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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

Neural ordinary differential equations (NODE) have been proposed as a continuous depth generalization to popular deep learning models such as Residual networks (ResNets). They provide parameter efficiency and automate the model selection…

Machine Learning · Computer Science 2021-12-24 Srinivas Anumasa , P. K. Srijith

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

Stochastic differential equations (SDEs) are established tools to model physical phenomena whose dynamics are affected by random noise. By estimating parameters of an SDE intrinsic randomness of a system around its drift can be identified…

Computation · Statistics 2012-05-03 Umberto Picchini , Susanne Ditlevsen

It is critical yet challenging for deep learning models to properly characterize uncertainty that is pervasive in real-world environments. Although a lot of efforts have been made, such as heteroscedastic neural networks (HNNs), little work…

Machine Learning · Computer Science 2021-03-30 Peng Cui , Zhijie Deng , Wenbo Hu , Jun Zhu

This study examines the challenges of modeling complex and noisy data related to socioeconomic factors over time, with a focus on data from various districts in Odisha, India. Traditional time-series models struggle to capture both trends…

Machine Learning · Computer Science 2026-04-02 Sandeep Kumar Samota , Reema Gupta , Snehashish Chakraverty

Recent years have witnessed significant progress in developing effective training and fast sampling techniques for diffusion models. A remarkable advancement is the use of stochastic differential equations (SDEs) and their…

Computer Vision and Pattern Recognition · Computer Science 2024-08-26 Defang Chen , Zhenyu Zhou , Jian-Ping Mei , Chunhua Shen , Chun Chen , Can Wang

Many successful methods to learn dynamical systems from data have recently been introduced. However, ensuring that the inferred dynamics preserve known constraints, such as conservation laws or restrictions on the allowed system states,…

Machine Learning · Computer Science 2024-02-16 Alistair White , Niki Kilbertus , Maximilian Gelbrecht , Niklas Boers

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

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

Neural ordinary differential equations (NODE) have been recently proposed as a promising approach for nonlinear system identification tasks. In this work, we systematically compare their predictive performance with current state-of-the-art…

Machine Learning · Computer Science 2022-03-16 Aowabin Rahman , Ján Drgoňa , Aaron Tuor , Jan Strube

Time series with non-uniform intervals occur in many applications, and are difficult to model using standard recurrent neural networks (RNNs). We generalize RNNs to have continuous-time hidden dynamics defined by ordinary differential…

Machine Learning · Computer Science 2019-07-10 Yulia Rubanova , Ricky T. Q. Chen , David Duvenaud

Probabilistic solvers for ordinary differential equations (ODEs) provide efficient quantification of numerical uncertainty associated with simulation of dynamical systems. Their convergence rates have been established by a growing body of…

Machine Learning · Statistics 2020-12-21 Nicholas Krämer , Philipp Hennig

Neural Stochastic Differential Equations (NSDE) have been trained as both Variational Autoencoders, and as GANs. However, the resulting Stochastic Differential Equations can be hard to interpret or analyse due to the generic nature of the…

Machine Learning · Computer Science 2022-11-18 Simon M. Koop , Mark A. Peletier , Jacobus W. Portegies , Vlado Menkovski

Neural Stochastic Differential Equations (NSDEs) model the drift and diffusion functions of a stochastic process as neural networks. While NSDEs are known to make accurate predictions, their uncertainty quantification properties have been…

Machine Learning · Computer Science 2022-09-13 Andreas Look , Melih Kandemir , Barbara Rakitsch , Jan Peters

Neural ordinary differential equations (NODE) have been proposed as a continuous depth generalization to popular deep learning models such as Residual networks (ResNets). They provide parameter efficiency and automate the model selection…

Machine Learning · Computer Science 2021-12-24 Srinivas Anumasa , P. K. Srijith

Neural ordinary differential equations (ODEs) have attracted much attention as continuous-time counterparts of deep residual neural networks (NNs), and numerous extensions for recurrent NNs have been proposed. Since the 1980s, ODEs have…

Machine Learning · Computer Science 2022-10-17 Kazuki Irie , Francesco Faccio , Jürgen Schmidhuber

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

Discovering the underlying relationships among variables from temporal observations has been a longstanding challenge in numerous scientific disciplines, including biology, finance, and climate science. The dynamics of such systems are…

Machine Learning · Computer Science 2024-05-07 Benjie Wang , Joel Jennings , Wenbo Gong

Neural Ordinary Differential Equations (NODEs) are a novel neural architecture, built around initial value problems with learned dynamics which are solved during inference. Thought to be inherently more robust against adversarial…

Machine Learning · Computer Science 2023-03-10 Mustafa Zeqiri , Mark Niklas Müller , Marc Fischer , Martin Vechev