arXiv subjects

Pedram Hassanzadeh

Publications and source records attributed to Pedram Hassanzadeh.

At least 19 recordsLinked to original sources

arXiv2026

Missing the Butterfly and Predicting the Past: Features or Bugs of Accurate AI Weather Models?

AI weather prediction (AIWP) models rival physics-based models, yet the sources of their unexpected forecast accuracy and the degree of their physical fidelity remain unclear. Here, across a hierarchy spanning observation-based reanalysis, a general circulation model, and the multi-scale Lorenz system, we show that AI models can be trained to skillfully predict the past (backcast), though backcasts are systematically less accurate than forecasts. However, skillful backcasting appears to violate the second law of thermodynamics, and all these forecasting and backcasting models miss the butterfly effect. We trace the surprising forecast accuracy, missing butterfly, and skillful backcasting to a single cause: inevitable coarse-graining of training data, which removes fast, small scales and/or some variables. From the Lorenz system to official Pangu-Weather models, reducing coarse-graining makes AI predictions more physics-like (arrow of time and butterfly-like effects emerge), but forecast accuracy declines. Results offer an explanation for AIWP models' forecast skill: unlike physics-based models, they implicitly learn how fast, small scales affect large scales without inheriting their rapid error growth. Broader implications are that AI models' proliferation calls for revisiting predictability theories and long-term climate emulation strategies, and backcasting offers a useful, new lens for such analyses.

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

AI-boosted rare event sampling to characterize extreme weather

Weather extremes pose major societal risks, especially in a changing climate, but due to their rarity, they are difficult to study using limited observations or complex climate models. We introduce AI+RES, a framework coupling fast AI weather forecasts with a high-fidelity physics model using a rare-event algorithm to efficiently characterize extremes. This approach enables the study of the statistics and physics of very rare events, such as once per millennium heatwaves at two orders-of-magnitude lower computational cost. AI+RES can be applied broadly across climate science and other fields concerned with rare events.

physics.ao-ph↗

arXiv2026

Rigorous uncertainty quantification of probabilistic AI weather forecasts with conformal prediction

Probabilistic weather forecasting is undergoing rapid transformation with artificial intelligence (AI). In traditional numerical weather prediction, computing power can limit how well ensemble forecasts approximate the unknown statistical distribution of future states. AI models facilitate larger ensembles and are trained with probabilistic considerations, ideally leading to better uncertainty quantification. Forecasts from these state-of-the-art models are often considered well-calibrated. However, here we show that the statistical coverage of such models, the ultimate measure of calibration, can struggle, especially on extreme events. To address this shortcoming, we employ conformal prediction, a class of statistical methods that mathematically guarantees coverage under no distributional assumptions, unlike previous post-processing techniques. We apply online conformal prediction to temperature and precipitation forecasts (including extremes) of three leading global weather models, GenCast, NeuralGCM, and AIFS-ENS, ensuring calibrated uncertainty at no expense to other probabilistic metrics. This post-processing method can be applied to any forecasting model.

physics.ao-ph↗

arXiv2026

Semi-analytical eddy-viscosity and backscattering closures for 2D geophysical turbulence

Physics-based eddy-viscosity and backscattering closures are widely used for large-eddy simulation (LES) of geophysical turbulence, but their key parameters are often chosen empirically. Here, we develop a semi-analytical framework for estimating these parameters in 2D geophysical turbulence. Specifically, we extend a Lilly-type scaling argument, previously used for 3D turbulence, to 2D geophysical turbulence and obtain closed-form estimates, up to an amplitude constant, for the coefficients of the Leith and Smagorinsky eddy-viscosity closures, a biharmonic eddy-viscosity closure, and the Jansen--Held backscattering closure with a prescribed backscattering fraction. The amplitude constant appears in the turbulent kinetic energy direct-cascade spectrum and can be diagnosed from a few direct numerical simulation (DNS) or eddy-resolving snapshots. For the $β$-free cases, the diagnosed amplitude constant is consistent with previous theoretical estimates based on closure, renormalization-group, and mode-coupling methods. The resulting semi-analytical parameters closely match the online-learned values obtained using ensemble Kalman inversion across several 2D geophysical turbulence setups. LES using these parameters reproduces key DNS statistics, including the tails of the vorticity distribution, and robustly outperforms dynamic Leith and Smagorinsky baselines.

physics.flu-dyn↗

arXiv2026

Designing probabilistic AI monsoon forecasts to inform agricultural decision-making

Hundreds of millions of farmers make high-stakes decisions under uncertainty about future weather. Forecasts can inform these decisions, but available choices and their risks and benefits vary between farmers. We introduce a decision-theory framework for designing useful forecasts in settings where the forecaster cannot prescribe optimal actions because farmers' circumstances are heterogeneous. We apply this framework to the case of seasonal onset of monsoon rains, a key date for planting decisions and agricultural investments in many tropical countries. We develop a system for tailoring forecasts to the requirements of this framework by blending systematically benchmarked artificial intelligence (AI) weather prediction models with a new "evolving farmer expectations" statistical model. This statistical model applies Bayesian inference to historical observations to predict time-varying probabilities of first-occurrence events throughout a season. The blended system yields more skillful Indian monsoon forecasts at longer lead times than its components or any multi-model average. In 2025, this system was deployed operationally in a government-led program that delivered subseasonal monsoon onset forecasts to 38 million Indian farmers, skillfully predicting that year's early-summer anomalous dry period. This decision-theory framework and blending system offer a pathway for developing climate adaptation tools for large vulnerable populations around the world.

