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Reposted by Ashesh Chattopadhyay

Baskin Engineering at UC Santa Cruz @baskinengineering.bsky.social · 21/09/2026

A partnership with Fujitsu Research is enabling #BaskinEngineering Assistant Professor of Applied Mathematics Ashesh Chattopadhyay (@ashesh6810.bsky.social)to build energy-efficient AI models for climate predictions and solutions that analyze vulnerable regions. Learn more: bit.ly/4gUVMHC

bit.ly

Partnership with Fujitsu enables long-term impact forecasting of climate risks

Ashesh Chattopadhyay and Fujitsu Research are developing actionable AI-based climate models that reduce resource-guzzling computation time from months to minutes

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Reposted by Ashesh Chattopadhyay

Baskin Engineering at UC Santa Cruz @baskinengineering.bsky.social · 01/07/2026

Thrilled to share that Ashesh Chattopadhyay (@ashesh6810.bsky.social), assistant professor of applied mathematics at #BaskinEngineering, was awarded the 2026 SIAM Activity Group on Mathematics of Planet Earth Early Career Prize! Learn more: bit.ly/4wlKxNk

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Reposted by Ashesh Chattopadhyay

Baskin Engineering at UC Santa Cruz @baskinengineering.bsky.social · 17/02/2026

🌎 #BaskinEngineering Assistant Professor of Applied Mathematics @ashesh6810.bsky.social will build #AI models to project extreme Earth-system events with the support of the highly competitive Sloan Research Fellowship. Learn more: bit.ly/40f0UND

bit.ly

Ashesh Chattopadhyay wins Sloan Fellowship to build advanced AI for Earth-system modeling

Assistant Professor of Applied Mathematics Ashesh Chattopadhyay will build AI models to project extreme Earth-system events.

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 12/12/2025

10/10 🚀 Closing Our framework links spectral physics + SDE theory to define when diffusion models succeed or fail on multi-scale systems. This theory provides a blueprint for stable, high-fidelity generative modeling of physical dynamics.

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 12/12/2025

9/10 📌 Key Theoretical Insights ⚡ Spectral collapse is SDE-driven ⚡ Linear schedules are incompatible with power-law systems ⚡ β(τ) must be designed as a spectral operator ⚡ One-step generators emerge naturally from score geometry

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 12/12/2025

8/10 ➡️ Theory → Practice By aligning the diffusion process with spectral geometry, the model retains high-k modes, expands the learnable frequency band, and avoids SDE-induced instabilities. This is a theoretical refoundation of diffusion for physics.

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 12/12/2025

7/10 🧠 Lazy Diffusion: Geometric View Our theory shows the score field encodes local density geometry, allowing a one-step generator. Lazy Diffusion bypasses long reverse-SDE paths that reintroduce spectral collapse, enabling stable high-k reconstruction.

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 12/12/2025

6/10 ✨ Power-Law Insight The theory predicts an optimal range around γ ≈ 5, balancing stability and spectral fidelity. Large γ compresses noise injection and extends the learnable spectral window—while γ > 6 causes discrete-time instabilities.

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 12/12/2025

5/10 🧠 Noise Schedules as Spectral Operators We reinterpret β(τ) as a spectral regularizer. Standard linear schedules destroy high-k modes early. Power-law schedules β(τ) ∝ τ^γ reshape the SDE to preserve high-frequency coherence deeper into diffusion time.

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 12/12/2025

4/10 🧠 Fourier–SDE Theory Using a Fourier-space analysis, we derive closed-form SNR(k, τ) and show it decreases monotonically in |k| for power-law spectra. This reveals an intrinsic spectral bias embedded in the diffusion SDE itself.

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 12/12/2025

3/10 ⚠️ Spectral Collapse We prove that the forward diffusion SDE causes high-k SNR to decay far faster than low-k, so fine scales collapse to noise early. This limits the score model’s learnable spectrum and destabilizes downstream generators.

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 12/12/2025

2/10 🔍 Physical systems with power-law spectra rely on fine-scale structure. But the DDPM forward SDE erases high-frequency content too fast, making those modes impossible to learn. This is a theoretical mismatch, not a training issue.

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Reposted by Ashesh Chattopadhyay

Baskin Engineering at UC Santa Cruz @baskinengineering.bsky.social · 09/10/2025

🌊 Research led by #BaskinEngineering Assistant Professor of Applied Mathematics @ashesh6810.bsky.social shows that regional ocean dynamics in the Gulf of Mexico can be better emulated with #AI models—offering new possibilities for navigation and extreme weather monitoring. Read on: bit.ly/4n0AHvj

bit.ly

Regional ocean dynamics can be better emulated with AI models

Researchers show the success of their technical in a critical region: the Gulf of Mexico.

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 20/08/2025

🚀 Why it’s exciting: ✅ Physically grounded ✅ 10x–1000x faster than ROMS ✅ Enables regional “digital twins” ✅ Sets up for coupled ocean–atmosphere emulation ✅ Works across different reanalysis sources AI meets ocean science.

