Time series generation is a crucial aspect of data analysis, playing a pivotal role in learning the temporal patterns and their underlying dynamics across diverse fields. Conventional time series generation methods often struggle to capture extreme values adequately, diminishing their value in critical applications such as scenario planning and management for healthcare, finance, climate change adaptation, and beyond. In this paper, we introduce a conditional diffusion model called FIDE to address the challenge of preserving the distribution of extreme values in generative modeling for time series. FIDE employs a novel high-frequency inflation strategy in the frequency domain, preventing premature fade-out of the extreme value. It also extends traditional diffusion-based model, enabling the generation of samples conditioned on the block maxima, thereby enhancing the model's capacity to capture extreme events. Additionally, the FIDE framework incorporates the Generalized Extreme Value (GEV) distribution within its generative modeling framework, ensuring fidelity to both block maxima and overall data distribution.

This paper studies the use of a machine learning-based estimator as a control variate for mitigating the variance of Monte Carlo sampling. Specifically, we seek to uncover the key factors that influence the efficiency of control variates in reducing variance. We examine a prototype estimation problem that involves simulating the moments of a Sobolev function based on observations obtained from (random) quadrature nodes. Firstly, we establish an information-theoretic lower bound for the problem. We then study a specific quadrature rule that employs a nonparametric regression-adjusted control variate to reduce the variance of the Monte Carlo simulation. We demonstrate that this kind of quadrature rule can improve the Monte Carlo rate and achieve the minimax optimal rate under a sufficient smoothness assumption. Due to the Sobolev Embedding Theorem, the sufficient smoothness assumption eliminates the existence of rare and extreme events. Finally, we show that, in the presence of rare and extreme events, a truncated version of the Monte Carlo algorithm can achieve the minimax optimal rate while the control variate cannot improve the convergence rate.

Recent advancements in deep learning have led to the development of Foundation Models (FMs) for weather forecasting, yet their ability to predict extreme weather events remains limited. Existing approaches either focus on general weather conditions or specialize in specific-type extremes, neglecting the real-world atmospheric patterns of diversified extreme events. In this work, we identify two key characteristics of extreme events: (1) the spectral disparity against normal weather regimes, and (2) the hierarchical drivers and geographic blending of diverse extremes. Along this line, we propose UniExtreme, a universal extreme weather forecasting foundation model that integrates (1) an Adaptive Frequency Modulation (AFM) module that captures region-wise spectral differences between normal and extreme weather, through learnable Beta-distribution filters and multi-granularity spectral aggregation, and (2) an Event Prior Augmentation (EPA) module which incorporates region-specific extreme event priors to resolve hierarchical extreme diversity and composite extreme schema, via a dual-level memory fusion network. Extensive experiments demonstrate that UniExtreme outperforms state-of-the-art baselines in both extreme and general weather forecasting, showcasing superior adaptability across diverse extreme scenarios.

Extreme weather events are widely studied in fields such as agriculture, ecology, and meteorology. The spatio-temporal co-occurrence of extreme events can strengthen or weaken under changing climate conditions. In this paper, we propose a novel approach to model spatio-temporal extremes by integrating climate indices via a conditional variational autoencoder (cXVAE). A convolutional neural network (CNN) is embedded in the decoder to convolve climatological indices with the spatial dependence within the latent space, thereby allowing the decoder to be dependent on the climate variables. There are three main contributions here. First, we demonstrate through extensive simulations that the proposed conditional XVAE accurately emulates spatial fields and recovers spatially and temporally varying extremal dependence with very low computational cost post training. Second, we provide a simple, scalable approach to detecting condition-driven shifts and whether the dependence structure is invariant to the conditioning variable. Third, when dependence is found to be condition-sensitive, the conditional XVAE supports counterfactual experiments allowing intervention on the climate covariate and propagating the associated change through the learned decoder to quantify differences in joint tail risk, co-occurrence ranges, and return metrics. To demonstrate the practical utility and performance of the model in real-world scenarios, we apply our method to analyze the monthly maximum Fire Weather Index (FWI) over eastern Australia from 2014 to 2024 conditioned on the El Niño/Southern Oscillation (ENSO) index.

