arXiv subjects

Ashesh Chattopadhyay

Publications and source records attributed to Ashesh Chattopadhyay.

At least 19 recordsLinked to original sources

arXiv2026

AI Emulation of Stochastic Sudden Stratospheric Warming with Interpretable Latent Structure

Rare weather regime transitions pose a challenge for data-driven modeling due to class imbalance. In this study, we develop a probabilistic deep learning emulator for a prototypical system with regime transitions, the stochastic Holton--Mass model of stratospheric variability, and analyze the structure of its learned latent space. The Holton--Mass model exhibits two metastable regimes, a strong and a weak polar vortex, maintained by nonlinear wave--mean flow interactions, with weak stochastic forcing intermittently triggering rare transitions between these regimes that qualitatively represent SSW events. We employ a ResNet-inspired Conditional Variational Autoencoder with six-layer encoder and decoder layers and explicit current-state conditioning to model the distribution of the system's state at the next time step (one day). The emulator accurately reproduces short-term dynamics, steady-state probability distributions, regime persistence statistics, rare transition rates, the transition committor function, and the transition expected lead time of the physical model. Beyond emulation fidelity, we interrogate the learned latent representation to understand how the model internalizes the underlying metastable structure of the dynamics. Principal Component Analysis of the 32-dimensional latent space reveals a clear and unsupervised separation into four physically interpretable clusters corresponding to strong versus weak vortex regimes and stable versus transition-prone configurations. Such emergent regime separation in latent space is hard to identify for deep generative models applied to high-dimensional stochastic systems. Our results show that carefully designed probabilistic emulators can uncover physically meaningful manifolds governing extreme-event dynamics, potentially aiding the development of improved operational advanced warning systems.

physics.ao-ph↗

arXiv2026

Optimizing Geoengineering Interventions Using Differentiable Climate Models

The deployment of a geoengineering program to cool Earth's climate may be imminent. It is crucial that tools be developed to ensure that such a program would achieve its objectives while minimizing disruption. Here we exploit recently developed differentiable atmospheric models to demonstrate a novel geoengineering control strategy. In the differentiable primitive-equation atmospheric model JAX-GCM we impose a uniform $+4$\,K ocean warming and ask what pattern of sea-surface temperature cooling -- in five ocean-masked zonal bands of prescribed SST forcings whose amplitudes are free -- returns land near-surface air temperature closest to the model's own unwarmed climatology. This idealized set-up represents a cooling pattern that could be delivered physically either by marine cloud brightening or stratospheric aerosol injection. Gradients through chaotic dynamics decorrelate from the true sensitivity beyond the Lyapunov horizon, so we optimize greedily over segments of 8 to 14 days, following receding-horizon control. The learned strategy removes $92.3 \pm 0.4\%$ of the realized land warming across a ten-member ensemble of two-year rollouts, and a three-year run sustains it. If we use the spatial pattern of land temperature as the optimization objective, the distributions of precipitation, evaporation, and specific humidity over land are restored as well, even though they are not included in the objective function. The learned strategy from JAX-GCM replayed in the AI emulators LUCIE and NeuralGCM without re-optimization is successful, suggesting robustness. These promising results demonstrate a strategy for designing optimal climate interventions that can be applied broadly for geoengineering scenarios under consideration.

physics.ao-ph↗

arXiv2026

Eigenanalysis framework for autoregressive neural emulators of multi-scale chaotic dynamics

