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Due the complexity of modern power systems, modeling based on first-order principles becomes increasingly difficult. As an alternative, dynamical models for simulation and control design can be obtained by black-box identification…

Systems and Control · Electrical Eng. & Systems 2025-12-09 Hannes M. H. Wolf , Christian A. Hans

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

Neural ODEs (NODEs) have emerged as powerful tools for modeling time series data, offering the flexibility to adapt to varying input scales and capture complex dynamics. However, they face significant challenges: first, their reliance on…

Machine Learning · Computer Science 2025-10-07 Muhao Guo , Yang Weng

System identification through learning approaches is emerging as a promising strategy for understanding and simulating dynamical systems, which nevertheless faces considerable difficulty when confronted with power systems modeled by…

Systems and Control · Electrical Eng. & Systems 2023-12-14 Wenjie Mei , Muhammad Nadeem , MirSaleh Bahavarnia , Ahmad F. Taha

Modeling complex systems using standard neural ordinary differential equations (NODEs) often faces some essential challenges, including high computational costs and susceptibility to local optima. To address these challenges, we propose a…

Machine Learning · Computer Science 2024-05-24 Xin Li , Jingdong Zhang , Qunxi Zhu , Chengli Zhao , Xue Zhang , Xiaojun Duan , Wei Lin

We present a novel approach (DyNODE) that captures the underlying dynamics of a system by incorporating control in a neural ordinary differential equation framework. We conduct a systematic evaluation and comparison of our method and…

Machine Learning · Computer Science 2020-09-10 Victor M. Martinez Alvarez , Rareş Roşca , Cristian G. Fălcuţescu

The neural Ordinary Differential Equation (ODE) model has shown success in learning complex continuous-time processes from observations on discrete time stamps. In this work, we consider the modeling and forecasting of time series data that…

Machine Learning · Statistics 2023-06-05 Yixuan Tan , Liyan Xie , Xiuyuan Cheng

Measurement noise is an integral part while collecting data of a physical process. Thus, noise removal is necessary to draw conclusions from these data, and it often becomes essential to construct dynamical models using these data. We…

Machine Learning · Computer Science 2022-05-20 Pawan Goyal , Peter Benner

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

Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to…

Machine Learning · Computer Science 2025-02-11 Elisa Negrini , Yuxuan Liu , Liu Yang , Stanley J. Osher , Hayden Schaeffer

Neural Ordinary Differential Equations (ODEs) are elegant reinterpretations of deep networks where continuous time can replace the discrete notion of depth, ODE solvers perform forward propagation, and the adjoint method enables efficient,…

Identifying dynamical systems from experimental data is a notably difficult task. Prior knowledge generally helps, but the extent of this knowledge varies with the application, and customized models are often needed. Neural ordinary…

Systems and Control · Electrical Eng. & Systems 2023-01-13 Mona Buisson-Fenet , Valery Morgenthaler , Sebastian Trimpe , Florent Di Meglio

To better understand and improve the behavior of neural networks, a recent line of works bridged the connection between ordinary differential equations (ODEs) and deep neural networks (DNNs). The connections are made in two folds: (1) View…

Machine Learning · Computer Science 2019-11-05 Xinshi Chen

Neural networks have been identified as powerful tools for the study of complex systems. A noteworthy example is the neural network differential equation (NN DE) solver, which can provide functional approximations to the solutions of a wide…

Machine Learning · Computer Science 2021-01-29 Akshunna S. Dogra , William T Redman

Neural ordinary differential equations (Neural ODEs) propose the idea that a sequence of layers in a neural network is just a discretisation of an ODE, and thus can instead be directly modelled by a parameterised ODE. This idea has had…

Machine Learning · Computer Science 2024-05-07 Christina Runkel , Ander Biguri , Carola-Bibiane Schönlieb

Neural ordinary differential equations (NODE) have garnered significant attention for their design of continuous-depth neural networks and the ability to learn data/feature dynamics. However, for high-dimensional systems, estimating…

Machine Learning · Computer Science 2025-10-07 Muhao Guo , Haoran Li , Yang Weng

Recent works on optical flow estimation use neural networks to predict the flow field that maps positions of one image to positions of the other. These networks consist of a feature extractor, a correlation volume, and finally several…

Computer Vision and Pattern Recognition · Computer Science 2025-06-05 Leyla Mirvakhabova , Hong Cai , Jisoo Jeong , Hanno Ackermann , Farhad Zanjani , Fatih Porikli

Many physical processes such as weather phenomena or fluid mechanics are governed by partial differential equations (PDEs). Modelling such dynamical systems using Neural Networks is an active research field. However, current methods are…

Machine Learning · Computer Science 2022-10-12 Andrzej Dulny , Andreas Hotho , Anna Krause

The existing Neural ODE formulation relies on an explicit knowledge of the termination time. We extend Neural ODEs to implicitly defined termination criteria modeled by neural event functions, which can be chained together and…

Machine Learning · Computer Science 2021-10-28 Ricky T. Q. Chen , Brandon Amos , Maximilian Nickel

Neural ordinary differential equations (NODEs), one of the most influential works of the differential equation-based deep learning, are to continuously generalize residual networks and opened a new field. They are currently utilized for…

Machine Learning · Computer Science 2023-12-19 Woojin Cho , Seunghyeon Cho , Hyundong Jin , Jinsung Jeon , Kookjin Lee , Sanghyun Hong , Dongeun Lee , Jonghyun Choi , Noseong Park