相关论文: Numerical differentiation: local versus global met…

Shape calculus concerns the calculation of directional derivatives of some quantity of interest, typically expressed as an integral. This article introduces a type of shape calculus based on localized dilation of boundary faces through…

A new technique of global optimization and its applications in particular to neural networks are presented. The algorithm is also compared to other global optimization algorithms such as Gradient descent (GD), Monte Carlo (MC), Genetic…

Most multivariate outlier detection procedures ignore the spatial dependency of observations, which is present in many real data sets from various application areas. This paper introduces a new outlier detection method that accounts for a…

Numerical solutions to fractional differential equations can be extremely computationally intensive due to the effect of non-local derivatives in which all previous time points contribute to the current iteration. In finite difference…

We present an approach to reduced-order modelling that builds off recent graph-theoretic work for representation, exploration, and analysis of computed states of physical systems (Banerjee et al., Comp. Meth. App. Mech. Eng., 351, 501-530,…

This study introduces new time-stepping strategies with built-in global error estimators. The new methods propagate the defect along with the numerical solution much like solving for the correction or Zadunaisky's procedure; however, the…

Differentiable simulation is a promising toolkit for fast gradient-based policy optimization and system identification. However, existing approaches to differentiable simulation have largely tackled scenarios where obtaining smooth…

Anomaly detection aims to detect data that do not conform to regular patterns, and such data is also called outliers. The anomalies to be detected are often tiny in proportion, containing crucial information, and are suitable for…

Reliable probability estimation is of crucial importance in many real-world applications where there is inherent (aleatoric) uncertainty. Probability-estimation models are trained on observed outcomes (e.g. whether it has rained or not, or…

A frequently occurring challenge in experimental and numerical observation is how to resolve features, such as spectral peaks - with center, width, height - and derivatives from measured data with unavoidable noise. Therefore, we develop a…

In probabilistic coherence spaces, a denotational model of probabilistic functional languages, morphisms are analytic and therefore smooth. We explore two related applications of the corresponding derivatives. First we show how derivatives…

Robust estimation of location is a fundamental problem in statistics, particularly in scenarios where data contamination by outliers or model misspecification is a concern. In univariate settings, methods such as the sample median and…

We develop methods for parameter estimation in settings with large-scale data sets, where traditional methods are no longer tenable. Our methods rely on stochastic approximations, which are computationally efficient as they maintain one…

A variance reduction technique in nonparametric smoothing is proposed: at each point of estimation, form a linear combination of a preliminary estimator evaluated at nearby points with the coefficients specified so that the asymptotic bias…

This paper develops an in-depth treatment concerning the problem of approximating the Gaussian smoothing and Gaussian derivative computations in scale-space theory for application on discrete data. With close connections to previous…

Estimating spatial distributions is important in data analysis, such as traffic flow forecasting and epidemic prevention. To achieve accurate spatial distribution estimation, the analysis needs to collect sufficient user data. However,…

Neural networks have been identified as powerful tools for the study of complex systems. A noteworthy example is the neural network differential equation (NN DE) solver, which can provide functional approximations to the solutions of a wide…

Gradient-based optimization methods are commonly used to identify local optima in high-dimensional spaces. When derivatives cannot be evaluated directly, stochastic estimators can provide approximate gradients. However, these estimators'…

We have presented some practical consequences on the molecular-dynamics simulations arising from the numerical algorithm published recently in paper Int. J. Mod. Phys. C 16, 413 (2005). The algorithm is not a finite-difference method and…

Developing a suitable Deep Neural Network (DNN) often requires significant iteration, where different model versions are evaluated and compared. While metrics such as accuracy are a powerful means to succinctly describe a model's…