cs.LG↗

arXiv2026

Prediction of Extreme Events in Multiscale Simulations of Geophysical Turbulence using Reinforcement Learning

Accurate subgrid-scale closures are essential for weather/climate models, where predicting extreme events is critical. Traditional closures have structural errors, e.g., producing excessive diffusion that dampens extremes. Artificial intelligence has gained attention for closure modeling, but the prediction of extreme events remains challenging. Supervised offline learning needs abundant high-fidelity training data and can lead to instabilities. Online learning algorithms are emerging as an alternative, but reliance on differentiable numerical solvers or scalable optimizers hinders broad use. Here, we introduce SMARL to develop closures for canonical prototypes of atmospheric/oceanic turbulence, using only the enstrophy spectrum, estimated from a few high-fidelity samples, as reward. This reward ensures that the model captures the cascades of scales in these simulations. These online-learned closures enable stable simulations, with up to five orders of magnitude fewer degrees of freedom, that reproduce high-fidelity simulation statistics and capture in particular extremes. We interpret the closures by analyzing the SMARL policy and demonstrate generalization to other flows. The results highlight SMARL as a potent tool for developing closures capable of capturing extremes in atmospheric/oceanic flows, opening new capabilities for effective climate modeling.

physics.geo-ph↗

arXiv2026

Decision-oriented benchmarking to transform AI weather forecast access: Application to the Indian monsoon

Artificial intelligence weather prediction (AIWP) models now often outperform traditional physics-based models on common metrics while requiring orders-of-magnitude less computing resources and time. Open-access AIWP models thus hold promise as transformational tools for helping low- and middle-income populations make decisions in the face of high-impact weather shocks. Yet, current approaches to evaluating AIWP models focus mainly on aggregated meteorological metrics without considering local stakeholders' needs in decision-oriented, operational frameworks. Here, we introduce such a framework that connects meteorology, AI, and social sciences. As an example, we apply it to the 150-year-old problem of Indian monsoon forecasting, focusing on benefits to rain-fed agriculture, which is highly susceptible to climate change. AIWP models skillfully predict an agriculturally relevant onset index at regional scales weeks in advance when evaluated out-of-sample using deterministic and probabilistic metrics. This framework informed a government-led effort in 2025 to send 38 million Indian farmers AI-based monsoon onset forecasts, which captured an unusual weeks-long pause in monsoon progression. This decision-oriented benchmarking framework provides a key component of a blueprint for harnessing the power of AIWP models to help large vulnerable populations adapt to weather shocks in the face of climate variability and change.

cs.LG↗

arXiv2026

Predicting Beyond Training Data via Extrapolation versus Translocation: AI Weather Models and Dubai's Unprecedented 2024 Rainfall

Artificial intelligence (AI) models have transformed weather forecasting, but their skill for gray swan extremes is unclear. Here, we analyze GraphCast, AIFS, and FuXi forecasts of the unprecedented 2024 Dubai storm, which had twice the training set's highest rainfall in that region. Remarkably, GraphCast and AIFS accurately forecast this event up to 8 days ahead. FuXi forecasts the event, but underestimates the rainfall. Fine-tuning and receptive field analyses suggest that these models' success stems from "translocation": learning from comparable/stronger dynamically similar events in other regions during training. Evidence of "extrapolation" (learning from weaker events) is not found. Even events within the global distribution's tail are poorly forecasted, which is not just due to data imbalance (generalization error) but also spectral bias (optimization error). These findings demonstrate the potential of AI models to forecast regional gray swans and the opportunity to improve them through understanding the mechanisms behind their successes/limitations.

physics.ao-ph↗

arXiv2026

An Analytical and AI-discovered Stable, Accurate, and Generalizable Subgrid-scale Closure for Geophysical Turbulence

By combining AI and fluid physics, we discover a closed-form closure for 2D turbulence from small direct numerical simulation (DNS) data. Large-eddy simulation (LES) with this closure is accurate and stable, reproducing DNS statistics including those of extremes. We also show that the new closure could be derived from a 4th-order truncated Taylor expansion. Prior analytical and AI-based work only found the 2nd-order expansion, which led to unstable LES. The additional terms emerge only when inter-scale energy transfer is considered alongside standard reconstruction criterion in the sparse-equation discovery.

physics.ao-ph↗

arXiv2025

Benchmarking Regional Thermodynamic Trends in an AI emulator, ACE2, and a hybrid model, NeuralGCM

