💻 computer science

Samudra 2: Scaling Ocean Emulators across Resolutions

Samudra 2 is an advanced autoregressive neural ocean emulator that overcomes previous limitations in resolution and long-term stability through architectural and loss-function innovations, enabling high-fidelity, multi-year global simulations at up to $1/4^\circ$ resolution on a single GPU.

Original authors: Yuan Yuan, Jesse Rusak, Alexander Merose, Adam Subel, Pavel Perezhogin, Alistair Adcroft, Carlos Fernandez-Granda, Laure Zanna

Published 2026-06-03

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CC BY 4.0

Original authors: Yuan Yuan, Jesse Rusak, Alexander Merose, Adam Subel, Pavel Perezhogin, Alistair Adcroft, Carlos Fernandez-Granda, Laure Zanna

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the Earth's oceans as a giant, chaotic, and incredibly complex dance. Scientists use massive computer programs called "Ocean General Circulation Models" (OGCMs) to try to predict how this dance moves over decades or centuries. These programs are like super-accurate, high-definition movies, but they are so computationally expensive to run that they take millions of hours of computer time. This means scientists can only make a few "movies" to study different climate scenarios, which limits their ability to understand the full picture of climate change.

Enter Samudra 2, a new artificial intelligence (AI) tool designed to be a "speedy stand-in" for these massive computer programs. Think of it as a highly skilled improvisational actor who has watched the original movie thousands of times and can now recreate the scenes in a fraction of the time, running on a single graphics card (like the kind in a gaming computer) instead of a supercomputer.

Here is how the paper explains the improvements Samudra 2 brings to the table:

The Problem with the First Version (Samudra)

The original AI emulator, Samudra, was a breakthrough because it could run simulations for decades. However, it had two major "glitches" that made the long-term movies look wrong:

The "Boring Movie" Effect (Variance Collapse): Over time, the AI got lazy. Instead of showing the wild, chaotic waves and currents that actually happen, it started predicting that the ocean would just settle into a calm, average state. It lost the "spark" and excitement of the real ocean.
The "Ghosting" Effect (Imprinting Artifacts): The AI got confused between different parts of the ocean. It started copying the patterns of surface currents (like the Gulf Stream) and stamping them onto the deep, dark ocean floor where they don't belong. It was like a projector accidentally shining the image of a busy street onto a quiet bedroom wall. This created fake patterns and noise in the deep ocean data.

Additionally, the original Samudra could only see the ocean in "low resolution" (1 degree), which was too blurry to see important small-scale swirls called "eddies."

The Samudra 2 Upgrade

The researchers fixed these issues with two main upgrades:

1. A Bigger, Smarter Brain (Wider Architecture)
They made the AI's "brain" wider and more capable. Imagine upgrading from a small sketchpad to a massive, high-definition canvas. This new design allows the AI to see much finer details.

The Result: They successfully scaled the AI to run at 1/2 degree and 1/4 degree resolutions. At this higher resolution, the AI can finally "see" the small, swirling eddies and the sharp, fast currents along the edges of continents (like the Gulf Stream) that were previously invisible. It's like switching from a pixelated 1990s video game to a crisp 4K movie.

2. A Smarter Teacher (Dynamic Loss Function)
In machine learning, the "loss function" is the teacher that grades the AI's homework. The old teacher treated every part of the ocean equally. Since the surface of the ocean is very active and the deep ocean is very calm, the teacher paid too much attention to the surface and ignored the deep ocean.

The Fix: The new "Dynamic Loss" is a teacher that pays extra attention to the parts the AI is getting wrong. If the AI is doing a great job on the surface but messing up the deep ocean, the teacher says, "Hey, focus on the deep ocean!" It constantly reweights the grading to ensure the quiet, slow-moving deep ocean gets the attention it needs.
The Result: This stopped the "Ghosting" effect. The deep ocean predictions became much cleaner, and the fake patterns disappeared. The error in deep-ocean temperature predictions dropped by about seven times.

