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Related papers: Modular Neural Ordinary Differential Equations

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Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. Here, we explore the use of Neural Ordinary Differential Equations, a recently introduced family of…

Machine Learning · Computer Science 2021-04-30 Sourav Dutta , Peter Rivera-Casillas , Matthew W. Farthing

Since the advent of the ``Neural Ordinary Differential Equation (Neural ODE)'' paper, learning ODEs with deep learning has been applied to system identification, time-series forecasting, and related areas. Exploiting the diffeomorphic…

Machine Learning · Statistics 2025-08-27 Yuji Okamoto , Tomoya Takeuchi , Yusuke Sakemi

We propose heavy ball neural ordinary differential equations (HBNODEs), leveraging the continuous limit of the classical momentum accelerated gradient descent, to improve neural ODEs (NODEs) training and inference. HBNODEs have two…

Machine Learning · Computer Science 2021-10-12 Hedi Xia , Vai Suliafu , Hangjie Ji , Tan M. Nguyen , Andrea L. Bertozzi , Stanley J. Osher , Bao Wang

Neural Ordinary Differential Equations (NODEs) use a neural network to model the instantaneous rate of change in the state of a system. However, despite their apparent suitability for dynamics-governed time-series, NODEs present a few…

Machine Learning · Computer Science 2021-08-18 Alexander Norcliffe , Cristian Bodnar , Ben Day , Jacob Moss , Pietro Liò

Learning dynamics governed by differential equations is crucial for predicting and controlling the systems in science and engineering. Neural Ordinary Differential Equation (NODE), a deep learning model integrated with differential…

Machine Learning · Computer Science 2021-11-09 Shiqi Gong , Qi Meng , Yue Wang , Lijun Wu , Wei Chen , Zhi-Ming Ma , Tie-Yan Liu

Neural Ordinary Differential Equations (ODEs) represent a significant advancement at the intersection of machine learning and dynamical systems, offering a continuous-time analog to discrete neural networks. Despite their promise, deploying…

Numerical Analysis · Mathematics 2025-06-18 Matteo Caldana , Jan S. Hesthaven

A concept of using Neural Ordinary Differential Equations(NODE) for Transfer Learning has been introduced. In this paper we use the EfficientNets to explore transfer learning on CIFAR-10 dataset. We use NODE for fine-tuning our model. Using…

Machine Learning · Computer Science 2020-01-22 Rajath S , Sumukh Aithal K , Natarajan Subramanyam

Differential equations are frequently used in engineering domains, such as modeling and control of industrial systems, where safety and performance guarantees are of paramount importance. Traditional physics-based modeling approaches…

Systems and Control · Electrical Eng. & Systems 2020-11-30 Aaron Tuor , Jan Drgona , Draguna Vrabie

Neural differential equations are a promising new member in the neural network family. They show the potential of differential equations for time series data analysis. In this paper, the strength of the ordinary differential equation (ODE)…

Machine Learning · Computer Science 2020-05-21 Mansura Habiba , Barak A. Pearlmutter

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 advancement of human healthspan and bioengineering relies heavily on predicting the behavior of complex biological systems. While high-throughput multiomics data is becoming increasingly abundant, converting this data into actionable…

Machine Learning · Computer Science 2025-12-10 Udesh Habaraduwa , Andrei Lixandru

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

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

Owing to the remarkable development of deep learning technology, there have been a series of efforts to build deep learning-based climate models. Whereas most of them utilize recurrent neural networks and/or graph neural networks, we design…

Machine Learning · Computer Science 2021-11-12 Jeehyun Hwang , Jeongwhan Choi , Hwangyong Choi , Kookjin Lee , Dongeun Lee , Noseong Park

By interpreting the forward dynamics of the latent representation of neural networks as an ordinary differential equation, Neural Ordinary Differential Equation (Neural ODE) emerged as an effective framework for modeling a system dynamics…

Machine Learning · Computer Science 2020-10-19 Daehoon Gwak , Gyuhyeon Sim , Michael Poli , Stefano Massaroli , Jaegul Choo , Edward Choi

Neural differential equations offer a powerful approach for learning dynamics from data. However, they do not impose known constraints that should be obeyed by the learned model. It is well-known that enforcing constraints in surrogate…

Neural Ordinary Differential Equations (N-ODEs) are a powerful building block for learning systems, which extend residual networks to a continuous-time dynamical system. We propose a Bayesian version of N-ODEs that enables well-calibrated…

Machine Learning · Computer Science 2020-02-19 Andreas Look , Melih Kandemir

Neural Laplace is a unified framework for learning diverse classes of differential equations (DE). For different classes of DE, this framework outperforms other approaches relying on neural networks that aim to learn classes of ordinary…

Machine Learning · Computer Science 2024-06-10 Adrien Carrel

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

Neural differential equation models have garnered significant attention in recent years for their effectiveness in machine learning applications.Among these, fractional differential equations (FDEs) have emerged as a promising tool due to…

Machine Learning · Computer Science 2025-03-21 Wenjun Cui , Qiyu Kang , Xuhao Li , Kai Zhao , Wee Peng Tay , Weihua Deng , Yidong Li