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 20/08/2025

📊 Results: Beats interpolation Matches or outperforms ROMS in short-term accuracy Stays stable & realistic over 10 years Captures mean state and eddy variability Preserves spectral energy across scales No exploding gradients here 💥

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 20/08/2025

🧠 What’s different: We don't just super-resolve existing data. We downscale from an emulator that predicts ocean dynamics. Plus: our downscaler learns to correct both model bias and physical mismatch (GLORYS → CNAPS). That’s new.

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 20/08/2025

⚙️ Our framework (FCDS): An FNO emulator predicts SSH, SSU, SSV, SSKE daily at 8 km A UNet + PatchGAN-VAE downscales to 4 km & corrects bias Spectral loss + online fine-tuning ensures physical consistency Together: speed, structure, and stability.

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 20/08/2025

🌍 Why this matters: Regional ocean models like the Gulf of Mexico are hard—complex coastlines, eddies, Loop Current, chaotic boundary forcing. Physics models = accurate but slow. ML = fast, but unstable after a few weeks. We wanted the best of both.

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 10/07/2025

Led by @baskinengineering.bsky.social PhD students Niloofar & Lenny with Tianning Wu & Roy He @ncstate.bsky.social If you're working on GenAI for Earth systems, let’s connect — curious to hear your thoughts! #GenAI #ClimateAI #OceanML #FNO #DDPM #DataAssimilation

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 10/07/2025

Our method is: ⚡️ One-shot 🌀 Physics-consistent 🌐 Scalable It captures high-wavenumber, fine-scale structures other ML baselines miss. Spectral diagnostics & vorticity metrics confirm this. (4/5)

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 10/07/2025

🧠 The framework combines: • FNO (Fourier Neural Operator) • DDPM (Denoising Diffusion Probabilistic Model) ✅ Reconstructs high-resolution states from 1%–0.1% data ✅ Works on synthetic turbulence, GLORYS reanalysis & real satellite altimetry ✅ No forward solver required (3/5)

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 10/07/2025

Ocean observations are often sparse, noisy, and Lagrangian (they move with the flow). This makes reconstructing fine-scale ocean dynamics like eddies and fronts very hard — especially for forecasting. We tackle this using a diffusion model conditioned on a neural operator. (2/5)

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 10/07/2025

🚨 New preprint alert! “Generative Lagrangian Data Assimilation for Ocean Dynamics Under Extreme Sparsity” is live! 📄 arxiv.org/abs/2507.06479 🌊 Reconstructs high-res ocean states from just 0.1% data using #GenAI. No forward model needed. (1/5)

arxiv.org

Generative Lagrangian data assimilation for ocean dynamics under extreme sparsity

Reconstructing ocean dynamics from observational data is fundamentally limited by the sparse, irregular, and Lagrangian nature of spatial sampling, particularly in subsurface and remote regions. This ...

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 02/06/2025

A physical analysis of #OceanNet, our high-resolution regional ocean digital twins' predictions for the Loop Current led by Anna Lowe in collaboration with Michael Gray, Tianning Wu, and Ruoying He out in AMS AI for Earth systems. journals.ametsoc.org/view/journal...

journals.ametsoc.org

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Reposted by Ashesh Chattopadhyay

Baskin Engineering at UC Santa Cruz @baskinengineering.bsky.social · 28/05/2025

🌪️ Can #AI predict freak weather events? AI models handle daily forecasts well—but often miss rare extremes. A team including #BaskinEngineering Asst. Prof. @ashesh6810.bsky.social is exploring how adding physics-based principles could improve AI’s accuracy in extreme cases. bit.ly/3Foh7ta

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 21/05/2025

Check out our new work in @pnas.org exploring AI weather's capabilities to predict OOD gray swans.

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 23/04/2025

A key takeaway is that both a priori and a posteriori performance of ML-based parameterization (stability, accuracy, etc) can be derived from insights embedded in the spectral representation of neural networks. Take a look at some of our older work if interested. academic.oup.com/pnasnexus/ar...

academic.oup.com

Explaining the physics of transfer learning in data-driven turbulence modeling

Abstract. Transfer learning (TL), which enables neural networks (NNs) to generalize out-of-distribution via targeted re-training, is becoming a powerful to

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 23/04/2025

We find an interesting distribution of Gabor filters and low-pass filters before and after fine-tuning and predictable spectral dynamics of the hidden layers both during training and fine-tuning phase.

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 23/04/2025

The key idea lies in analyzing the network in spectral space during training, inference, and fine-tuning. Interestingly, more often than not, generalizing to a new system means generalizing to a new shape of the Fourier spectrum and that is a key indicator of model performance a priori.

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Reposted by Ashesh Chattopadhyay

Yao Lai @chingyaolai.bsky.social · 17/03/2025

Looking forward to learning about recent advances in #AI4Climate at the @apsphysics.bsky.social #GlobalPhysicsSummit meeting. Come check out the back-to-back focus sessions, "AI Applications in Weather and Climate I & II," on Tuesday from 9:00 AM to 1:30 PM! summit.aps.org/schedule/?c=...