Neural autoregressive models have rapidly emerged as powerful emulators of high-dimensional chaotic systems, yet their long-term instability and error growth remain poorly understood, leading to ad-hoc solutions. Here, we develop an eigenanalysis framework that reveals the dynamical origin of this error growth. By analyzing the Jacobian of the learned one-step update map with respect to the state, we show how inference-time error growth, and thus model stability, is governed by its spectral radius. Direct-step architectures (models that predict the next state from the previous one) generically admit unstable eigenvalues with magnitudes exceeding one, explaining the rapid divergence of these widely used models. In contrast, integration-constrained models (where the time derivative is estimated and integrated with a higher-order integrator) collapse their eigenspectrum onto the unit circle, yielding neutral stability and a universal linear error-scaling law. The largest eigenvalue of this Jacobian provides an architecture-agnostic, a priori diagnostic of short-term skill, long-term stability, and spectral bias, without requiring an expensive rollout. Leveraging this theory, we introduce a stability-promoting loss that explicitly regularizes Jacobian-driven error amplification, improving both forecast accuracy and dynamical robustness. Demonstrated across $29$ models spanning two architectures, several explicit and implicit integrators, and multiple loss functions on the Kuramoto-Sivashinsky system, our results establish a theoretical foundation for the design and evaluation of neural emulators of chaotic multi-scale dynamics. More broadly, our framework is a step toward the kind of a priori stability analysis that numerical analysis provides for discretizations of differential equations and that scientific machine learning currently lacks.

cs.AI↗

arXiv2026

High-Resolution Climate Projections Using Diffusion-Based Downscaling of a Lightweight Climate Emulator

The proliferation of data-driven models in weather and climate sciences has marked a significant paradigm shift, with advanced models demonstrating exceptional skill in medium-range forecasting. However, these models are often limited by long-term instabilities, climatological drift, and substantial computational costs during training and inference, restricting their broader application for climate studies. Addressing these limitations, Guan et al. (2024) introduced LUCIE, a lightweight, physically consistent climate emulator utilizing a Spherical Fourier Neural Operator (SFNO) architecture. This model is able to reproduce accurate long-term statistics including climatological mean and seasonal variability. However, LUCIE's native resolution (~300 km) is inadequate for detailed regional impact assessments. To overcome this limitation, we introduce a deep learning-based downscaling framework, leveraging probabilistic diffusion-based generative models with conditional and posterior sampling frameworks. These models downscale coarse LUCIE outputs to 25 km resolution. They are trained on approximately 14,000 ERA5 timesteps spanning 2000-2009 and evaluated on LUCIE predictions from 2010 to 2020. Model performance is assessed through diverse metrics, including latitude-averaged RMSE, power spectrum, probability density functions and First Empirical Orthogonal Function of the zonal wind. We observe that the proposed approach is able to preserve the coarse-grained dynamics from LUCIE while generating fine-scaled climatological statistics at ~28km resolution.

cs.LG↗

arXiv2026

High-resolution probabilistic estimation of three-dimensional regional ocean dynamics from sparse surface observations

The ocean interior regulates Earth's climate but remains sparsely observed due to limited in situ measurements, while satellite observations are restricted to the surface. We present a depth-aware generative framework for reconstructing high-resolution three-dimensional ocean states from extremely sparse surface data. Our approach employs a conditional denoising diffusion probabilistic model (DDPM) trained on sea surface height and temperature observations with up to 99.9 percent sparsity, without reliance on a background dynamical model. By incorporating continuous depth embeddings, the model learns a unified vertical representation of the ocean states and generalizes to previously unseen depths. Applied to the Gulf of Mexico, the framework accurately reconstructs subsurface temperature, salinity, and velocity fields across multiple depths. Evaluations using statistical metrics, spectral analysis, and heat transport diagnostics demonstrate recovery of both large-scale circulation and multiscale variability. These results establish generative diffusion models as a scalable approach for probabilistic ocean reconstruction in data-limited regimes, with implications for climate monitoring and forecasting.

