The workshop will feature the latest research on statistical methods and modeling to address real-world challenges in health, environment, and sustainability.

Earth system models (ESMs) are fundamental for understanding Earth's complex climate system. However, the computational demands and storage requirements of ESM simulations limit their utility. For the newly published CESM2-LENS2 data, which suffer from this issue, we propose a novel stochastic generator (SG) as a practical complement to the CESM2, capable of rapidly producing emulations closely mirroring training simulations. Our SG leverages the spherical harmonic transformation (SHT) to shift from spatial to spectral domains, enabling efficient low-rank approximations that significantly reduce computational and storage costs. By accounting for axial symmetry and retaining distinct ranks for land and ocean regions, our SG captures intricate non-stationary spatial dependencies. Additionally, a modified Tukey g-and-h (TGH) transformation accommodates non-Gaussianity in high-temporal-resolution data. We apply the proposed SG to generate emulations for surface temperature simulations from the CESM2-LENS2 data across various scales, marking the first attempt of reproducing daily data. These emulations are then meticulously validated against training simulations. This work offers a promising complementary pathway for efficient climate modeling and analysis while overcoming computational and storage limitations.

We present a doubly enriched finite volume method for precisely computing highly dynamic fluid-particle interaction. This involves forces beeing exchanged between the particles and the fluid at the interface. In an earlier work we derived a monolithic scheme which includes the interaction forces and rigied-body motions into the Navier-Stokes equations by extending the test space. In highly dynamic particle-fluid interaction cases, pressure oscillations are a common issue.

Dear CEMSE Faculty, Staff, and Students,

Non-convex Machine Learning problems typically do not adhere to the standard smoothness assumption. Based on empirical findings a more realistic generalized smoothness assumption was proposed, though it remains largely unexplored. Many existing algorithms designed for standard smooth problems need to be revised. In this paper we propose and analyze new Federated Learning methods with local steps, partial participation of clients, and Random Reshuffling without extra restrictive assumptions beyond generalized smoothness. Our theory is consistent with the known results for standard smooth problems, and our experimental results support the theoretical insights.

This presentation explores mean field games (MFGs) through the lens of functional analysis, focusing on the role of monotonicity methods in understanding their properties and deriving solutions. We begin by introducing MFGs as models for large populations of interacting rational agents, illustrating their derivation for deterministic problems. We then examine key questions of the existence and uniqueness of MFG solutions.

Traditional Topological Data Analysis (TDA) methods, such as Persistent Homology (PH), rely on distance measures (e.g., cross-correlation, partial correlation, coherence, and partial coherence) that are symmetric by definition. While useful for studying topological patterns in functional brain connectivity, the main limitation of these methods is their inability to capture the directional dynamics - which is crucial for understanding effective brain connectivity.

Free boundary problems emerge naturally in mathematical models representing physical, biological, or financial phenomena, such as ice melting, population dynamics, or stock market behavior. These problems involve solving partial differential equations for both an unknown function and an unknown domain. This talk will explore several free boundary problems and different methods to address them.

We introduce a parallel hybrid approach for Bayesian inference of large spatio-temporal Gaussian processes, combining domain decomposition with the Rao-Blackwellized Monte Carlo estimator. This method enhances speed and scalability by integrating iterative Krylov methods with direct factorizations, improving accuracy and robustness in large-scale datasets.

In the realm of fast and scalable approximated Bayesian Inference, two highly sought-after approaches have traditionally been the Laplace Method and Variational Bayes.

Second-order partial differential equations (PDEs) are traditionally classified as being parabolic, elliptic, or hyperbolic in nature, and this classification largely determines the kind of analytical and numerical techniques that can be successfully applied to them.

The design of efficient parallel/distributed optimization methods and tight analysis of their theoretical properties are important research endeavors. While minimax complexities are known for sequential optimization methods, the theory of parallel optimization methods is surprisingly much less explored, especially in the presence of data, compute and communication heterogeneity.