How Well Does It Work?

The team tested Samudra 2 by letting it run a simulation for about 8 years on a single computer chip. They compared its "movie" to the real, high-fidelity computer model (OM4).

Temperature: It got much better at predicting the temperature of the upper ocean (the top 700 meters), improving its accuracy score significantly.
Deep Ocean: While it still struggles to perfectly predict the deep ocean (which is incredibly hard because the changes there are tiny), it reduced the errors drastically compared to the old version.
Speed: Because it runs so fast, scientists can now run hundreds or thousands of these simulations (ensembles) to better understand uncertainty in climate predictions, something that was previously too expensive to do.

The Bottom Line

Samudra 2 is a faster, sharper, and more stable AI emulator for the ocean. It fixes the "boring" and "ghostly" mistakes of its predecessor and can now see the ocean in high definition, capturing the small swirls and currents that matter for climate science. While it still has work to do on the deepest parts of the ocean, it opens the door for scientists to run massive, detailed climate experiments that were previously impossible due to cost and time.

Technical Summary: Samudra 2: Scaling Ocean Emulators across Resolutions

Problem Statement

Ocean General Circulation Models (OGCMs) are fundamental to climate science for simulating the transport of heat, salt, carbon, and momentum. However, their computational expense severely limits the ability to run large ensembles or explore diverse forcing scenarios, particularly when high spatial resolution is required to resolve mesoscale eddies and sharp frontal structures. While neural emulators offer potential speedups, existing ocean emulators have struggled to combine fine spatial resolution with long-term dynamical stability.

The authors identify three specific failure modes in their predecessor, Samudra, which was limited to $1^\circ$ resolution:

Variance Collapse: Autoregressive error accumulation causes predictions to regress toward the climatological mean, suppressing temporal variability, especially in the deep ocean.
Imprinting Artifacts: Spatial patterns from velocity fields "leak" into temperature and salinity fields, creating nonphysical banding and high-frequency noise that amplifies over multi-year rollouts.
Resolution Limitation: The inability to operate at resolutions finer than $1^\circ$ prevents the emulation of mesoscale eddies and western boundary current structures that are critical for climate variability.

Methodology

Samudra 2 addresses these challenges through two complementary architectural and training modifications applied to a U-Net backbone built from modified ConvNeXt-style blocks.

1. Architectural Scaling

To support higher resolutions ( $1/2^\circ$ and $1/4^\circ$ ), the authors widened the U-Net backbone rather than deepening it.

Channel Width: The channel widths across the encoder-decoder stages were increased from $[200, 250, 300, 400]$ to $[280, 380, 480, 520]$ .
Expansion Factor: The internal expansion factor within the modified ConvNeXt blocks was reduced from 4 to 2. This design shifts parameter capacity from the block-internal bottleneck to the inter-stage feature dimensions, balancing representational capacity with computational cost.

2. Dynamic Loss Function

To address variance collapse and imprinting, the authors replaced the standard Mean Squared Error (MSE) loss with a dynamic, channel-weighted loss.

Mechanism: Standard MSE is dominated by high-variance surface fields, causing the optimizer to neglect slow-evolving deep-ocean signals. The new loss function reweights each output channel inversely proportional to its running prediction error.
Implementation: Weights are updated online using an Exponential Moving Average (EMA) of the inverse per-channel MSE. This adaptively amplifies the gradient signal for channels with small errors (typically deep-ocean fields) while preventing high-variance surface channels from dominating the loss.
Clamping: Weights are clamped to a ratio (set to $L=20$ ) to prevent over-amplification of channels with negligible learnable signal.

Training and Evaluation Setup

Data: The models are trained on output from the GFDL OM4p25 ocean model ( $1/4^\circ$ native), regridded to $1^\circ$ , $1/2^\circ$ , and $1/4^\circ$ .
Variables: The emulator predicts 77 channels (potential temperature, salinity, zonal/meridional velocity at 19 depth levels, and sea surface height) driven by atmospheric forcing.
Rollouts: Training uses short autoregressive rollouts ( $K=4$ steps, 40 days). Evaluation involves long-horizon autoregressive rollouts of approximately 8 years (~580 steps) without ground-truth feedback, assessing metrics like temporal variance, spectral distributions, and climate indices (e.g., Niño 3.4).

