Related papers: An Efficient Solver for Cumulative Density Functio…
The method of distributions is developed for systems that are governed by hyperbolic conservation laws with stochastic forcing. The method yields a deterministic equation for the cumulative density distribution (CDF) of a system state,…
Conditional density estimation (CDE) is a fundamental task in machine learning that aims to model the full conditional law $\mathbb{P}(\mathbf{y} \mid \mathbf{x})$, beyond mere point prediction (e.g., mean, mode). A core challenge is…
In this paper, we extend a recently introduced multi-fidelity control variate for the uncertainty quantification of the Boltzmann equation to the case of kinetic models arising in the study of multiagent systems. For these phenomena, where…
Normalizing flows model a complex target distribution in terms of a bijective transform operating on a simple base distribution. As such, they enable tractable computation of a number of important statistical quantities, particularly…
Deployment of machine learning algorithms into real-world practice is still a difficult task. One of the challenges lies in the unpredictable variability of input data, which may differ significantly among individual users, institutions,…
This paper presents MPC-CDF, a new approach integrating control density functions (CDFs) within a model predictive control (MPC) framework to ensure safety-critical control in nonlinear dynamical systems. By using the dual formulation of…
We introduce a novel approach for safe control design based on the density function. A control density function (CDF) is introduced to synthesize a safe controller for a nonlinear dynamic system. The CDF can be viewed as a dual to the…
Hyperbolic balance laws with uncertain (random) parameters and inputs are ubiquitous in science and engineering. Quantification of uncertainty in predictions derived from such laws, and reduction of predictive uncertainty via data…
We consider the problem of navigating a nonlinear dynamical system from some initial set to some target set while avoiding collision with an unsafe set. We extend the concept of density function to control density function (CDF) for solving…
The statistical characterization of the sum of random variables (RVs) are useful for investigating the performance of wireless communication systems. We derive exact closed-form expressions for the probability density function (PDF) and…
Learning the multivariate distribution of data is a core challenge in statistics and machine learning. Traditional methods aim for the probability density function (PDF) and are limited by the curse of dimensionality. Modern neural methods…
Motivated by the statistical description of turbulence, we study statistical conservation laws in the form of kinetic-type PDEs for joint probability density functions (PDFs) and cumulative distribution functions (CDFs) associated with…
Computational Fluid Dynamics (CFD) simulation by the numerical solution of the Navier-Stokes equations is an essential tool in a wide range of applications from engineering design to climate modeling. However, the computational cost and…
This article describes two Monte Carlo methods for calculating confidence intervals on cumulative density function (CDF) based multivariate normal quantiles that allows for controlling the tail regions of a multivariate distribution where…
Estimating the density of a continuous random variable X has been studied extensively in statistics, in the setting where n independent observations of X are given a priori and one wishes to estimate the density from that. Popular methods…
A model-based collaborative filtering (CF) approach utilizing fast adaptive randomized singular value decomposition (SVD) is proposed for the matrix completion problem in recommender system. Firstly, a fast adaptive PCA frameworkis…
We report a new multicanonical Monte Carlo algorithm to obtain the density of states for physical systems with continuous state variables in statistical mechanics. Our algorithm is able to obtain a closed-form expression for the density of…
The selective frequency damping (SFD) method is an alternative to classical Newton's method to obtain unstable steady-state solutions of dynamical systems. However this method has two main limitations: it does not converge for arbitrary…
Computational Fluid Dynamics (CFD) is a major sub-field of engineering. Corresponding flow simulations are typically characterized by heavy computational resource requirements. Often, very fine and complex meshes are required to resolve…
In this study, we develop a probabilistic approach to map the parametric uncertainty to the output state uncertainty in first-order hyperbolic conservation laws. We analyze this problem for nonlinear immiscible two-phase transport in…