Related papers: WENDy for Nonlinear-in-Parameters ODEs
In this work, high-order discrete well-balanced methods for one-dimensional hyperbolic systems of balance laws are proposed. We aim to construct a method whose discrete steady states correspond to solutions of arbitrary high-order ODE…
We develop a weak-form sparse identification method for interacting particle systems (IPS) with the primary goals of reducing computational complexity for large particle number $N$ and offering robustness to either intrinsic or extrinsic…
In this paper, we introduce a novel, data-driven approach for solving high-dimensional Bayesian inverse problems based on partial differential equations (PDEs), called Weak Neural Variational Inference (WNVI). The method complements real…
Real-time nonlinear Bayesian filtering algorithms are overwhelmed by data volume, velocity and increasing complexity of computational models. In this paper, we propose a novel ensemble based nonlinear Bayesian filtering approach which only…
Ordinary differential equations (ODEs) are used to model dynamic systems appearing in engineering, physics, biomedical sciences and many other fields. These equations contain unknown parameters, say $\bm\theta$ of physical significance…
In the present paper we consider the varying coefficient model which represents a useful tool for exploring dynamic patterns in many applications. Existing methods typically provide asymptotic evaluation of precision of estimation…
Diffusion models have exhibited excellent performance in various domains. The probability flow ordinary differential equation (ODE) of diffusion models (i.e., diffusion ODEs) is a particular case of continuous normalizing flows (CNFs),…
In extreme value theory and other related risk analysis fields, probability weighted moments (PWM) have been frequently used to estimate the parameters of classical extreme value distributions. This method-of-moment technique can be applied…
Early detection of faults in induction motors is crucial for ensuring uninterrupted operations in industrial settings. Among the various fault types encountered in induction motors, bearing, rotor, and stator faults are the most prevalent.…
The remarkable flexibility and adaptability of both deep learning models and ensemble methods have led to the proliferation for their application in understanding many physical phenomena. Traditionally, these two techniques have largely…
Finite mixture models are widely used in econometric analyses to capture unobserved heterogeneity. This paper shows that maximum likelihood estimation of finite mixtures of parametric densities can suffer from substantial finite-sample bias…
This paper presents an anomaly detection model that combines the strong statistical foundation of density-estimation-based anomaly detection methods with the representation-learning ability of deep-learning models. The method combines an…
A refined a priori error analysis of the lowest order (linear) nonconforming Virtual Element Method (VEM) for approximating a model Poisson problem is developed in both 2D and 3D. A set of new geometric assumptions is proposed on shape…
In many applications, parameters of interest are estimated by solving some non-smooth estimating equations with $U$-statistic structure. Jackknife empirical likelihood (JEL) approach can solve this problem efficiently by reducing the…
We propose a trajectory-based quasiclassical method for approximating dynamics in condensed phase systems. Building upon the previously developed Optimized Mean Trajectory (OMT) approximation that has been used to compute linear and…
In this paper, we adopt a probability distribution estimation perspective to explore the optimization mechanisms of supervised classification using deep neural networks. We demonstrate that, when employing the Fenchel-Young loss, despite…
We propose a novel model to obtain the subgrid-scale velocity in the context of large-eddy simulation (LES) of particle-laden turbulent flows, to recover accurate particle statistics. In the new wavelet enrichment model, the subgrid-scale…
Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations.…
We introduce the Optimizing a Discrete Loss (ODIL) framework for the numerical solution of Partial Differential Equations (PDE) using machine learning tools. The framework formulates numerical methods as a minimization of discrete residuals…
Classification and probability estimation are fundamental tasks with broad applications across modern machine learning and data science, spanning fields such as biology, medicine, engineering, and computer science. Recent development of…