Urban transportation systems face increasing resilience challenges from extreme weather events, but current assessment methods rely on surface-level recovery indicators that miss hidden structural damage. Existing approaches cannot distinguish between true recovery and "false recovery," where traffic metrics normalize, but the underlying system dynamics permanently degrade. To address this, a new physics-constrained Hamiltonian learning algorithm combining "structural irreversibility detection" and "energy landscape reconstruction" has been developed. Our approach extracts low-dimensional state representations, identifies quasi-Hamiltonian structures through physics-constrained optimization, and quantifies structural changes via energy landscape comparison. Analysis of London's extreme rainfall in 2021 demonstrates that while surface indicators were fully recovered, our algorithm detected 64.8\% structural damage missed by traditional monitoring. Our framework provides tools for proactive structural risk assessment, enabling infrastructure investments based on true system health rather than misleading surface metrics.

Extreme weather events pose escalating risks to global society, underscoring the urgent need to unravel their underlying physical mechanisms. Yet the prevailing expert-driven, labor-intensive diagnostic paradigm has created a critical analytical bottleneck, stalling scientific progress. While AI for Earth Science has achieved notable advances in prediction, the equally essential challenge of automated diagnostic reasoning remains largely unexplored. We present the Extreme Weather Expert (EWE), the first intelligent agent framework dedicated to this task. EWE emulates expert workflows through knowledge-guided planning, closed-loop reasoning, and a domain-tailored meteorological toolkit. It autonomously produces and interprets multimodal visualizations from raw meteorological data, enabling comprehensive diagnostic analyses. To catalyze progress, we introduce the first benchmark for this emerging field, comprising a curated dataset of 103 high-impact events and a novel step-wise evaluation metric. EWE marks a step toward automated scientific discovery and offers the potential to democratize expertise and intellectual resources, particularly for developing nations vulnerable to extreme weather.

Understanding the plausible upper bounds of extreme weather events is essential for risk assessment in a warming climate. Existing methods, based on large ensembles of physics-based models, are often computationally expensive or lack the fidelity needed to simulate rare, high-impact extremes. Here, we present a novel framework that leverages a differentiable hybrid climate model, NeuralGCM, to optimize initial conditions and generate physically consistent worst-case heatwave trajectories. Applied to the 2021 Pacific Northwest heatwave, our method produces heatwave intensity up to 3.7 $^\circ$C above the most extreme member of a 75-member ensemble. These trajectories feature intensified atmospheric blocking and amplified Rossby wave patterns-hallmarks of severe heat events. Our results demonstrate that differentiable climate models can efficiently explore the upper tails of event likelihoods, providing a powerful new approach for constructing targeted storylines of extreme weather under climate change.

In this work, we propose a first approach and benchmarks to tackle this challenge.

Accurate short-range prediction of extreme air temperature events remains a fundamental challenge in operational climate-risk management. We present Multi-Modal Weather State Transition Model with Anomaly-Driven Recurrent Attention Network Plus (MMWSTM-ADRAN+), a dual-stream deep learning architecture that couples a regime-aware dynamics model with an anomaly-focused attention mechanism to forecast daily maximum temperature and its extremes. The first stream, MMWSTM, combines bidirectional Long Short-Term Memory (BiLSTM) units with a learnable Markov state transition matrix to capture synoptic-scale weather regime changes. The second stream, ADRAN, integrates bidirectional Gated Recurrent Units (BiGRUs), multi-head self-attention, and a novel anomaly amplification layer to enhance sensitivity to low-probability signals. A lightweight attentive fusion gate adaptively determines the contribution of each stream to the final prediction. Model optimization employs a custom ExtremeWeatherLoss function that up-weights errors on the upper 5% and lower 5% of the temperature distribution, and a time-series data augmentation suite (jittering, scaling, time/magnitude warping) that effectively quadruples the training data