physics.ao-ph↗

arXiv2025

Generative forecasting with joint probability models

Chaotic dynamical systems exhibit strong sensitivity to initial conditions and often contain unresolved multiscale processes, making deterministic forecasting fundamentally limited. Generative models offer an appealing alternative by learning distributions over plausible system evolutions; yet, most existing approaches focus on next-step conditional prediction rather than the structure of the underlying dynamics. In this work, we reframe forecasting as a fully generative problem by learning the joint probability distribution of lagged system states over short temporal windows and obtaining forecasts through marginalization. This new perspective allows the model to capture nonlinear temporal dependencies, represent multistep trajectory segments, and produce next-step predictions consistent with the learned joint distribution. We also introduce a general, model-agnostic training and inference framework for joint generative forecasting and show how it enables assessment of forecast robustness and reliability using three complementary uncertainty quantification metrics (ensemble variance, short-horizon autocorrelation, and cumulative Wasserstein drift), without access to ground truth. We evaluate the performance of the proposed method on two canonical chaotic dynamical systems, the Lorenz-63 system and the Kuramoto-Sivashinsky equation, and show that joint generative models yield improved short-term predictive skill, preserve attractor geometry, and achieve substantially more accurate long-range statistical behaviour than conventional conditional next-step models.

cs.LG↗

arXiv2025

Lazy Diffusion: Mitigating spectral collapse in generative diffusion-based stable autoregressive emulation of turbulent flows

Turbulent flows posses broadband, power-law spectra in which multiscale interactions couple high-wavenumber fluctuations to large-scale dynamics. Although diffusion-based generative models offer a principled probabilistic forecasting framework, we show that standard DDPMs induce a fundamental \emph{spectral collapse}: a Fourier-space analysis of the forward SDE reveals a closed-form, mode-wise signal-to-noise ratio (SNR) that decays monotonically in wavenumber, $|k|$ for spectra $S(k)\!\propto\!|k|^{-λ}$, rendering high-wavenumber modes indistinguishable from noise and producing an intrinsic spectral bias. We reinterpret the noise schedule as a spectral regularizer and introduce power-law schedules $β(τ)\!\propto\!τ^γ$ that preserve fine-scale structure deeper into diffusion time, along with \emph{Lazy Diffusion}, a one-step distillation method that leverages the learned score geometry to bypass long reverse-time trajectories and prevent high-$k$ degradation. Applied to high-Reynolds-number 2D Kolmogorov turbulence and $1/12^\circ$ Gulf of Mexico ocean reanalysis, these methods resolve spectral collapse, stabilize long-horizon autoregression, and restore physically realistic inertial-range scaling. Together, they show that naïve Gaussian scheduling is structurally incompatible with power-law physics and that physics-aware diffusion processes can yield accurate, efficient, and fully probabilistic surrogates for multiscale dynamical systems.

physics.flu-dyn↗

arXiv2025

SWR-Viz: AI-assisted Interactive Visual Analytics Framework for Ship Weather Routing

Efficient and sustainable maritime transport increasingly depends on reliable forecasting and adaptive routing, yet operational adoption remains difficult due to forecast latencies and the need for human judgment in rapid decision-making under changing ocean conditions. We introduce SWR-Viz, an AI-assisted visual analytics framework that combines a physics-informed Fourier Neural Operator wave forecast model with SIMROUTE-based routing and interactive emissions analytics. The framework generates near-term forecasts directly from current conditions, supports data assimilation with sparse observations, and enables rapid exploration of what-if routing scenarios. We evaluate the forecast models and SWR-Viz framework along key shipping corridors in the Japan Coast and Gulf of Mexico, showing both improved forecast stability and realistic routing outcomes comparable to ground-truth reanalysis wave products. Expert feedback highlights the usability of SWR-Viz, its ability to isolate voyage segments with high emission reduction potential, and its value as a practical decision-support system. More broadly, this work illustrates how lightweight AI forecasting can be integrated with interactive visual analytics to support human-centered decision-making in complex geospatial and environmental domains.

cs.HC↗

arXiv2025

Deep learning the sources of MJO predictability: a spectral view of learned features

