English
Related papers

Related papers: Neural ODE Processes

200 papers

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

Stochastic differential equations (SDEs) have been widely used to model real world random phenomena. Existing works mainly focus on the case where the time series is modeled by a single SDE, which might be restrictive for modeling time…

Machine Learning · Computer Science 2024-01-23 Zhongchang Sun , Yousef El-Laham , Svitlana Vyetrenko

Control problems frequently arise in scientific and industrial applications, where the objective is to steer a dynamical system from an initial state to a desired target state. Recent advances in deep learning and automatic differentiation…

Systems and Control · Electrical Eng. & Systems 2026-01-09 Lucas Böttcher

Modeling sequential patterns from data is at the core of various time series forecasting tasks. Deep learning models have greatly outperformed many traditional models, but these black-box models generally lack explainability in prediction…

Machine Learning · Computer Science 2023-05-23 Yingtao Luo , Chang Xu , Yang Liu , Weiqing Liu , Shun Zheng , Jiang Bian

Ordinary Differential Equations (ODE) based models have become popular as foundation models for solving many time series problems. Combining neural ODEs with traditional RNN models has provided the best representation for irregular time…

Machine Learning · Computer Science 2024-08-06 Futoon M. Abushaqra , Hao Xue , Yongli Ren , Flora D. Salim

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

Recent research in deep learning has shown that neural networks can learn differential equations governing dynamical systems. In this paper, we adapt this concept to Virtual Analog (VA) modeling to learn the ordinary differential equations…

Audio and Speech Processing · Electrical Eng. & Systems 2022-08-09 Jan Wilczek , Alec Wright , Vesa Välimäki , Emanuël Habets

In this work, we study the feasibility of using neural ordinary differential equations (NODEs) to model systems with intrinsic privacy properties. Unlike conventional feedforward neural networks, which have unlimited expressivity and can…

Cryptography and Security · Computer Science 2025-06-24 Sanghyun Hong , Fan Wu , Anthony Gruber , Kookjin Lee

Neural CDEs provide a natural way to process the temporal evolution of irregular time series. The number of function evaluations (NFE) is these systems' natural analog of depth (the number of layers in traditional neural networks). It is…

Machine Learning · Computer Science 2026-01-27 Ilya Kuleshov , Evgenia Romanenkova , Vladislav Zhuzhel , Galina Boeva , Evgeni Vorsin , Alexey Zaytsev

Despite their elegant formulation and lightweight memory cost, neural ordinary differential equations (NODEs) suffer from known representational limitations. In particular, the single flow learned by NODEs cannot express all homeomorphisms…

Machine Learning · Computer Science 2021-04-16 Mathieu Chalvidal , Matthew Ricci , Rufin VanRullen , Thomas Serre

Stochastic differential equations (SDEs) are well suited to modelling noisy and irregularly sampled time series found in finance, physics, and machine learning. Traditional approaches require costly numerical solvers to sample between…

Machine Learning · Computer Science 2025-10-30 Naoki Kiyohara , Edward Johns , Yingzhen Li

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

This work introduces Neural Chronos Ordinary Differential Equations (Neural CODE), a deep neural network architecture that fits a continuous-time ODE dynamics for predicting the chronology of a system both forward and backward in time. To…

Machine Learning · Computer Science 2025-03-27 C. Coelho , M. Fernanda P. Costa , L. L. Ferrás

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

This short, self-contained article seeks to introduce and survey continuous-time deep learning approaches that are based on neural ordinary differential equations (neural ODEs). It primarily targets readers familiar with ordinary and…

Machine Learning · Computer Science 2024-01-09 Lars Ruthotto

Optimal control problems naturally arise in many scientific applications where one wishes to steer a dynamical system from a certain initial state $\mathbf{x}_0$ to a desired target state $\mathbf{x}^*$ in finite time $T$. Recent advances…

Machine Learning · Computer Science 2022-09-20 Lucas Böttcher , Thomas Asikis

A neural network (NN) is a parameterised function that can be tuned via gradient descent to approximate a labelled collection of data with high precision. A Gaussian process (GP), on the other hand, is a probabilistic model that defines a…

Machine Learning · Computer Science 2018-07-05 Marta Garnelo , Jonathan Schwarz , Dan Rosenbaum , Fabio Viola , Danilo J. Rezende , S. M. Ali Eslami , Yee Whye Teh

Neural ordinary differential equations (NODEs) have been proven useful for learning non-linear dynamics of arbitrary trajectories. However, current NODE methods capture variations across trajectories only via the initial state value or by…

Machine Learning · Computer Science 2023-11-14 Ilze Amanda Auzina , Çağatay Yıldız , Sara Magliacane , Matthias Bethge , Efstratios Gavves

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

We explore how neural differential equations (NDEs) may be trained on highly resolved fluid-dynamical models of unresolved scales providing an ideal framework for data-driven parameterizations in climate models. NDEs overcome some of the…