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Ordinary differential equations (ODEs) are widely used to describe the time evolution of natural phenomena across various scientific fields. Estimating the parameters of these systems from data is a challenging task, particularly when…

Numerical Analysis · Mathematics 2025-01-23 S. Syafiie , Aries Subiantoro , Vivi Andasari , Fernando Tadeo

Ordinary differential equations (ODEs), via their induced flow maps, provide a powerful framework to parameterize invertible transformations for the purpose of representing complex probability distributions. While such models have achieved…

Statistics Theory · Mathematics 2023-09-06 Youssef Marzouk , Zhi Ren , Sven Wang , Jakob Zech

Parameter estimation for ordinary differential equations (ODEs) plays a fundamental role in the analysis of dynamical systems. Generally lacking closed-form solutions, ODEs are traditionally approximated using deterministic solvers.…

Computation · Statistics 2025-06-30 Mohan Wu , Martin Lysy

In this paper we address the challenging problem of designing globally convergent estimators for the parameters of nonlinear systems containing a non-separable exponential nonlinearity. This class of terms appears in many practical…

Dynamical Systems · Mathematics 2022-11-17 Romeo Ortega , Alexey Bobtsov , Ramon Costa-Castello , Nikolay Nikolaev

In this paper, we investigate the parameter estimation problem for reflected OU processes. Both the estimates based on continuously observed processes and discretely observed processes are considered. The explicit formulas for the…

Methodology · Statistics 2022-05-03 Han Yuecai , Zhang Dingwen

We consider the problem of parameter estimation for a system of ordinary differential equations from noisy observations on a solution of the system. In case the system is nonlinear, as it typically is in practical applications, an analytic…

Statistics Theory · Mathematics 2012-07-27 Shota Gugushvili , Chris A. J. Klaassen

Ordinary differential equations (ODEs) are foundational in modeling intricate dynamics across a gamut of scientific disciplines. Yet, a possibility to represent a single phenomenon through multiple ODE models, driven by different…

Methodology · Statistics 2023-09-01 Itai Dattner , Shota Gugushvili , Oleksandr Laskorunskyi

In conventional ODE modelling coefficients of an equation driving the system state forward in time are estimated. However, for many complex systems it is practically impossible to determine the equations or interactions governing the…

Machine Learning · Statistics 2018-03-13 Markus Heinonen , Cagatay Yildiz , Henrik Mannerström , Jukka Intosalmi , Harri Lähdesmäki

Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…

Machine Learning · Computer Science 2021-06-11 Sifan Wang , Paris Perdikaris

Compartmental ordinary differential equation (ODE) models are used extensively in mathematical biology. When transit between compartments occurs at a constant rate, the well-known linear chain trick can be used to show that the ODE model is…

Dynamical Systems · Mathematics 2021-09-17 Tyler Cassidy

Ordinary differential equations (ODEs) are widely used to describe dynamical systems in science, but identifying parameters that explain experimental measurements is challenging. In particular, although ODEs are differentiable and would…

Machine Learning · Computer Science 2024-07-22 Jonas Beck , Nathanael Bosch , Michael Deistler , Kyra L. Kadhim , Jakob H. Macke , Philipp Hennig , Philipp Berens

We present a new method for parameter identification of ODE system descriptions based on data measurements. Our method works by splitting the system into a number of subsystems and working on each of them separately, thereby being easily…

Computational Engineering, Finance, and Science · Computer Science 2012-08-21 Anastasis Georgoulas , Allan Clark , Andrea Ocone , Stephen Gilmore , Guido Sanguinetti

Inverse problem or parameter estimation of ordinary differential equations (ODEs), the iterative process of minimizing the mismatch between model-predicted and experimental states by tuning the parameter values within an optimization…

Systems and Control · Electrical Eng. & Systems 2026-04-21 Siddharth Prabhu , Srinivas Rangarajan , Mayuresh Kothare

We present a parameter estimation method for nonlinear mixed effect models based on ordinary differential equations (NLME-ODEs). The method presented here aims at regularizing the estimation problem in presence of model misspecifications,…

Methodology · Statistics 2021-02-24 Quentin Clairon , Chloé Pasin , Irene Balelli , Rodolphe Thiébaut , Mélanie Prague

The solution of systems of non-autonomous linear ordinary differential equations is crucial in a variety of applications, such us nuclear magnetic resonance spectroscopy. A new method with spectral accuracy has been recently introduced in…

Numerical Analysis · Mathematics 2022-10-14 Stefano Pozza , Niel Van Buggenhout

State-of-the-art methods for forecasting irregularly sampled time series with missing values predominantly rely on just four datasets and a few small toy examples for evaluation. While ordinary differential equations (ODE) are the prevalent…

In this paper we study application of Le Cam's one-step method to parameter estimation in ordinary differential equations models. This computationally simple technique can serve as an alternative to numerical evaluation of the popular…

Methodology · Statistics 2018-04-20 Itai Dattner , Shota Gugushvili

Ordinary differential equations (ODEs) are widely used to characterize the dynamics of complex systems in real applications. In this article, we propose a novel joint estimation approach for generalized sparse additive ODEs where…

Methodology · Statistics 2022-08-19 Nan Zhang , Muye Nanshan , Jiguo Cao

In this paper we propose a solution to the problem of parameter estimation of nonlinearly parameterized regressions--continuous or discrete time--and apply it for system identification and adaptive control. We restrict our attention to…

Optimization and Control · Mathematics 2019-10-18 Romeo Ortega , Vladislav Gromov , Emmanuel Nuño , Anton Pyrkin , Jose Guadalupe Romero

Definite integrals with parameters of holonomic functions satisfy holonomic systems of linear partial differential equations. When we restrict parameters to a one dimensional curve, the system becomes a linear ordinary differential equation…

Numerical Analysis · Mathematics 2026-04-10 Nobuki Takayama , Takaharu Yaguchi , Yi Zhang