The Madden-Julian oscillation (MJO) is a planetary-scale, intraseasonal tropical rainfall phenomenon crucial for global weather and climate; however, its dynamics and predictability remain poorly understood. Here, we leverage deep learning (DL) to investigate the sources of MJO predictability, motivated by a central difference in MJO theories: which spatial scales are essential for driving the MJO? We first develop a deep convolutional neural network (DCNN) to forecast the MJO indices (RMM and ROMI). Our model predicts RMM and ROMI up to 21 and 33 days, respectively, achieving skills comparable to leading subseasonal-to-seasonal models such as NCEP. To identify the spatial scales most relevant for MJO forecasting, we conduct spectral analysis of the latent feature space and find that large-scale patterns dominate the learned signals. Additional experiments show that models using only large-scale signals as the input have the same skills as those using all the scales, supporting the large-scale view of the MJO. Meanwhile, we find that small-scale signals remain informative: surprisingly, models using only small-scale input can still produce skillful forecasts up to 1-2 weeks ahead. We show that this is achieved by reconstructing the large-scale envelope of the small-scale activities, which aligns with the multi-scale view of the MJO. Altogether, our findings support that large-scale patterns--whether directly included or reconstructed--may be the primary source of MJO predictability.

physics.ao-ph↗

arXiv2025

LUCIE-3D: A three-dimensional climate emulator for forced responses

We introduce LUCIE-3D, a lightweight three-dimensional climate emulator designed to capture the vertical structure of the atmosphere, respond to climate change forcings, and maintain computational efficiency with long-term stability. Building on the original LUCIE-2D framework, LUCIE-3D employs a Spherical Fourier Neural Operator (SFNO) backbone and is trained on 30 years of ERA5 reanalysis data spanning eight vertical σ-levels. The model incorporates atmospheric CO2 as a forcing variable and optionally integrates prescribed sea surface temperature (SST) to simulate coupled ocean--atmosphere dynamics. Results demonstrate that LUCIE-3D successfully reproduces climatological means, variability, and long-term climate change signals, including surface warming and stratospheric cooling under increasing CO2 concentrations. The model further captures key dynamical processes such as equatorial Kelvin waves, the Madden--Julian Oscillation, and annular modes, while showing credible behavior in the statistics of extreme events. Despite requiring longer training than its 2D predecessor, LUCIE-3D remains efficient, training in under five hours on four GPUs. Its combination of stability, physical consistency, and accessibility makes it a valuable tool for rapid experimentation, ablation studies, and the exploration of coupled climate dynamics, with potential applications extending to paleoclimate research and future Earth system emulation.

cs.LG↗

arXiv2025

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 sparsity poses significant challenges for forecasting key phenomena such as eddy shedding and rogue waves. Traditional data assimilation methods and deep learning models often struggle to recover mesoscale turbulence under such constraints. We leverage a deep learning framework that combines neural operators with denoising diffusion probabilistic models (DDPMs) to reconstruct high-resolution ocean states from extremely sparse Lagrangian observations. By conditioning the generative model on neural operator outputs, the framework accurately captures small-scale, high-wavenumber dynamics even at $99\%$ sparsity (for synthetic data) and $99.9\%$ sparsity (for real satellite observations). We validate our method on benchmark systems, synthetic float observations, and real satellite data, demonstrating robust performance under severe spatial sampling limitations as compared to other deep learning baselines.

physics.ao-ph↗

arXiv2025

Can AI weather models predict out-of-distribution gray swan tropical cyclones?