Key Contributions

Samudra 2 Model: An improved AI ocean emulator that integrates a wider ConvNeXt U-Net with a dynamic variance-weighted loss. It successfully mitigates variance collapse and imprinting artifacts in long-horizon autoregressive emulation.
Multi-Resolution Scaling: The first demonstration of multi-year ocean emulation at $1/2^\circ$ and $1/4^\circ$ resolutions. The models recover mesoscale structures (eddies, meanders, filaments) and sharp western boundary currents that are unresolved at $1^\circ$ .
Diagnostic Framework: A comprehensive evaluation showing that while short-term accuracy is necessary, long-horizon climate diagnostics (variance, spectral distribution) are essential for validating ocean emulators intended for climate projection.

Results

Performance at $1^\circ$ Resolution

Upper Ocean: The $R^2$ for global-mean upper-ocean temperature improved from 0.56 (Samudra) to 0.87 (Samudra 2).
Deep Ocean: Deep-ocean temperature error was reduced by approximately sevenfold. While $R^2$ values remained negative (indicating performance worse than a temporal mean baseline), the magnitude of the error was significantly reduced (from $-111.36$ to $-16.14$).
Imprinting: Visual and statistical analysis confirmed the suppression of velocity-imprinting artifacts in deep-ocean temperature and salinity fields.

Multi-Resolution Performance ( $1/2^\circ$ and $1/4^\circ$ )

Spatial Fidelity: Higher resolutions progressively resolved finer spatial scales. The $1/4^\circ$ model captured mesoscale eddies and western boundary current hotspots (Gulf Stream, Kuroshio, Agulhas) with variance structures closely matching the OM4 reference.
Spectral Fidelity: The $1/4^\circ$ model extended the resolved wavenumber range by a factor of four compared to the $1^\circ$ model, accessing mesoscale dynamics absent in coarser grids.
Temporal Tracking: All resolutions tracked upper-ocean variability well ( $R^2 = 0.84–0.92$ ). Intermediate depth performance improved with resolution (e.g., $R^2$ at $1/4^\circ$ approached 0.01), though deep-ocean tracking ( $2000–7000$ m) remained an open challenge with negative $R^2$ across all resolutions.

Ablation Studies

Ablation experiments at $1^\circ$ revealed a strong synergistic interaction between the two modifications:

Wider Architecture Alone: Did not improve upper-ocean performance ( $R^2 = 0.50$ ) and degraded intermediate-depth salinity.
Dynamic Loss Alone: Did not improve upper-ocean performance ( $R^2 = 0.51$ ) but was the primary driver for reducing deep-ocean error.
Combined (Samudra 2): Achieved $R^2 = 0.87$ in the upper ocean, demonstrating that the wider architecture provides the necessary capacity for the dynamic loss to function effectively.

Significance and Claims

The paper claims that Samudra 2 enables larger ensembles for sea-level projections, ocean heat uptake studies, and climate variability analysis by running on a single GPU. By resolving mesoscale features at $1/4^\circ$ , the emulator offers a tractable alternative for studying processes dependent on eddy dynamics.

The authors maintain a modest stance regarding deep-ocean fidelity, acknowledging that predictions below $\sim700$ m remain an open challenge due to extremely weak training signals and the dominance of background variance. They position Samudra 2 as a significant step forward that addresses specific long-horizon failure modes (variance collapse, imprinting) and scales to higher resolutions, while noting that physics-based simulations remain the more reliable reference for deep-ocean variability. The work is framed as contributing to a broader class of long-horizon autoregressive ML problems, addressing issues like spectral bias and cross-variable loss imbalance.