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Spurred by tremendous success in pattern matching and prediction tasks, researchers increasingly resort to machine learning to aid original scientific discovery. Given large amounts of observational data about a system, can we uncover the…

Machine Learning · Computer Science 2025-01-31 Hananeh Aliee , Fabian J. Theis , Niki Kilbertus

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…

Methodology · Statistics 2023-10-25 Mingwei Xu , Samuel W. K. Wong , Peijun Sang

End-to-end learning of dynamical systems with black-box models, such as neural ordinary differential equations (ODEs), provides a flexible framework for learning dynamics from data without prescribing a mathematical model for the dynamics.…

Machine Learning · Statistics 2022-06-20 Paidamoyo Chapfuwa , Sherri Rose , Lawrence Carin , Edward Meeds , Ricardo Henao

Ordinary differential equations (ODEs) are commonly used to model dynamic behavior of a system. Because many parameters are unknown and have to be estimated from the observed data, there is growing interest in statistics to develop…

Statistics Theory · Mathematics 2010-01-13 Xin Qi , Hongyu Zhao

This paper considers the problem of linear time-invariant (LTI) system identification using input/output data. Recent work has provided non-asymptotic results on partially observed LTI system identification using a single trajectory but is…

Optimization and Control · Mathematics 2021-11-23 Yang Zheng , Na Li

Reliable predictions from systems biology models require knowing whether parameters can be estimated from available data, and with what certainty. Identifiability analysis reveals whether parameters are learnable in principle (structural…

Structural identifiability is a property of an ODE model with parameters that allows for the parameters to be determined from continuous noise-free data. This is a natural prerequisite for practical identifiability. Conducting multiple…

Algebraic Geometry · Mathematics 2021-08-18 Alexey Ovchinnikov , Anand Pillay , Gleb Pogudin , Thomas Scanlon

We study the problem of estimating the coefficients in linear ordinary differential equations (ODE's) with a diverging number of variables when the solutions are observed with noise. The solution trajectories are first smoothed with local…

Statistics Theory · Mathematics 2008-04-29 Heng Lian

Ordinary differential equations (ODE) have been widely used for modeling dynamical complex systems. For high-dimensional ODE models where the number of differential equations is large, it remains challenging to estimate the ODE parameters…

Methodology · Statistics 2022-06-20 Muye Nanshan , Nan Zhang , Xiaolei Xun , Jiguo Cao

Nonlinear ordinary differential equations (ODEs) are powerful tools for modeling real-world dynamical systems. However, propagating initial state uncertainty through nonlinear dynamics, especially when the ODE is unknown and learned from…

Systems and Control · Electrical Eng. & Systems 2026-02-06 Peter Amorese , Morteza Lahijanian

For mathematical and experimental ease, models with time varying parameters are often simplified to assume constant parameters. However, this simplification can potentially lead to identifiability issues (lack of uniqueness of parameter…

Quantitative Methods · Quantitative Biology 2026-03-24 Jessica R Conrad , James M Hyman , Marisa C Eisenberg

Dynamical systems, prevalent in various scientific and engineering domains, are susceptible to anomalies that can significantly impact their performance and reliability. This paper addresses the critical challenges of anomaly detection,…

Machine Learning · Computer Science 2025-07-18 Yue Sun , Rick S. Blum , Parv Venkitasubramaniam

We describe a method for the identification of models for dynamical systems from observational data. The method is based on the concept of symbolic regression and uses genetic programming to evolve a system of ordinary differential…

Machine Learning · Computer Science 2021-07-14 Gabriel Kronberger , Lukas Kammerer , Michael Kommenda

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.…

Methodology · Statistics 2021-10-26 Xiaowu Dai , Lexin Li

Random ordinary differential equations (RODEs), i.e. ODEs with random parameters, are often used to model complex dynamics. Most existing methods to identify unknown governing RODEs from observed data often rely on strong prior knowledge.…

Numerical Analysis · Mathematics 2020-06-04 Junyu Liu , Zichao Long , Ranran Wang , Jie Sun , Bin Dong

Machines of all kinds from vehicles to industrial equipment are increasingly instrumented with hundreds of sensors. Using such data to detect anomalous behaviour is critical for safety and efficient maintenance. However, anomalies occur…

Artificial Intelligence · Computer Science 2016-05-06 Mohit Yadav , Pankaj Malhotra , Lovekesh Vig , K Sriram , Gautam Shroff

Structural identifiability is an important property of parametric ODE models. When conducting an experiment and inferring the parameter value from the time-series data, we want to know if the value is globally, locally, or non-identifiable.…

Discrete Mathematics · Computer Science 2024-06-25 Natali Gogishvili

In engineering, accurately modeling nonlinear dynamic systems from data contaminated by noise is both essential and complex. Established Sequential Monte Carlo (SMC) methods, used for the Bayesian identification of these systems, facilitate…

Machine Learning · Statistics 2024-04-25 Joe D. Longbottom , Max D. Champneys , Timothy J. Rogers

Ordinary differential equation (ODE) models are widely used to describe chemical or biological processes. This article considers the estimation and assessment of such models on the basis of time-course data. Due to experimental limitations,…

Molecular Networks · Quantitative Biology 2023-02-14 Samuel W. K. Wong , Shihao Yang , S. C. Kou

Learning models of dynamical systems with external inputs, which may be, for example, nonsmooth or piecewise, is crucial for studying complex phenomena and predicting future state evolution, which is essential for applications such as…

Machine Learning · Computer Science 2025-04-16 Zhaoyi Li , Wenjie Mei , Ke Yu , Yang Bai , Shihua Li