Predicting gray swan weather extremes, which are possible but so rare that they are absent from the training dataset, is a major concern for AI weather models and long-term climate emulators. An important open question is whether AI models can extrapolate from weaker weather events present in the training set to stronger, unseen weather extremes. To test this, we train independent versions of the AI model FourCastNet on the 1979-2015 ERA5 dataset with all data, or with Category 3-5 tropical cyclones (TCs) removed, either globally or only over the North Atlantic or Western Pacific basin. We then test these versions of FourCastNet on 2018-2023 Category 5 TCs (gray swans). All versions yield similar accuracy for global weather, but the one trained without Category 3-5 TCs cannot accurately forecast Category 5 TCs, indicating that these models cannot extrapolate from weaker storms. The versions trained without Category 3-5 TCs in one basin show some skill forecasting Category 5 TCs in that basin, suggesting that FourCastNet can generalize across tropical basins. This is encouraging and surprising because regional information is implicitly encoded in inputs. Given that current state-of-the-art AI weather and climate models have similar learning strategies, we expect our findings to apply to other models. Other types of weather extremes need to be similarly investigated. Our work demonstrates that novel learning strategies are needed for AI models to reliably provide early warning or estimated statistics for the rarest, most impactful TCs, and, possibly, other weather extremes.

physics.ao-ph↗

arXiv2025

Fourier analysis of the physics of transfer learning for data-driven subgrid-scale models of ocean turbulence

Transfer learning (TL) is a powerful tool for enhancing the performance of neural networks (NNs) in applications such as weather and climate prediction and turbulence modeling. TL enables models to generalize to out-of-distribution data with minimal training data from the new system. In this study, we employ a 9-layer convolutional NN to predict the subgrid forcing in a two-layer ocean quasi-geostrophic system and examine which metrics best describe its performance and generalizability to unseen dynamical regimes. Fourier analysis of the NN kernels reveals that they learn low-pass, Gabor, and high-pass filters, regardless of whether the training data are isotropic or anisotropic. By analyzing the activation spectra, we identify why NNs fail to generalize without TL and how TL can overcome these limitations: the learned weights and biases from one dataset underestimate the out-of-distribution sample spectra as they pass through the network, leading to an underestimation of output spectra. By re-training only one layer with data from the target system, this underestimation is corrected, enabling the NN to produce predictions that match the target spectra. These findings are broadly applicable to data-driven parameterization of dynamical systems.

cs.LG↗

arXiv2025

LUCIE: A Lightweight Uncoupled ClImate Emulator with long-term stability and physical consistency for O(1000)-member ensembles

We present a lightweight, easy-to-train, low-resolution, fully data-driven climate emulator, LUCIE, that can be trained on as low as $2$ years of $6$-hourly ERA5 data. Unlike most state-of-the-art AI weather models, LUCIE remains stable and physically consistent for $100$ years of autoregressive simulation with $100$ ensemble members. Long-term mean climatology from LUCIE's simulation of temperature, wind, precipitation, and humidity matches that of ERA5 data, along with the variability. We further demonstrate how well extreme weather events and their return periods can be estimated from a large ensemble of long-term simulations. We further discuss an improved training strategy with a hard-constrained first-order integrator to suppress autoregressive error growth, a novel spectral regularization strategy to better capture fine-scale dynamics, and finally an optimization algorithm that enables data-limited (as low as $2$ years of $6$-hourly data) training of the emulator without losing stability and physical consistency. Finally, we provide a scaling experiment to compare the long-term bias of LUCIE with respect to the number of training samples. Importantly, LUCIE is an easy to use model that can be trained in just $2.4$h on a single A-100 GPU, allowing for multiple experiments that can explore important scientific questions that could be answered with large ensembles of long-term simulations, e.g., the impact of different variables on the simulation, dynamic response to external forcing, and estimation of extreme weather events, amongst others.

cs.LG↗

arXiv2025

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. Regional ocean emulation presents unique challenges owing to the complex bathymetry and lateral boundary conditions as well as from fundamental biases in deep learning-based frameworks, such as instability and hallucinations. In this paper, we develop a deep learning-based framework to autoregressively integrate ocean-surface variables over the Gulf of Mexico at $8$ Km spatial resolution without unphysical drifts over decadal time scales and simulataneously downscale and bias-correct it to $4$ Km resolution using a physics-constrained generative model. The framework shows both short-term skills as well as accurate long-term statistics in terms of mean and variability.

