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Scientific machine learning is an emerging field that broadly describes the combination of scientific computing and machine learning to address challenges in science and engineering. Within the context of differential equations, this has…

Machine Learning · Computer Science 2026-04-03 Laurens R. Lueg , Victor Alves , Daniel Schicksnus , John R. Kitchin , Carl D. Laird , Lorenz T. Biegler

Neural ordinary differential equations (Neural ODEs) are an effective framework for learning dynamical systems from irregularly sampled time series data. These models provide a continuous-time latent representation of the underlying…

Machine Learning · Computer Science 2023-03-06 Edward De Brouwer , Rahul G. Krishnan

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,…

Differential equations are used to model problems that originate in disciplines such as physics, biology, chemistry, and engineering. In recent times, due to the abundance of data, there is an active search for data-driven methods to learn…

Machine Learning · Computer Science 2022-05-24 K. D. Olumoyin

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 ordinary differential equations (ODEs) are an emerging class of deep learning models for dynamical systems. They are particularly useful for learning an ODE vector field from observed trajectories (i.e., inverse problems). We here…

Machine Learning · Computer Science 2023-05-23 Katharina Ott , Michael Tiemann , Philipp Hennig

The time evolution of dynamical systems is frequently described by ordinary differential equations (ODEs), which must be solved for given initial conditions. Most standard approaches numerically integrate ODEs producing a single solution…

Machine Learning · Computer Science 2020-06-26 Cedric Flamant , Pavlos Protopapas , David Sondak

The order/dimension of models derived on the basis of data is commonly restricted by the number of observations, or in the context of monitored systems, sensing nodes. This is particularly true for structural systems (e.g., civil or…

Machine Learning · Computer Science 2022-12-01 Zhilu Lai , Wei Liu , Xudong Jian , Kiran Bacsa , Limin Sun , Eleni Chatzi

We introduce a new family of deep neural network models. Instead of specifying a discrete sequence of hidden layers, we parameterize the derivative of the hidden state using a neural network. The output of the network is computed using a…

Machine Learning · Computer Science 2019-12-17 Ricky T. Q. Chen , Yulia Rubanova , Jesse Bettencourt , David Duvenaud

Neural Ordinary Differential Equations (NODEs) have proven to be a powerful modeling tool for approximating (interpolation) and forecasting (extrapolation) irregularly sampled time series data. However, their performance degrades…

Machine Learning · Computer Science 2020-04-29 Hammad A. Ayyubi , Yi Yao , Ajay Divakaran

Neural ordinary differential equations describe how values change in time. This is the reason why they gained importance in modeling sequential data, especially when the observations are made at irregular intervals. In this paper we propose…

Machine Learning · Computer Science 2021-10-26 Marin Biloš , Johanna Sommer , Syama Sundar Rangapuram , Tim Januschowski , Stephan Günnemann

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 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

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

This paper studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs), a.k.a. (Ordinary) Difference Equations. It presents a new framework using these equations as a central tool for computation and…

Logic in Computer Science · Computer Science 2022-09-27 Olivier Bournez , Arnaud Durand

Classical neural ODEs trained with explicit methods are intrinsically limited by stability, crippling their efficiency and robustness for stiff learning problems that are common in graph learning and scientific machine learning. We present…

Machine Learning · Computer Science 2024-12-17 Hong Zhang , Ying Liu , Romit Maulik

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

The idea of neural Ordinary Differential Equations (ODE) is to approximate the derivative of a function (data model) instead of the function itself. In residual networks, instead of having a discrete sequence of hidden layers, the…

Computer Vision and Pattern Recognition · Computer Science 2022-09-20 Seyedalireza Khoshsirat , Chandra Kambhamettu

The intersection of machine learning and dynamical systems has generated considerable interest recently. Neural Ordinary Differential Equations (NODEs) represent a rich overlap between these fields. In this paper, we develop a continuous…

Optimization and Control · Mathematics 2023-06-16 Maria Oprea , Mark Walth , Robert Stephany , Gabriella Torres Nothaft , Arnaldo Rodriguez-Gonzalez , William Clark

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