Related papers: Estimation of ordinary differential equation model…
Differential Equations are among the most important Mathematical tools used in creating models in the science, engineering, economics, mathematics, physics, aeronautics, astronomy, dynamics, biology, chemistry, medicine, environmental…
We propose new a posteriori error estimators for non-conforming finite element discretizations of second-order elliptic PDE problems. These estimators are based on novel reformulations of the standard Prager-Synge identity, and enable to…
This note studies a method for the efficient estimation of a finite number of unknown parameters from linear equations, which are perturbed by Gaussian noise. In case the unknown parameters have only few nonzero entries, the proposed…
Neural networks are discrete entities: subdivided into discrete layers and parametrized by weights which are iteratively optimized via difference equations. Recent work proposes networks with layer outputs which are no longer quantized but…
Numerical ordinary differential equation (ODE) solvers are indispensable tools in various engineering domains, enabling the simulation and analysis of dynamic systems. In this work, we utilize 5 different numerical ODE solvers namely:…
Probabilistic solvers for ordinary differential equations assign a posterior measure to the solution of an initial value problem. The joint covariance of this distribution provides an estimate of the (global) approximation error. The…
We propose a kernel compression method for solving Distributed-Order (DO) Fractional Partial Differential Equations (DOFPDEs) at the cost of solving corresponding local-in-time PDEs. The key concepts are (1) discretization of the integral…
Differential equations in general and neural ODEs in particular are an essential technique in continuous-time system identification. While many deterministic learning algorithms have been designed based on numerical integration via the…
This paper studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs), a.k.a. (Ordinary) Difference Equations. It presents a new framework using these equations as a central tool for computation and…
In this work we develop an ordinary differential equations (ODE) model of physiological regulation of glycemia in type 1 diabetes mellitus (T1DM) patients in response to meals and intravenous insulin infusion. Unlike for the majority of…
Effectively modeling phenomena present in highly nonlinear dynamical systems whilst also accurately quantifying uncertainty is a challenging task, which often requires problem-specific techniques. We present a novel, domain-agnostic…
This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations. This construction enables the solution of Bayesian inverse problems while accounting for…
A method for approximating sixth-order ordinary differential equations is proposed, which utilizes a deep learning feedforward artificial neural network, referred to as a neural solver. The efficacy of this unsupervised machine learning…
In this paper we study the stability of explicit finite difference discretizations of linear advection-diffusion equations (ADE) with arbitrary order of accuracy in the context of method of lines. The analysis first focuses on the stability…
We show a general method allowing the solution calculation, in the form of a power series, for a very large class of nonlinear Ordinary Differential Equations (ODEs), namely the real analytic $\sigma\pi$-ODEs (and, more in general, the real…
The estimation of distributed parameters in partial differential equations (PDE) from measures of the solution of the PDE may lead to under-determination problems. The choice of a parameterization is a usual way of adding a-priori…
This paper introduces an Ordinary Differential Equation (ODE) notion for survival analysis. The ODE notion not only provides a unified modeling framework, but more importantly, also enables the development of a widely applicable, scalable,…
Recent works have shown that deep neural networks can be employed to solve partial differential equations, giving rise to the framework of physics informed neural networks. We introduce a generalization for these methods that manifests as a…
Neural differential equations are a promising new member in the neural network family. They show the potential of differential equations for time series data analysis. In this paper, the strength of the ordinary differential equation (ODE)…
The covariate shift is a challenging problem in supervised learning that results from the discrepancy between the training and test distributions. An effective approach which recently drew a considerable attention in the research community…