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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…

Numerical Analysis · Mathematics 2021-10-04 Suyong Kim , Weiqi Ji , Sili Deng , Yingbo Ma , Christopher Rackauckas

We present the interpretable meta neural ordinary differential equation (iMODE) method to rapidly learn generalizable (i.e., not parameter-specific) dynamics from trajectories of multiple dynamical systems that vary in their physical…

Machine Learning · Computer Science 2023-09-28 Qiaofeng Li , Tianyi Wang , Vwani Roychowdhury , M. Khalid Jawed

Neural networks with physics based inductive biases such as Lagrangian neural networks (LNN), and Hamiltonian neural networks (HNN) learn the dynamics of physical systems by encoding strong inductive biases. Alternatively, Neural ODEs with…

Machine Learning · Computer Science 2024-06-18 Suresh Bishnoi , Ravinder Bhattoo , Sayan Ranu , N. M. Anoop Krishnan

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…

Dynamical Systems · Mathematics 2022-06-22 Sandor Beregi , David A. W. Barton , Djamel Rezgui , Simon A. Neild

Embedding nonlinear dynamical systems into artificial neural networks is a powerful new formalism for machine learning. By parameterizing ordinary differential equations (ODEs) as neural network layers, these Neural ODEs are…

Machine Learning · Computer Science 2024-10-28 Mikko Lehtimäki , Lassi Paunonen , Marja-Leena Linne

Ordinary differential equations (ODEs) describe dynamical systems evolving deterministically in continuous time. Accurate data-driven modeling of systems as ODEs, a central problem across the natural sciences, remains challenging,…

Machine Learning · Computer Science 2025-10-15 Maximilian Mauel , Manuel Hinz , Patrick Seifner , David Berghaus , Ramses J. Sanchez

Stochastic differential equations (SDEs) are used to describe a wide variety of complex stochastic dynamical systems. Learning the hidden physics within SDEs is crucial for unraveling fundamental understanding of these systems' stochastic…

Machine Learning · Computer Science 2022-07-26 Jared O'Leary , Joel A. Paulson , Ali Mesbah

The neural ordinary differential equation (ODE) framework has emerged as a powerful tool for developing accelerated surrogate models of complex physical systems governed by partial differential equations (PDEs). A popular approach for PDE…

Fluid Dynamics · Physics 2025-03-26 Ashish S. Nair , Shivam Barwey , Pinaki Pal , Jonathan F. MacArt , Troy Arcomano , Romit Maulik

We propose a data-driven framework for learning reduced-order moment dynamics from PDE-governed systems using Neural ODEs. In contrast to derivative-based methods like SINDy, which necessitate densely sampled data and are sensitive to…

Pattern Formation and Solitons · Physics 2025-06-06 Shaoxuan Chen , Su Yang , Panayotis G. Kevrekidis , Wei Zhu

In order to make data-driven models of physical systems interpretable and reliable, it is essential to include prior physical knowledge in the modeling framework. Hamiltonian Neural Networks (HNNs) implement Hamiltonian theory in deep…

Systems and Control · Electrical Eng. & Systems 2023-05-03 Sarvin Moradi , Nick Jaensson , Roland Tóth , Maarten Schoukens

Understanding environment dynamics is necessary for robots to act safely and optimally in the world. In realistic scenarios, dynamics are non-stationary and the causal variables such as environment parameters cannot necessarily be precisely…

Robotics · Computer Science 2022-03-11 Ben Evans , Abitha Thankaraj , Lerrel Pinto

We present a new data-driven reduced-order modeling approach to efficiently solve parametrized partial differential equations (PDEs) for many-query problems. This work is inspired by the concept of implicit neural representation (INR),…

Numerical Analysis · Mathematics 2023-11-30 Tianshu Wen , Kookjin Lee , Youngsoo Choi

Stiff systems of ordinary differential equations (ODEs) are pervasive in many science and engineering fields, yet standard neural ODE approaches struggle to learn them. This limitation is the main barrier to the widespread adoption of…

Numerical Analysis · Mathematics 2024-10-10 Colby Fronk , Linda Petzold

Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and…

Machine Learning · Computer Science 2021-11-17 Zhao Chen , Yang Liu , Hao Sun

Modeling dynamical systems is crucial across the science and engineering fields for accurate prediction, control, and decision-making. Recently, machine learning (ML) approaches, particularly neural ordinary differential equations (NODEs),…

Systems and Control · Electrical Eng. & Systems 2026-04-20 Fatima Al-Janahi , Min-Seung Ko , Hao Zhu

Data-driven modelling and scientific machine learning have been responsible for significant advances in determining suitable models to describe data. Within dynamical systems, neural ordinary differential equations (ODEs), where the system…

Machine Learning · Computer Science 2024-05-08 Gevik Grigorian , Sandip V. George , Simon Arridge

We consider learning underlying laws of dynamical systems governed by ordinary differential equations (ODE). A key challenge is how to discover intrinsic dynamics across multiple environments while circumventing environment-specific…

Machine Learning · Computer Science 2025-06-12 Shurui Gui , Xiner Li , Shuiwang Ji

State estimation is an important aspect in many robotics applications. In this work, we consider the task of obtaining accurate state estimates for robotic systems by enhancing the dynamics model used in state estimation algorithms.…

Robotics · Computer Science 2023-02-16 Kong Yao Chee , M. Ani Hsieh

When learning dynamical systems from data, embedding physical structure can constrain the solution space and improve generalization, but many physics-informed models assume access to the full system state. This limits their use in partially…

Machine Learning · Computer Science 2026-05-25 Sunniva Meltzer , Sølve Eidnes , Alexander Johannes Stasik

This work proposes an extension of neural ordinary differential equations (NODEs) by introducing an additional set of ODE input parameters to NODEs. This extension allows NODEs to learn multiple dynamics specified by the input parameter…

Computational Physics · Physics 2021-11-17 Kookjin Lee , Eric J. Parish