Related papers: A bridge between invariant dynamical structures an…

This paper introduces a novel uncertainty quantification framework for regression models where the response takes values in a separable metric space, and the predictors are in a Euclidean space. The proposed algorithms can efficiently…

Models are often given in terms of differential equations to represent physical systems. In the presence of uncertainty, accurate prediction of the behavior of these systems using the models requires understanding the effect of uncertainty…

We investigate a method to deal with congestion of sectors and delays in the tactical phase of air traffic flow and capacity management. It relies on temporal objectives given for every point of the flight plans and shared among the…

Data-driven models (DDM) based on machine learning and other AI techniques play an important role in the perception of increasingly autonomous systems. Due to the merely implicit definition of their behavior mainly based on the data used…

This work introduces the conditioned Vehicle Motion Diffusion (cVMD) model, a novel network architecture for highway trajectory prediction using diffusion models. The proposed model ensures the drivability of the predicted trajectory by…

We present a critical survey on the consistency of uncertainty quantification used in deep learning and highlight partial uncertainty coverage and many inconsistencies. We then provide a comprehensive and statistically consistent framework…

An uncertainty quantification framework is developed for Eulerian-Lagrangian models of particle-laden flows, where the fluid is modeled through a system of partial differential equations in the Eulerian frame and inertial particles are…

Quantifying the impact of parametric and model-form uncertainty on the predictions of stochastic models is a key challenge in many applications. Previous work has shown that the relative entropy rate is an effective tool for deriving…

We present the design and development of a data stream system that captures data uncertainty from data collection to query processing to final result generation. Our system focuses on data that is naturally modeled as continuous random…

We consider the problems of exploration and point-goal navigation in previously unseen environments, where the spatial complexity of indoor scenes and partial observability constitute these tasks challenging. We argue that learning…

Using the dynamics of information propagation on a network as our illustrative example, we present and discuss a systematic approach to quantifying heterogeneity and its propagation that borrows established tools from Uncertainty…

Reconstructions of Lagrangian drift, for example for objects lost at sea, are often uncertain due to unresolved physical phenomena within the data. Uncertainty is usually overcome by introducing stochasticity into the drift, but this…

We employ unsupervised learning tools to identify different phases and their transition in quantum systems subject to the combined action of unitary evolution and stochastic measurements. Specifically, we consider principal component…

Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the…

We propose a numerical method for discovering unknown parameterized dynamical systems by using observational data of the state variables. Our method is built upon and extends the recent work of discovering unknown dynamical systems, in…

A dynamical systems approach to turbulence envisions the flow as a trajectory through a high-dimensional state space transiently visiting the neighbourhoods of unstable simple invariant solutions (E. Hopf, Commun. Appl. Maths 1, 303, 1948).…

We describe a setup for obtaining uncertainty relations for arbitrary pairs of observables related by Fourier transform. The physical examples discussed here are standard position and momentum, number and angle, finite qudit systems, and…

Trajectory prediction models that can infer both finite future trajectories and their associated uncertainties of the target vehicles in an online setting (e.g., real-world application scenarios) is crucial for ensuring the safe and robust…

Modeling fluid turbulence using a 'skeleton' of coherent structures has traditionally progressed by focusing on a few canonical experiments, such as pipe flow and Taylor-Couette flow. We here consider an alternative canonical experiment,…

In this paper we demonstrate the only available scalable information bounds for quantities of interest of high dimensional probabilistic models. Scalability of inequalities allows us to (a) obtain uncertainty quantification bounds for…