相关论文: Post-Regularization Confidence Bands for Ordinary …

Neural Ordinary Differential Equations (NODEs) have proven successful in learning dynamical systems in terms of accurately recovering the observed trajectories. While different types of sparsity have been proposed to improve robustness, the…

Kernel density estimation on a finite interval poses an outstanding challenge because of the well-recognized bias at the boundaries of the interval. Motivated by an application in cancer research, we consider a boundary constraint linking…

Reduced basis approximations of Optimal Control Problems (OCPs) governed by steady partial differential equations (PDEs) with random parametric inputs are analyzed and constructed. Such approximations are based on a Reduced Order Model,…

Parameter inference in ordinary differential equations is an important problem in many applied sciences and in engineering, especially in a data-scarce setting. In this work, we introduce a novel generative modeling approach based on…

Given a sample from some unknown continuous density $f:\mathbb{R}\to\mathbb{R}$, we construct adaptive confidence bands that are honest for all densities in a "generic" subset of the union of $t$-H\"older balls, $0<t\le r$, where $r$ is a…

Here we present an expository, general analysis of valid post-selection or post-regularization inference about a low-dimensional target parameter, $\alpha$, in the presence of a very high-dimensional nuisance parameter, $\eta$, which is…

We give a development of the ODE method for the analysis of recursive algorithms described by a stochastic recursion. With variability modelled via an underlying Markov process, and under general assumptions, the following results are…

Profile likelihood provides a general framework to infer on a scalar parameter of a statistical model. A confidence interval is obtained by numerically finding the two abscissas where the profile log-likelihood curve intersects an…

We present a new approach for estimating parameters in rational ODE models from given (measured) time series data. In typical existing approaches, an initial guess for the parameter values is made from a given search interval. Then, in a…

Stochastic regularization of neural networks (e.g. dropout) is a wide-spread technique in deep learning that allows for better generalization. Despite its success, continuous-time models, such as neural ordinary differential equation (ODE),…

Ordinary differential equations (ODEs) are a mathematical model used in many application areas such as climatology, bioinformatics, and chemical engineering with its intuitive appeal to modeling. Despite ODE's wide usage in modeling, the…

Based on a progressively type-II censored sample from the exponential distribution with unknown location and scale parameter, confidence bands are proposed for the underlying distribution function by using confidence regions for the…

The idea of neural Ordinary Differential Equations (ODE) is to approximate the derivative of a function (data model) instead of the function itself. In residual networks, instead of having a discrete sequence of hidden layers, the…

Neural ordinary differential equations (NODE) have garnered significant attention for their design of continuous-depth neural networks and the ability to learn data/feature dynamics. However, for high-dimensional systems, estimating…

This paper addresses the training of Neural Ordinary Differential Equations (neural ODEs), and in particular explores the interplay between numerical integration techniques, stability regions, step size, and initialization techniques. It is…

In this paper, we construct the simultaneous confidence band (SCB) for the nonparametric component in partially linear panel data models with fixed effects. We remove the fixed effects, and further obtain the estimators of parametric and…

Given an autonomous system of ordinary differential equations (ODE), we consider developing practical models for the deterministic, slow/coarse behavior of the ODE system. Two types of coarse variables are considered. The first type…

This work proposes an extension of neural ordinary differential equations (NODEs) by introducing an additional set of ODE input parameters to NODEs. This extension allows NODEs to learn multiple dynamics specified by the input parameter…

Recently established equivalences between differential equations and the structure of neural networks enabled some interpretation of training of a neural network as partial-differential-equation (PDE) constrained optimization. We add to the…

Mathematical modeling with Ordinary Differential Equations (ODEs) has proven to be extremely successful in a variety of fields, including biology. However, these models are completely deterministic given a certain set of initial conditions.…