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Reposted by Ashesh Chattopadhyay

Ashesh Chattopadhyay @ashesh6810.bsky.social · 19/11/2024

I am hiring for a #postdocposition for scientific ML + climate dynamics. Folks with deep learning, scientific computing skills; preferably some background in climate, please reach out! This is part of an #NSF project in collaboration with Nicole Feldl and Geoff Vallis. recruit.ucsc.edu/JPF01844

recruit.ucsc.edu

Postdoctoral Scholar - Chattopadhyay Lab

University of California, Santa Cruz is hiring. Apply now!

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 10/01/2025

We have released the codes and the framework as a part of the pre-print. Do check it out if you are interested or work in this space. The framework is adaptable to other areas of geophysics and generally Earth system modeling beyond just the ocean and atmosphere.

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 10/01/2025

The 8Km emulated ocean is then downscaled to a 4KM reanalysis product with a generative model. The coupled emulator + downscaling framework is long-term stable, demonstrates accurate kinetic energy spectrum, and has the right mean and variability over decadal time scales.

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 10/01/2025

Some the key ideas in the work involves building a framework where instead of costly reanalysis products or forecasts which are downscaled, we built an ocean emulator at 8Km over the Gulf of Mexico which is long-stable, does not drift, and remain physically consistent.

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 10/01/2025

We have released a new pre-print on AI-based long-term regional ocean modeling and downscaling. arxiv.org/abs/2501.05058. This is work led by my PhD students Lenny and Moein with collaborators Roy He, Michael Gray, and Tianning Wu at NCSU and Subhashis Hazarika and Anthony Wong at Fujitsu Research

arxiv.org

Simultaneous emulation and downscaling with physically-consistent deep learning-based regional ocean emulators

Building on top of the success in AI-based atmospheric emulation, we propose an AI-based ocean emulation and downscaling framework focusing on the high-resolution regional ocean over Gulf of Mexico. R...

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 09/12/2024

5. And finally, some cool results on out-of-distribution generalization (a.k.a extrapolation) capabilities and lack-thereof for SOTA AI weather models on gray swan extremes from @pedramh.bsky.social's group and collaborators. agu.confex.com/agu/agu24/me... 5/5

agu.confex.com

Can AI weather models predict grey swan extreme events?

Short to medium-range forecasting has been transformed by AI weather models. Mo...

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 09/12/2024

4. We will also show some cool results on pen-and-paper stability analysis of autoregressive emulators, predicting model behavior in an architecture-agnostic fashion, and some interesting scaling laws on error growth and eigenvalues for deep learning emulators. agu.confex.com/agu/agu24/me.... 4/5

agu.confex.com

Jacobian Eigenvalue analysis for the stability of Neural Autoregressive Models of chaotic dynamic systems

Current state of the art methods for data driven climate and weather forecastin...

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 09/12/2024

3. If you are around on Wednesday, check out our high-resolution ocean emulator with simultaneous downscaling at 4KM regionally. agu.confex.com/agu/agu24/me... 3/5

agu.confex.com

Multi-scale, Long-term Stable, and Physically-consistent AI-based Ocean Modeling and Downscaling

While data-driven approaches demonstrate great potential in atmospheric modelin...

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 09/12/2024

2. Haiwen will present joint work with Romit Maulik and Troy Arcomano on LUICE, our cheap long-term stable, climate emulator agu.confex.com/agu/agu24/me.... You can also see our paper here: arxiv.org/abs/2405.16297 2/5

agu.confex.com

LUCIE: A Lightweight Uncoupled ClImate Emulator with Long-term Stability and Physical Consistency for O(1000)-member Ensembles

We present LUCIE, a data-driven atmospheric emulator that remains stable during...

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 09/12/2024

If you are around at #AGU2024 and interested in ML for climate, please check out these talks from my group and collaborators. 1. Biases, instability, hallucinations in ML emulators of weather and climate. agu.confex.com/agu/agu24/me.... You can also see our paper here: arxiv.org/abs/2304.07029 1/5

agu.confex.com

Understanding and mitigating hallucinations in AI-based Earth system emulators: Towards seamless weather to climate models

Recent efforts in building AI-based weather forecasting applications have recei...

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 26/11/2024

I guess, being careful about the discretization difference between the training data (ERA5), the IC (some other obs product), and numerics in the JAX solver. Some of the instabilities in online models might have nothing do with physics, but simply diff in grid/numerics. Love to chat more.

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 25/11/2024

We show that some of these issues arise from structural difference in numerics, grid resolution, ICs in IVPs, and the errors can be analytically expressed ( via Taylor series expansions), diagnosed a priori with linear stability analysis. We can say a lot about the model behavior and failure mode.

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Ashesh Chattopadhyay @ashesh6810.bsky.social · 25/11/2024

Many intrinsic instabilities, errors, failure to generalize in neural PDE/ODE, hybrid models, ML-based parameterization, e.g., in climate models is cast under the blanket of generalization error, sometimes, OOD error, especially in “extrapolation regime”. In this paper, we revisit this.

e.is

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