ENSO remains the dominant source of interannual climate variability, and the quality of weather and climate forecasts directly depends on our ability to predict its phases. Existing dynamical models suffer from systematic errors, while purely statistical approaches lose skill beyond 9 months. Deep neural networks have improved accuracy, but their 'black box' nature prevents understanding which physical processes they have learned. This work sits at the intersection of two fields: hybrid ocean modeling and interpretable machine learning. Nearby in the archive are studies on forecasting El Niño 18 months ahead, training neural networks on the Ising model, and fiber-optic ocean sensing, but none address the dual challenge of long-term and physically meaningful ENSO prediction.
PTSTnet integrates three ideas: physics-encoding learning, cross-scale fusion of spatiotemporal features, and a recurrent prediction strategy. Input data consist of global grids of sea surface temperature, upper-layer heat content, and zonal and meridional winds over 12 consecutive months. Hidden states pass through convolutional tensor transformations that capture relationships across scales, while physical constraints (wave and diffusion processes) are added to the loss function. The recurrent strategy uses previous forecasts as context to reduce error accumulation. The model was trained on reanalysis data from 1982 to 2015 and tested on 2016–2022.
On the test period 2016–2022, PTSTnet achieved a correlation above 0.5 for the Niño 3.4 index at all lead times up to 24 months, and for some seasons up to 30 months. For comparison, the IRI dynamical models lose skill after 9 months, and the best deep learning counterparts (3D-Geoformer, ENSO-GTC) do not provide forecasts beyond 20 months. Prediction errors propagate from the western equatorial Pacific to the eastern and then to global scales, consistent with observed upwelling dynamics and trade wind intensification. The model accurately reproduced the 2015–2016 super El Niño and multi-phase events, including the multi-year La Niña, and also mitigated the spring predictability barrier.
PTSTnet is the first example of hybrid modeling where physical laws are embedded in the neural network architecture for ENSO forecasting, rather than used as post-processing. Unlike neighboring works that either predict shorter lead times or lack physical interpretation, here interpretability is achieved through error propagation analysis and feature significance maps. This shifts the approach to ocean modeling: instead of a black box, we get a tool that can be used to test hypotheses about ENSO mechanisms. The work sits on the periphery of the thematic map, but its method could become a bridge between machine learning and physical oceanography.
Adding new physical processes, such as momentum conservation, could improve predictions. Transfer learning with freezing of shallow layers could help adapt the model to regions with sparse data. In the future, PTSTnet could be extended to forecast other climate modes, such as the Indian Ocean Dipole or the Atlantic Dipole.
The method will affect operational climate forecast centers, which could receive more reliable El Niño warnings two years in advance. It is also useful for agriculture, water resource management, and the insurance sector, which depend on seasonal forecasts.
Test the model on independent data beyond 2022 and on other ocean basins. Integrate additional variables (salinity, currents) and compare with ensemble forecasts from dynamical models.
For oceanography, a key unresolved problem is ENSO predictability beyond one year, especially overcoming the spring barrier. This work directly attacks that problem, showing that hybrid models can maintain skill up to 24 months. An open question remains whether physical interpretability truly reflects causal relationships rather than correlations in the data.
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
The authors built PTSTnet, a hybrid neural network that predicts ENSO up to 24 months ahead by combining deep learning with physical constraints. The model was trained on 12 months of global sea surface temperature, ocean heat content, and wind data, and achieved correlations above 0.5 at all lead times up to 24 months, outperforming dynamical and other deep-learning models. Error propagation analysis showed errors moving from the western to the eastern Pacific, consistent with Bjerknes feedback theory.
Where its strength is
The strength of this work lies in merging physical laws with neural network architecture, which not only enables prediction but also allows interpretation of ENSO mechanisms through error analysis and saliency maps. This paves the way for testing hypotheses about ocean dynamics.
Where it could go next
Worth trying
Why this may matter
Successful long-lead ENSO prediction with physical interpretation could improve seasonal and decadal climate forecasts, which is critical for agriculture, water resource management, and preparedness for extreme weather events.
Nearby works in our archive
The closest work in the archive sits at 0.61 by meaning — the usual level for our corpus.
The model was able to predict the 2015–2016 super El Niño, initializing as early as February 2015, when most dynamical models gave large uncertainty.
In Kim Stanley Robinson's novel 'Forty Signs of Rain', scientists struggle for accurate prediction of climate shifts; PTSTnet resembles a step toward such a system, where physics and data merge into a transparent tool.