approaches promise a way around both sets of limitations — if the data are good enough and the architecture is chosen wisely.

Modern navigation buoys are no longer dumb markers. Equipped with GPS receivers, anemometers and current meters, they stream continuous records of their own position alongside the wind and current conditions around them. That multivariate stream is exactly the kind of raw material a recurrent neural network thrives on. Yet the authors argue that many existing studies have undersold the opportunity, relying on shallow, unidirectional recurrent networks that read the historical record only forwards, and feeding them wind and current as bare scalar speeds and angles — a choice that quietly corrupts the physics.

That corruption is subtler than it sounds. Wind direction is a circular quantity: 1 degree and 359 degrees are numerically far apart but physically almost identical. Hand raw angles to a neural network and it will treat a gentle veer across north as a violent 358-degree swing. The team’s answer is what they call a physics-informed feature framework — physics-informed in the sense that domain knowledge shapes the inputs, not that physical equations constrain the training. Wind and current speed–direction pairs are converted into orthogonal horizontal vector components, and the relative orientation between wind and current is encoded with sine and cosine terms, capturing whether the two forces cooperate or oppose. Meteorological wind directions, which conventionally point from where the wind comes, were converted to a common ‘toward’ convention to match current measurements. Three temporal variables — hour, day of week and month — round out a 13-dimensional input vector.

On top of this feature engineering sits LSTMNet, a two-layer bidirectional long short-term memory network. Each directional LSTM carries 64 hidden units, and the forward and backward hidden states are concatenated into a 128-dimensional representation of the recent past. The first recurrent layer extracts short-term patterns among wind, current, temporal and derived directional features; the second integrates those patterns into a higher-level picture of the evolving environment. Dropout with a probability of 0.2 sits between the layers to curb overfitting, and a fully connected output layer maps the learned representation to the buoy’s predicted latitude and longitude one hour ahead. Crucially, the bidirectional processing looks only backwards — it reads the 24-hour observation window in both chronological and reverse order, never peeking at the future.

The evaluation used operational data from a single moored navigation buoy in the coastal waters of Shanghai, recorded throughout May 2026. Buoy positions arrived hourly from GPS, while wind and current readings came in at one-minute intervals and were aggregated to hourly values, with directional variables handled using circular statistics. After screening out sensor glitches, interpolating gaps and normalising with training-set statistics only — a guard against information leakage — the data were split chronologically 80:10:10 into training, validation and test sets. The model trained for 150 epochs with the AdamW optimiser, a learning rate of 0.001 and a batch size of 32, using mean squared error as the loss.

The headline result: on the held-out test set, LSTMNet achieved a mean geodesic distance error of 18.297 metres, measured with the Haversine formula that computes true great-circle distances rather than naive Euclidean gaps between latitude–longitude pairs. That is a 9.747% improvement over a conventional single-layer unidirectional LSTM baseline, which managed 20.273 metres. The authors are careful to note that the gain reflects the combined effect of bidirectional encoding, network depth and model capacity, not bidirectionality alone — an unusually candid caveat in a field prone to overclaiming.

More striking is how LSTMNet fared against flashier competitors. Benchmarked under identical preprocessing, windows, horizons and training conditions, it outperformed CNNBiGRUAtt (21.546 m, a 15.08% reduction), GADNN (22.051 m, 17.02%), ResNetGRUAtt (23.280 m, 21.40%) and AttBiGRU (28.014 m, a striking 34.69%). Models stuffed with convolutional feature extractors, residual connections and attention mechanisms did worse than the compact stacked Bi-LSTM. The lesson, the authors suggest, is that architectural complexity is not a substitute for a temporal representation suited to the data’s scale: with a short 24-hour window and strong local continuity in the trajectory, attention weighting appears to add parameters without adding insight. In a telling detail, GADNN actually achieved the lowest validation loss, yet LSTMNet produced the smallest test-set distance error — a reminder that mean squared error on standardised coordinates and real-world spatial accuracy are different currencies, and that trajectory models should be judged in metres, not in loss curves.

Visualisations reinforce the quantitative story. Both LSTMNet and the baseline reproduce the overall wobble of the buoy around its watch circle near 30.726°N, 122.018°E, but LSTMNet tracks consecutive directional changes more closely, while the baseline’s predictions run smoother and slightly lag the observations — a known side effect of MSE losses that penalise large deviations and thereby favour averaged-out trajectories. Sample-wise error plots show most predictions landing near 20 metres, with LSTMNet exhibiting fewer and smaller spikes than its rivals, though it too stumbles at certain moments, hinting at unmeasured drivers such as waves, which the monitoring system did not record and which the authors explicitly treat as a source of uncertainty.

The team is equally frank about the study’s limits. The evidence comes from one moored buoy over one month, so the results demonstrate effectiveness for this case, not universal generalizability across buoy types, seasons, regions or storms. The reported numbers rest on a single training run with a fixed random seed, and the authors call for multiple independent runs and multi-buoy, multi-season validation. Future work should add wave height, wave period, tidal level, mooring condition, water depth and nearby vessel traffic as inputs, and move from deterministic point forecasts to probabilistic ones with prediction intervals — the kind of uncertainty quantification that risk-informed operational decisions genuinely need. Even so, the framework’s practical promise is clear: a data-driven model that needs no explicit formulation of buoy dynamics, runs on the sensors already mounted on modern buoys, and predicts position to within about 18 metres an hour ahead. For navigation authorities weighing the costs of drift warnings, maintenance scheduling and search-and-recovery operations, that is a small number with potentially large consequences.

Subject of Research: Deep learning prediction of short-term marine buoy trajectory drift under dynamic ocean conditions

Article Title: Physics-informed LSTMNet for short-term marine buoy trajectory prediction under dynamic ocean environmental conditions

Article References: Zhou, T., Wang, J., & Li, H. (2026). Physics-informed LSTMNet for short-term marine buoy trajectory prediction under dynamic ocean environmental conditions. Frontiers in Marine Science, 13, Article 1953622. https://doi.org/10.3389/fmars.2026.1953622

Image Credits: AI Generated

DOI: 10.3389/fmars.2026.1953622

Keywords: marine buoys, trajectory prediction, bidirectional LSTM, deep learning, navigational safety, ocean currents, wind forcing, time-series forecasting, Haversine distance, maritime infrastructure, Shanghai coastal waters, physics-informed features