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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 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

Deep neural networks can be fragile and sensitive to small input perturbations that might cause a significant change in the output. In this paper, we employ contraction theory to improve the robustness of neural ODEs (NODEs). A dynamical…

Machine Learning · Computer Science 2022-07-12 Muhammad Zakwan , Liang Xu , Giancarlo Ferrari-Trecate

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

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

Deep neural networks are capable of training fast and generalizing well within many domains. Despite their promising performance, deep networks have shown sensitivities to perturbations of their inputs (e.g., adversarial examples) and their…

Machine Learning · Computer Science 2020-07-09 Justin Goodwin , Olivia Brown , Victoria Helus

In this work, we investigate a method for simulation-free training of Neural Ordinary Differential Equations (NODEs) for learning deterministic mappings between paired data. Despite the analogy of NODEs as continuous-depth residual…

Machine Learning · Computer Science 2024-10-31 Semin Kim , Jaehoon Yoo , Jinwoo Kim , Yeonwoo Cha , Saehoon Kim , Seunghoon Hong

Recent works show that Graph Neural Networks (GNNs) are highly non-robust with respect to adversarial attacks on both the graph structure and the node attributes, making their outcomes unreliable. We propose the first method for certifiable…

Machine Learning · Computer Science 2019-07-01 Daniel Zügner , Stephan Günnemann

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

Deep Learning has emerged as one of the most significant innovations in machine learning. However, a notable limitation of this field lies in the ``black box" decision-making processes, which have led to skepticism within groups like…

Machine Learning · Computer Science 2025-03-06 Shi Li

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

Irregular sampling intervals and missing values in real-world time series data present challenges for conventional methods that assume consistent intervals and complete data. Neural Ordinary Differential Equations (Neural ODEs) offer an…

Machine Learning · Computer Science 2025-01-28 YongKyung Oh , Dong-Young Lim , Sungil Kim

Adversarial examples pose a security threat to many critical systems built on neural networks (such as face recognition systems, and self-driving cars). While many methods have been proposed to build robust models, how to build certifiably…

Machine Learning · Computer Science 2023-09-06 Ruihan Zhang , Peixin Zhang , Jun Sun

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

Implicit neural networks are a general class of learning models that replace the layers in traditional feedforward models with implicit algebraic equations. Compared to traditional learning models, implicit networks offer competitive…

Machine Learning · Computer Science 2021-12-13 Saber Jafarpour , Matthew Abate , Alexander Davydov , Francesco Bullo , Samuel Coogan

Real-world systems are often formulated as constrained optimization problems. Techniques to incorporate constraints into Neural Networks (NN), such as Neural Ordinary Differential Equations (Neural ODEs), have been used. However, these…

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

We propose Characteristic-Neural Ordinary Differential Equations (C-NODEs), a framework for extending Neural Ordinary Differential Equations (NODEs) beyond ODEs. While NODEs model the evolution of a latent variables as the solution to an…

Machine Learning · Computer Science 2022-11-10 Xingzi Xu , Ali Hasan , Khalil Elkhalil , Jie Ding , Vahid Tarokh

Neural ordinary differential equations (NODEs) presented a new paradigm to construct (continuous-time) neural networks. While showing several good characteristics in terms of the number of parameters and the flexibility in constructing…

Machine Learning · Computer Science 2021-06-01 Sheo Yon Jhin , Minju Jo , Taeyong Kong , Jinsung Jeon , Noseong Park

Neural Ordinary Differential Equations (NODEs), a framework of continuous-depth neural networks, have been widely applied, showing exceptional efficacy in coping with some representative datasets. Recently, an augmented framework has been…

Machine Learning · Computer Science 2021-02-23 Qunxi Zhu , Yao Guo , Wei Lin

Operator learning has emerged as a promising paradigm for developing efficient surrogate models to solve partial differential equations (PDEs). However, existing approaches often overlook the domain knowledge inherent in the underlying PDEs…

Machine Learning · Computer Science 2025-10-20 Ziqian Li , Kang Liu , Yongcun Song , Hangrui Yue , Enrique Zuazua