Lattice models are widely used to study various statistical and quantum physics phenomena. For instance, to model fluid percolation, one takes a part of a honeycomb lattice inside a fixed rectangle and a random coloring of the hexagons into two colors, blue and yellow. A typical question is then to find the probability of a blue path between opposite sides of the rectangle as the hexagons become smaller and smaller.

The 3-day lecture series will discuss fundamental principles and contemporary trends in statistical inference for finite populations. With some cases presented, participants will gain practical insights into real-world applications of sampling methodologies and their implications. With the discussion of current trends, this equips researchers with the knowledge and tools necessary to conduct inference in finite populations, ensuring the generation of valuable insights for informed decision-making in various disciplines.

Environmental statistics play a critical role in various interconnected domains, encompassing weather and climate forecasting, air quality monitoring, and sustainable urban planning. However, because of their high inherent unpredictability and nonstationarity, modeling complex spatio-temporal dynamics of environmental processes is challenging. This dissertation develops a set of DNN based methods for large-scale spatial and spatio-temporal processes.

This thesis explores advanced statistical models and methods for analyzing multivariate and functional time series data. It focuses on various aspects of statistical analysis, including visualization, robust outlier detection, inference, and forecasting. It addresses challenges in outlier detection for functional data, quantile spectral estimation for multivariate time series, and high-dimensional functional time series forecasting, with applications in environmental, financial, and demographic fields.

Rare, low-probability events often lead to the biggest impacts. Therefore, the development of statistical approaches for modeling, predicting and quantifying environmental risks associated with natural hazards is of utmost importance. In this seminar, I will show how statistical deep-learning methods can help solve challenges that arise when modeling complex and massive spatiotemporal extremes data.

Given the complex nature of brain signals and the challenges involved in estimating its dependence and analyzing the emerging topological patterns, this dissertation introduces innovative statistical tools designed to explore both the functional and effective connectivity within brain networks. It sheds light on frequency-specific patterns in ADHD subjects and introduces a novel approach for examining the hierarchical structure of brain regions during seizures. Our work provides a novel perspective on the organization of brain networks and presents insight into how various conditions influence their complex structure.

We introduce a framework for calibrating machine learning models so that their predictions satisfy explicit, finite-sample statistical guarantees. Our calibration algorithms work with any underlying model and (unknown) data-generating distribution and do not require model refitting.

Artificial intelligence (AI) has focused on a paradigm in which intelligence inheres in a single, autonomous agent. Social issues are entirely secondary in this paradigm. When AI systems are deployed in social contexts, however, the overall design of such systems is often naive --- a centralized entity provides services to passive agents and reaps the rewards. Such a paradigm need not be the dominant paradigm for information technology. In a broader framing, agents are active, they are cooperative, and they wish to obtain value from their participation in learning-based systems. Agents may supply data and other resources to the system, only if it is in their interest to do so. Critically, intelligence inheres as much in the overall system as it does in individual agents, be they humans or computers. This is a perspective that is familiar in the social sciences, and a key theme in my work is that of bringing economics into contact with foundational issues in computing and data sciences. I'll emphasize some of the mathematical challenges that arise at this tripartite interface.

Traveling wave solutions of reaction-diffusion systems have been studied to explain wave propagation phenomena in biological organisms.

Despite the significant advancements deep learning models have brought to solving complex problems in the real world, their lack of transparency remains a significant barrier, particularly in deploying them within safety-critical contexts.

Neural ODEs have surfaced in the last decade as a new perspective on modelling dynamics by learning the time-derivative that drives the system evolution forward as a neural network.

As more and more modern time series data sets are becoming high dimensional, the problem of classification in this context has received increasing attention. We propose a statistical framework for classifying multivariate stationary Gaussian time series where the number of covariates, the length of the series, and the sample size, all grow to infinity.

In this work, we employ importance sampling (IS) techniques to track a small over-threshold probability of a running maximum associated with the solution of a stochastic differential equation (SDE) within the framework of ensemble Kalman filtering (EnKF).