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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 risk 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 values. It also extends the 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. Experimental results on real-world and synthetic data showcase the efficacy of FIDE over baseline methods, highlighting its potential in advancing Generative AI for time series analysis, specifically in accurately modeling extreme events. 

Abstract Crucial to the assessment of future water security is how the land model component of Earth System Models partition precipitation into evapotranspiration and runoff, and the sensitivity of this partitioning to climate. This sensitivity is not explicitly constrained in land models nor the model parameters important for this sensitivity identified. Here, we seek to understand parametric controls on runoff sensitivity to precipitation and temperature in a state‐of‐the‐science land model, the Community Land Model version 5 (CLM5). Process‐parameter interactions underlying these two climate sensitivities are investigated using the sophisticated variance‐based sensitivity analysis. This analysis focuses on three snow‐dominated basins in the Colorado River headwaters region, a prominent exemplar where land models display a wide disparity in runoff sensitivities. Runoff sensitivities are dominated by indirect or interaction effects between a few parameters of subsurface, snow, and plant processes. A focus on only one kind of parameters would therefore limit the ability to constrain the others. Surface runoff exhibits strong sensitivity to parameters of snow and subsurface processes. Constraining snow simulations would require explicit representation of the spatial variability across large elevation gradients. Subsurface runoff and soil evaporation exhibit very similar sensitivities. Model calibration against the subsurface runoff flux would therefore constrain soil evaporation. The push toward a mechanistic treatment of processes in CLM5 have dampened the sensitivity of parameters compared to earlier model versions. A focus on the sensitive parameters and processes identified here can help characterize and reduce uncertainty in water resource sensitivity to climate change. 

Abstract While many freshwater lakes have witnessed a rapid increase in surface water temperatures, the trends in subsurface water temperatures are not well-understood. This study explored the long-term subsurface water temperature change and its connection to climate change and human activities in Seneca Lake. Utilizing linear regression and the Theil-Sen estimator, the study identified a significant monotonic temperature trend in the subsurface water. Principal component and contribution analyses revealed that climate changes, particularly air warming, were more critical in explaining water temperature patterns, and human activities such as land cover change could exacerbate the impact of climate change. Using remotely sensed surface water temperature data, the study found a significant positive correlation between thermal pollution and water temperatures in the northern region of the lake, and after incorporating control variables, the regression analysis suggested that the adverse effects of thermal pollution are primarily confined to the area adjacent to the power plant. This research can offer fresh insights into lake ecology improvement and management strategies. 

Forecasting the block maxima of a future time window is a challenging task due to the difficulty in inferring the tail distribution of a target variable. As the historical observations alone may not be sufficient to train robust models to predict the block maxima, domain-driven process models are often available in many scientific domains to supplement the observation data and improve the forecast accuracy. Unfortunately, coupling the historical observations with process model outputs is a challenge due to their disparate temporal coverage. This paper presents Self-Recover, a deep learning framework to predict the block maxima of a time window by employing self-supervised learning to address the varying temporal data coverage problem. Specifically Self-Recover uses a combination of contrastive and generative self-supervised learning schemes along with a denoising autoencoder to impute the missing values. The framework also combines representations of the historical observations with process model outputs via a residual learning approach and learns the generalized extreme value (GEV) distribution characterizing the block maxima values. This enables the framework to reliably estimate the block maxima of each time window along with its confidence interval. Extensive experiments on real-world datasets demonstrate the superiority of Self-Recover compared to other state-of-the-art forecasting methods. 

Normalizing flows—a popular class of deep generative models—often fail to represent extreme phenomena observed in real-world processes. In particular, existing normalizing flow architectures struggle to model multivariate extremes, characterized by heavy-tailed marginal distributions and asymmetric tail dependence among variables. In light of this shortcoming, we propose COMET (COpula Multivariate ExTreme) Flows, which decompose the process of modeling a joint distribution into two parts: (i) modeling its marginal distributions, and (ii) modeling its copula distribution. COMET Flows capture heavy-tailed marginal distributions by combining a parametric tail belief at extreme quantiles of the marginals with an empirical kernel density function at mid-quantiles. In addition, COMET Flows capture asymmetric tail dependence among multivariate extremes by viewing such dependence as inducing a low-dimensional manifold structure in feature space. Experimental results on both synthetic and real-world datasets demonstrate the effectiveness of COMET flows in capturing both heavy-tailed marginals and asymmetric tail dependence compared to other state-of-the-art baseline architectures. All code is available at https://github.com/andrewmcdonald27/COMETFlows. 

Geospatio-temporal data are pervasive across numerous application domains.These rich datasets can be harnessed to predict extreme events such as disease outbreaks, flooding, crime spikes, etc.However, since the extreme events are rare, predicting them is a hard problem. Statistical methods based on extreme value theory provide a systematic way for modeling the distribution of extreme values. In particular, the generalized Pareto distribution (GPD) is useful for modeling the distribution of excess values above a certain threshold. However, applying such methods to large-scale geospatio-temporal data is a challenge due to the difficulty in capturing the complex spatial relationships between extreme events at multiple locations. This paper presents a deep learning framework for long-term prediction of the distribution of extreme values at different locations. We highlight its computational challenges and present a novel framework that combines convolutional neural networks with deep set and GPD. We demonstrate the effectiveness of our approach on a real-world dataset for modeling extreme climate events. 

Zero-inflated, heavy-tailed spatiotemporal data is common across science and engineering, from climate science to meteorology and seismology. A central modeling objective in such settings is to forecast the intensity, frequency, and timing of extreme and non-extreme events; yet in the context of deep learning, this objective presents several key challenges. First, a deep learning framework applied to such data must unify a mixture of distributions characterizing the zero events, moderate events, and extreme events. Second, the framework must be capable of enforcing parameter constraints across each component of the mixture distribution. Finally, the framework must be flexible enough to accommodate for any changes in the threshold used to define an extreme event after training. To address these challenges, we propose Deep Extreme Mixture Model (DEMM), fusing a deep learning-based hurdle model with extreme value theory to enable point and distribution prediction of zero-inflated, heavy-tailed spatiotemporal variables. The framework enables users to dynamically set a threshold for defining extreme events at inference-time without the need for retraining. We present an extensive experimental analysis applying DEMM to precipitation forecasting, and observe significant improvements in point and distribution prediction. All code is available at https://github.com/andrewmcdonald27/DeepExtremeMixtureModel. 

Accurate forecasting of extreme values in time series is critical due to the significant impact of extreme events on human and natural systems. This paper presents DeepExtrema, a novel framework that combines a deep neural network (DNN) with generalized extreme value (GEV) distribution to forecast the block maximum value of a time series. Implementing such a network is a challenge as the framework must preserve the inter-dependent constraints among the GEV model parameters even when the DNN is initialized. We describe our approach to address this challenge and present an architecture that enables both conditional mean and quantile prediction of the block maxima. The extensive experiments performed on both real-world and synthetic data demonstrated the superiority of DeepExtrema compared to other baseline methods.