相关论文: Lagrangian uncertainty quantification and informat…

Uncertainty quantification is a critical yet unsolved challenge for deep learning, especially for the time series imputation with irregularly sampled measurements. To tackle this problem, we propose a novel framework based on the principles…

The dynamics of Lagrangian particles in turbulence play a crucial role in mixing, transport, and dispersion in complex flows. Their trajectories exhibit highly non-trivial statistical behavior, motivating the development of surrogate models…

Uncertainty quantification is crucial for building reliable and trustable machine learning systems. We propose to estimate uncertainty in recurrent neural networks (RNNs) via stochastic discrete state transitions over recurrent timesteps.…

Deploying Lagrangian drifters that facilitate the state estimation of the underlying flow field within a future time interval is practically important. However, the uncertainty in estimating the flow field prevents using standard…

Deep generative frameworks including GANs and normalizing flow models have proven successful at filling in missing values in partially observed data samples by effectively learning -- either explicitly or implicitly -- complex,…

We have recently proposed a rigorous framework for Uncertainty Quantification (UQ) in which UQ objectives and assumption/information set are brought into the forefront, providing a framework for the communication and comparison of UQ…

In this paper we describe the construction of an efficient probabilistic parameterization that could be used in a coarse-resolution numerical model in which the variation of moisture is not properly resolved. An Eulerian model using a…

We present a framework for learning of modeling uncertainties in Linear Time Invariant (LTI) systems. We propose a methodology to extend the dynamics of an LTI (without uncertainty) with an uncertainty model, based on measured data, to…

In this paper, we establish a set of criteria which are applied to discuss various formulations under which Lagrangian stochastic models can be found. These models are used for the simulation of fluid particles in single-phase turbulence as…

General characterizations of physical measurements are discussed within the framework of the classical information theory. The uncertainty relation for simultaneous measurements of two physical observables is defined in this framework for…

In this paper, we establish an iterative data-driven approach to derive guaranteed bounds on nonlinearity measures of unknown nonlinear systems. In this context, nonlinearity measures quantify the strength of the nonlinearity of a dynamical…

Information-theory based variational principles have proven effective at providing scalable uncertainty quantification (i.e. robustness) bounds for quantities of interest in the presence of nonparametric model-form uncertainty. In this…

Multimodal foundation models offer promising advancements for enhancing driving perception systems, but their high computational and financial costs pose challenges. We develop a method that leverages foundation models to refine predictions…

Traditional approaches to ensure group fairness in algorithmic decision making aim to equalize ``total'' error rates for different subgroups in the population. In contrast, we argue that the fairness approaches should instead focus only on…

The goal of this research is to derive an approach to assess uncertainty in an arbitrary volume conditioned by sampling data, without using geostatistical simulation. We have accomplished this goal by deriving an numerical tool suitable for…

It has been known for some time that a 3D incompressible Euler flow that has initially a barely smooth velocity field nonetheless has Lagrangian fluid particle trajectories that are analytic in time for at least a finite time (Ph. Serfati…

Advances in experimental techniques allow the collection of high-resolution spatio-temporal data that track individual motile entities. These tracking data can be used to calibrate mathematical models describing the motility of individual…

A variant of the usual Lagrangian scheme is developed which describes both the equations of motion and the variational equations of a system. The required (prolonged) Lagrangian is defined in an extended configuration space comprising both…

Quantifying and reducing uncertainty in Earth system model parameterizations is essential to improving their reliability in decision-making. Forward uncertainty propagation is used to derive parameter sensitivity but requires physically…

As large language models (LLMs) continue to evolve, understanding and quantifying the uncertainty in their predictions is critical for enhancing application credibility. However, the existing literature relevant to LLM uncertainty…