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Polynomial chaos expansions (PCE) have proven efficiency in a number of fields for propagating parametric uncertainties through computational models of complex systems, namely structural and fluid mechanics, chemical reactions and…
Diffusion based generative models have achieved unprecedented fidelity in synthesizing high dimensional data, yet the theoretical mechanisms governing multimodal generation remain poorly understood. Here, we present a theoretical framework…
Time series forecasting has witnessed significant progress with deep learning. While prevailing approaches enhance forecasting performance by modifying architectures or introducing novel enhancement strategies, they often fail to…
Many data-driven decision problems are formulated using a nominal distribution estimated from historical data, while performance is ultimately determined by a deployment distribution that may be shifted, context-dependent, partially…
Voltage prediction in distribution grids is a critical yet difficult task for maintaining power system stability. Machine learning approaches, particularly Graph Neural Networks (GNNs), offer significant speedups but suffer from poor…
High-fidelity numerical simulations of chaotic, high dimensional nonlinear dynamical systems are computationally expensive, necessitating the development of efficient surrogate models. Most surrogate models for such systems are…
Diffusion models have garnered significant attention since they can effectively learn complex multivariate Gaussian distributions, resulting in diverse, high-quality outcomes. They introduce Gaussian noise into training data and reconstruct…
We present a new class of control pulses designed to transfer co-located ensembles without relying on frequency selectivity, thereby allowing much faster state-transitions. A geometric approach allows us to construct sequences which are…
In this paper we develop a method capable of modeling the space-time focusing of nondiffracting pulses. The new pulses can possess arbitrary peak velocities and, in addition to being resistant to diffraction, can have their peak intensities…
Probabilistic forecasting provides a principled framework for uncertainty quantification in dynamical systems by representing predictions as probability distributions rather than deterministic trajectories. However, existing forecasting…
Irregularly sampled multivariate event streams remain a stubbornly difficult modality for generative modeling: tokenization-based approaches break down when inter-event intervals vary by orders of magnitude, and neural temporal point…
Many data-driven modules in smart grid rely on access to high-quality power flow data; however, real-world data are often limited due to privacy and operational constraints. This paper presents a physics-informed generative framework based…
We investigate the problem of stochastic network optimization in the presence of imperfect state prediction and non-stationarity. Based on a novel distribution-accuracy curve prediction model, we develop the predictive learning-aided…
We establish a general framework using a diffusion approximation to simulate forward-in-time state counts or frequencies for cladogenetic state-dependent speciation-extinction (ClaSSE) models. We apply the framework to various two- and…
In this paper, a first sample-based formulation of the recently considered population observers, or ensemble observers, which estimate the state distribution of dynamic populations from measurements of the output distribution is…
Learning behavioral patterns from observational data has been a de-facto approach to motion forecasting. Yet, the current paradigm suffers from two shortcomings: brittle under distribution shifts and inefficient for knowledge transfer. In…
Diffusion-based models have recently shown strong performance in trajectory planning, as they are capable of capturing diverse, multimodal distributions of complex behaviors. A key limitation of these models is their slow inference speed,…
Conditional diffusion models provide a natural framework for probabilistic prediction of dynamical systems and have been successfully applied to fluid dynamics and weather prediction. However, in many settings, the available information at…
Real-world time series forecasting faces the fundamental challenge of non-stationary statistical properties, including shifts in mean and variance over time. While reversible instance normalization (RevIN) has shown promise by…
The estimation of Remaining Useful Life (RUL) plays a pivotal role in intelligent manufacturing systems and Industry 4.0 technologies. While recent advancements have improved RUL prediction, many models still face interpretability and…