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Precipitation in complex terrain is governed by orographic processes operating at scales of a few kilometers, yet climate models typically run at resolutions of 50--100~km where this topographic detail is absent. Dynamical downscaling with…

Spatial maps of extreme precipitation are crucial in flood protection. With the aim of producing maps of precipitation return levels, we propose a novel approach to model a collection of spatially distributed time series where the…

Inference on the extremal behaviour of spatial aggregates of precipitation is important for quantifying river flood risk. There are two classes of previous approach, with one failing to ensure self-consistency in inference across different…

Time series models often deal with extreme events and anomalies, both prevalent in real-world datasets. Such models often need to provide careful probabilistic forecasting, which is vital in risk management for extreme events such as…

In this paper, we introduce a new spatial model that incorporates heteroscedastic variance depending on neighboring locations. The proposed process is regarded as the spatial equivalent to the temporal autoregressive conditional…

GARCH-type time series (characterized by Generalized Autoregressive Conditional Heteroskedasticity) exhibit pronounced volatility, autocorrelation, and heteroskedasticity. To address these challenges and enhance predictive accuracy, this…

We propose a framework for studying predictability of extreme events in complex systems. Major conceptual elements -- hierarchical structure, spatial dynamics, and external driving -- are combined in a classical branching diffusion with…

We propose a physics-constrained machine learning method-based on reservoir computing- to time-accurately predict extreme events and long-term velocity statistics in a model of turbulent shear flow. The method leverages the strengths of two…

Point processes offer a versatile framework for sequential event modeling. However, the computational challenges and constrained representational power of the existing point process models have impeded their potential for wider…

Building on recent advances in scientific machine learning and generative modeling for computational fluid dynamics, we propose a conditional score-based diffusion model designed for multi-scenarios fluid flow prediction. Our model…

We have witnessed and experienced increasing compound extreme events resulting from simultaneous or sequential occurrence of multiple events in a changing climate. In addition to a growing demand for a clearer explanation of compound risks…

We propose a new class of financial volatility models, called the REcurrent Conditional Heteroskedastic (RECH) models, to improve both in-sample analysis and out-ofsample forecasting of the traditional conditional heteroskedastic models. In…

Event cameras have shown promise in vision applications like optical flow estimation and stereo matching, with many specialized architectures leveraging the asynchronous and sparse nature of event data. However, existing works only focus…

In complex systems, events occur at irregular intervals that inherently encode the underlying dynamics of the system. Analyzing the temporal clustering of these events reveals critical insights into the non-random patterns and the temporal…

In many real-world scenarios, such as gas leak detection or environmental pollutant tracking, solving the Inverse Source Localization and Characterization problem involves navigating complex, dynamic fields with sparse and noisy…

Emergence, a global property of complex adaptive systems (CASs) constituted by interactive agents, is prevalent in real-world dynamic systems, e.g., network-level traffic congestions. Detecting its formation and evaporation helps to monitor…

Temporal event data are collected across a broad range of domains, and a variety of visual analytics techniques have been developed to empower analysts working with this form of data. These techniques generally display aggregate statistics…

Human action-reaction synthesis, a fundamental challenge in modeling causal human interactions, plays a critical role in applications ranging from virtual reality to social robotics. While diffusion-based models have demonstrated promising…

Interacting systems are prevalent in nature. It is challenging to accurately predict the dynamics of the system if its constituent components are analyzed independently. We develop a graph-based model that unveils the systemic interactions…

Modeling distributions of covariates, or density estimation, is a core challenge in unsupervised learning. However, the majority of work only considers the joint distribution, which has limited utility in practical situations. A more…