Related papers: Estimating and Assessing Differential Equation Mod…
Parameter estimation for nonlinear dynamic system models, represented by ordinary differential equations (ODEs), using noisy and sparse data is a vital task in many fields. We propose a fast and accurate method, MAGI (MAnifold-constrained…
Identification of parameters in ordinary differential equations (ODEs) is an important and challenging task when modeling dynamic systems in biomedical research and other scientific areas, especially with the presence of time-varying…
Ordinary differential equations (ODEs), commonly used to characterize the dynamic systems, are difficult to propose in closed-form for many complicated scientific applications, even with the help of domain expert. We propose a fast and…
This article presents the MAGI software package for the inference of dynamic systems. The focus of MAGI is on dynamics modeled by nonlinear ordinary differential equations with unknown parameters. While such models are widely used in…
This work builds off the manifold-constrained Gaussian process inference (MAGI) method for Bayesian parameter inference and trajectory reconstruction of ODE-based dynamical systems, focusing primarily on sparse and noisy data conditions.…
The capture of changes in dynamic systems, especially ordinary differential equations (ODEs), is an important and challenging task, with multiple applications in biomedical research and other scientific areas. This article proposes a fast…
Pharmacokinetic modeling using ordinary differential equations (ODEs) has an important role in dose optimization studies, where dosing must balance sustained therapeutic efficacy with the risk of adverse side effects. Such ODE models…
Dynamic systems described by differential equations often involve feedback among system components. When there are time delays for components to sense and respond to feedback, delay differential equation (DDE) models are commonly used. This…
Ordinary differential equations (ODEs) are widely used to model dynamical behavior of systems. It is important to perform identifiability analysis prior to estimating unknown parameters in ODEs (a.k.a. inverse problem), because if a system…
Augmenting mechanistic ordinary differential equation (ODE) models with machine-learnable structures is an novel approach to create highly accurate, low-dimensional models of engineering systems incorporating both expert knowledge and…
Ordinary differential equation (ODE) models are widely used to describe systems in many areas of science. To ensure these models provide accurate and interpretable representations of real-world dynamics, it is often necessary to infer…
The understanding and modeling of complex physical phenomena through dynamical systems has historically driven scientific progress, as it provides the tools for predicting the behavior of different systems under diverse conditions through…
Ordinary differential equations (ODEs) are a mathematical model used in many application areas such as climatology, bioinformatics, and chemical engineering with its intuitive appeal to modeling. Despite ODE's wide usage in modeling, the…
Parameter inference in ordinary differential equations is an important problem in many applied sciences and in engineering, especially in a data-scarce setting. In this work, we introduce a novel generative modeling approach based on…
Recent advances in learning techniques have enabled the modelling of dynamical systems for scientific and engineering applications directly from data. However, in many contexts explicit data collection is expensive and learning algorithms…
Ordinary differential equations (ODE's) are widespread models in physics, chemistry and biology. In particular, this mathematical formalism is used for describing the evolution of complex systems and it might consist of high-dimensional…
Statistical models can involve implicitly defined quantities, such as solutions to nonlinear ordinary differential equations (ODEs), that unavoidably need to be numerically approximated in order to evaluate the model. The approximation…
Statistical regression models whose mean functions are represented by ordinary differential equations (ODEs) can be used to describe phenomenons dynamical in nature, which are abundant in areas such as biology, climatology and genetics. The…
Inferring the parameters of ordinary differential equations (ODEs) from noisy observations is an important problem in many scientific fields. Currently, most parameter estimation methods that bypass numerical integration tend to rely on…
Neural Ordinary Differential Equations (ODE) are a promising approach to learn dynamic models from time-series data in science and engineering applications. This work aims at learning Neural ODE for stiff systems, which are usually raised…