Related papers: Parameter Estimation of Differential Equation Mode…
Curve fitting is a fundamental technique in engineering and scientific research, serving as a critical tool for extracting insights from data. This study explores the application of various statistical equations to estimate outcomes in…
A unified theoretical framework is suggested to examine the energy dissipation properties at all stages of additive implicit-explicit Runge-Kutta (IERK) methods up to fourth-order accuracy for gradient flow problems. We construct some…
Ordinary differential equations (ODEs) provide a powerful framework for modeling dynamic systems arising in a wide range of scientific domains. However, most existing ODE methods focus on a single system, and do not adequately address the…
Many processes in biology, chemistry, physics, medicine, and engineering are modeled by a system of differential equations. Such a system is usually characterized via unknown parameters and estimating their 'true' value is thus required. In…
Explicit Runge-Kutta schemes with large stable step sizes are developed for integration of high order spectral difference spatial discretization on quadrilateral grids. The new schemes permit an effective time step that is substantially…
The logistic equation has been extensively used to model biological phenomena across a variety of disciplines and has provided valuable insight into how our universe operates. Incorporating time-dependent parameters into the logistic…
Exponential time differencing methods is a power tool for high-performance numerical simulation of computationally challenging problems in condensed matter physics, fluid dynamics, chemical and biological physics, where mathematical models…
We present a C++ implementation of a fifth order semi-implicit Runge-Kutta algorithm for solving Ordinary Differential Equations. This algorithm can be used for studying many different problems and in particular it can be applied for…
There exist many Runge-Kutta methods (explicit or implicit), more or less adapted to specific problems. Some of them have interesting properties, such as stability for stiff problems or symplectic capability for problems with energy…
Robot design optimization, imitation learning and system identification share a common problem which requires optimization over robot or task parameters at the same time as optimizing the robot motion. To solve these problems, we can use…
We consider the problem of parameter estimation in dynamic systems described by ordinary differential equations. A review of the existing literature emphasizes the need for deterministic global optimization methods due to the nonconvex…
In this technical note a general procedure is described to construct internally consistent splitting methods for the numerical solution of differential equations, starting from matching pairs of explicit and diagonally implicit Runge-Kutta…
We present a parameter estimation method in Ordinary Differential Equation (ODE) models. Due to complex relationships between parameters and states the use of standard techniques such as nonlinear least squares can lead to the presence of…
The differentiable programming paradigm is a cornerstone of modern scientific computing. It refers to numerical methods for computing the gradient of a numerical model's output. Many scientific models are based on differential equations,…
Delayed processes are ubiquitous throughout biology. These delays may arise through maturation processes or as the result of complex multi-step networks, and mathematical models with distributed delays are increasingly used to capture the…
This paper presents an adaptive multiple-shooting method to solve stochastic multi-point boundary value problems. The heuristic to choose the shooting points is based on separating the effects of drift and diffusion terms and comparing the…
Differential equations are frequently used in engineering domains, such as modeling and control of industrial systems, where safety and performance guarantees are of paramount importance. Traditional physics-based modeling approaches…
We introduce a novel kernel-based framework for learning differential equations and their solution maps that is efficient in data requirements, in terms of solution examples and amount of measurements from each example, and computational…
Many time-dependent differential equations are equipped with invariants. Preserving such invariants under discretization can be important, e.g., to improve the qualitative and quantitative properties of numerical solutions. Recently,…
In this manuscript we discuss weighted reduced order methods for stochastic partial differential equations. Random inputs (such as forcing terms, equation coefficients, boundary conditions) are considered as parameters of the equations. We…