physics.ao-ph↗

arXiv2024

Challenges of learning multi-scale dynamics with AI weather models: Implications for stability and one solution

Long-term stability and physical consistency are critical properties for AI-based weather models if they are going to be used for subseasonal-to-seasonal forecasts or beyond, e.g., climate change projection. However, current AI-based weather models can only provide short-term forecasts accurately since they become unstable or physically inconsistent when time-integrated beyond a few weeks or a few months. Either they exhibit numerical blow-up or hallucinate unrealistic dynamics of the atmospheric variables, akin to the current class of autoregressive large language models. The cause of the instabilities is unknown, and the methods that are used to improve their stability horizons are ad-hoc and lack rigorous theory. In this paper, we reveal that the universal causal mechanism for these instabilities in any turbulent flow is due to \textit{spectral bias} wherein, \textit{any} deep learning architecture is biased to learn only the large-scale dynamics and ignores the small scales completely. We further elucidate how turbulence physics and the absence of convergence in deep learning-based time-integrators amplify this bias, leading to unstable error propagation. Finally, using the quasi-geostrophic flow and European Center for Medium-Range Weather Forecasting (ECMWF) Reanalysis data as test cases, we bridge the gap between deep learning theory and numerical analysis to propose one mitigative solution to such unphysical behavior. We develop long-term physically-consistent data-driven models for the climate system and demonstrate accurate short-term forecasts, and hundreds of years of time-integration with accurate mean and variability.

physics.flu-dyn↗

arXiv2024

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts

Physics-informed neural networks (PINNs) commonly address ill-posed inverse problems by uncovering unknown physics. This study presents a novel unsupervised learning framework that identifies spatial subdomains with specific governing physics. It uses the partition of unity networks (POUs) to divide the space into subdomains, assigning unique nonlinear model parameters to each, which are integrated into the physics model. A vital feature of this method is a physics residual-based loss function that detects variations in physical properties without requiring labeled data. This approach enables the discovery of spatial decompositions and nonlinear parameters in partial differential equations (PDEs), optimizing the solution space by dividing it into subdomains and improving accuracy. Its effectiveness is demonstrated through applications in porous media thermal ablation and ice-sheet modeling, showcasing its potential for tackling real-world physics challenges.

cs.LG↗

arXiv2024

What You See is Not What You Get: Neural Partial Differential Equations and The Illusion of Learning

Differentiable Programming for scientific machine learning (SciML) has recently seen considerable interest and success, as it directly embeds neural networks inside PDEs, often called as NeuralPDEs, derived from first principle physics. Therefore, there is a widespread assumption in the community that NeuralPDEs are more trustworthy and generalizable than black box models. However, like any SciML model, differentiable programming relies predominantly on high-quality PDE simulations as "ground truth" for training. However, mathematics dictates that these are only discrete numerical approximations of the true physics. Therefore, we ask: Are NeuralPDEs and differentiable programming models trained on PDE simulations as physically interpretable as we think? In this work, we rigorously attempt to answer these questions, using established ideas from numerical analysis, experiments, and analysis of model Jacobians. Our study shows that NeuralPDEs learn the artifacts in the simulation training data arising from the discretized Taylor Series truncation error of the spatial derivatives. Additionally, NeuralPDE models are systematically biased, and their generalization capability is likely enabled by a fortuitous interplay of numerical dissipation and truncation error in the training dataset and NeuralPDE, which seldom happens in practical applications. This bias manifests aggressively even in relatively accessible 1-D equations, raising concerns about the veracity of differentiable programming on complex, high-dimensional, real-world PDEs, and in dataset integrity of foundation models. Further, we observe that the initial condition constrains the truncation error in initial-value problems in PDEs, thereby exerting limitations to extrapolation. Finally, we demonstrate that an eigenanalysis of model weights can indicate a priori if the model will be inaccurate for out-of-distribution testing.

cs.LG↗