AI models have emerged as potential complements to physics-based models, but their skill in capturing observed regional climate trends with important societal impacts has not been explored. Here, we benchmark satellite-era regional thermodynamic trends, including extremes, in an AI emulator (ACE2) and a hybrid model (NeuralGCM). We also compare the AI models' skill to physics-based land-atmosphere models. Both AI models show skill in capturing regional temperature trends such as Arctic Amplification. ACE2 outperforms other models in capturing vertical temperature trends in the midlatitudes. However, the AI models do not capture regional trends in heat extremes over the US Southwest. Furthermore, they do not capture drying trends in arid regions, even though they generally perform better than physics-based models. Our results also show that a data-driven AI emulator can perform comparably to, or better than, hybrid and physics-based models in capturing regional thermodynamic trends.

physics.ao-ph↗

arXiv2025

Benchmarking atmospheric circulation variability in an AI emulator, ACE2, and a hybrid model, NeuralGCM

Physics-based atmosphere-land models with prescribed sea surface temperature have notable successes but also biases in their ability to represent atmospheric variability compared to observations. Recently, AI emulators and hybrid models have emerged with the potential to overcome these biases, but still require systematic evaluation against metrics grounded in fundamental atmospheric dynamics. Here, we evaluate the representation of four atmospheric variability benchmarking metrics in a fully data-driven AI emulator (ACE2-ERA5) and hybrid model (NeuralGCM). The hybrid model and emulator can capture the spectra of large-scale tropical waves and extratropical eddy-mean flow interactions, including critical levels. However, both struggle to capture the timescales associated with quasi-biennial oscillation (QBO, $\sim 28$ months) and Southern annular mode propagation ($\sim 150$ days). These dynamical metrics serve as an initial benchmarking tool to inform AI model development and understand their limitations, which may be essential for out-of-distribution applications (e.g., extrapolating to unseen climates).

physics.ao-ph↗

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

Reframing Generative Models for Physical Systems using Stochastic Interpolants

Generative models have recently emerged as powerful surrogates for physical systems, demonstrating increased accuracy, stability, and/or statistical fidelity. Most approaches rely on iteratively denoising a Gaussian, a choice that may not be the most effective for autoregressive prediction tasks in PDEs and dynamical systems such as climate. In this work, we benchmark generative models across diverse physical domains and tasks, and highlight the role of stochastic interpolants. By directly learning a stochastic process between current and future states, stochastic interpolants can leverage the proximity of successive physical distributions. This allows for generative models that can use fewer sampling steps and produce more accurate predictions than models relying on transporting Gaussian noise. Our experiments suggest that generative models need to balance deterministic accuracy, spectral consistency, and probabilistic calibration, and that stochastic interpolants can potentially fulfill these requirements by adjusting their sampling. This study establishes stochastic interpolants as a competitive baseline for physical emulation and gives insight into the abilities of different generative modeling frameworks.

cs.LG↗

arXiv2025

Hierarchical Implicit Neural Emulators

Neural PDE solvers offer a powerful tool for modeling complex dynamical systems, but often struggle with error accumulation over long time horizons and maintaining stability and physical consistency. We introduce a multiscale implicit neural emulator that enhances long-term prediction accuracy by conditioning on a hierarchy of lower-dimensional future state representations. Drawing inspiration from the stability properties of numerical implicit time-stepping methods, our approach leverages predictions several steps ahead in time at increasing compression rates for next-timestep refinements. By actively adjusting the temporal downsampling ratios, our design enables the model to capture dynamics across multiple granularities and enforce long-range temporal coherence. Experiments on turbulent fluid dynamics show that our method achieves high short-term accuracy and produces long-term stable forecasts, significantly outperforming autoregressive baselines while adding minimal computational overhead.

cs.LG↗

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

Online learning of eddy-viscosity and backscattering closures for geophysical turbulence using ensemble Kalman inversion

Different approaches to using data-driven methods for subgrid-scale closure modeling have emerged recently. Most of these approaches are data-hungry, and lack interpretability and out-of-distribution generalizability. Here, we use {online} learning to address parametric uncertainty of well-known physics-based large-eddy simulation (LES) closures: the Smagorinsky (Smag) and Leith eddy-viscosity models (1 free parameter) and the Jansen-Held (JH) backscattering model (2 free parameters). For 8 cases of 2D geophysical turbulence, optimal parameters are estimated, using ensemble Kalman inversion (EKI), such that for each case, the LES' energy spectrum matches that of direct numerical simulation (DNS). Only a small training dataset is needed to calculate the DNS spectra (i.e., the approach is {data-efficient}). We find the optimized parameter(s) of each closure to be constant across broad flow regimes that differ in dominant length scales, eddy/jet structures, and dynamics, suggesting that these closures are {generalizable}. In a-posteriori tests based on the enstrophy spectra and probability density functions (PDFs) of vorticity, LES with optimized closures outperform the baselines (LES with standard Smag, dynamic Smag or Leith), particularly at the tails of the PDFs (extreme events). In a-priori tests, the optimized JH significantly outperforms the baselines and optimized Smag and Leith in terms of interscale enstrophy and energy transfers (still, optimized Smag noticeably outperforms standard Smag). The results show the promise of combining advances in physics-based modeling (e.g., JH) and data-driven modeling (e.g., {online} learning with EKI) to develop data-efficient frameworks for accurate, interpretable, and generalizable closures.

physics.flu-dyn↗

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↗