Neural ODEs

ODE: Ordinary Differential Equation

Follow this topic Ask about this topic

Momentum

3 papers in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

Jul 13Week of Sep 28

Latest papers 67

All topics

A Weak Penalty Neural ODE for Learning Chaotic Dynamics from Noisy Time Series
Nov 10, 2025Xuyang Li, John Harlim, Dibyajyoti Chakraborty +1Nonlinear System Identification Neural ODEs
aSchool of Construction, University of North Carolina at Charlotte, Charlotte, 28223, NC, USA · cDepartment of Mathematics, Institute for Computational and Data Sciences, The Pennsylvania State University, University Park, 16802, PA, USA · bCollege of Information Sciences and Technology, The Pennsylvania State University, University Park, 16802, PA, USA +1
Deep Neural Networks Inspired by Differential Equations
Oct 9, 2025Yongshuai Liu, Lianfang Wang, Kuilin Qin +6Neural Network Generalization Dynamic Neural Networks
School of Mathematical Sciences, Beijing Normal University, Beijing, China · Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong
TANDEM: Temporal Attention-guided Neural Differential Equations for Missingness in Time Series Classification
Aug 24, 2025YongKyung Oh, Dong-Young Lim, Sungil Kim +1Time Series Classification Neural ODEs
University of California, Los Angeles, Los Angeles, CA, USA · Ulsan National Institute of Science and Technology, Ulsan, Republic of Korea
Projected Neural Differential Equations for Learning Constrained Dynamics
Oct 31, 2024Alistair White, Anna Büttner, Maximilian Gelbrecht +4Dynamical Systems Neural ODEs
Munich Climate Center and Earth System Modelling Group, Department of Aerospace and Geodesy, School of Engineering and Design, Technical University of Munich, Munich, Germany · Potsdam Institute for Climate Impact Research, Potsdam, Germany · California Institute of Technology, Pasadena, California, USA +4
Certified Robust Invariant Polytope Training in Neural Controlled ODEs
Aug 2, 2024Akash Harapanahalli, Samuel CooganNeural Controlled Differential Equations Robust Control
School of Electrical and Computer Engineering, Georgia Institute of Technology
DualDynamics: Synergizing Implicit and Explicit Methods for Robust Irregular Time Series Analysis
Jan 10, 2024YongKyung Oh, Dong-Young Lim, Sungil KimIrregular Time-Series Modeling Time Series Imputation
Medical & Imaging Informatics (MII) Group, University of California, Los Angeles (UCLA), CA, USA · Department of Industrial Engineering, Ulsan National Institute of Science and Technology (UNIST), Republic of Korea · Artificial Intelligence Graduate School, Ulsan National Institute of Science and Technology (UNIST), Republic of Korea
Autonomous-Flow-Based Generation
Date pendingHossein Rouhvarzi, Anastasis KratsiosUniversal Approximation Continuous Normalizing Flows
McMaster University and the Vector Institute Department of Mathematics 1280 Main Street West, Hamilton, Ontario, L8S 4K1, Canada

Nov 10, 2025, cs.LGJ/K move · Enter open · S save

A Weak Penalty Neural ODE for Learning Chaotic Dynamics from Noisy Time Series

Xuyang Li, John Harlim, Dibyajyoti Chakraborty, Romit Maulik

aSchool of Construction, University of North Carolina at Charlotte, Charlotte, 28223, NC, USA · cDepartment of Mathematics, Institute for Computational and Data Sciences, The Pennsylvania State University, University Park, 16802, PA, USA · bCollege of Information Sciences and Technology, The Pennsylvania State University, University Park, 16802, PA, USA+1

Nonlinear System Identification Neural ODEs Chaotic Time-Series Prediction

Open paper AskPDF arXiv

The accurate forecasting of complex, high-dimensional dynamical systems from observational data is a fundamental task across numerous scientific and engineering disciplines. A significant challenge arises from noise-corrupted measurements, which severely degrade the performance of data-driven models. In chaotic dynamical systems, where small initial errors amplify exponentially, it is particularly difficult to develop a model from noisy data that achieves short-term accuracy while preserving long-term invariant properties. To overcome this, we consider the weak formulation as a complementary approach to the classical

L2

-loss function for training models of dynamical systems. We empirically verify that the weak formulation, with a proper choice of test function and integration domain, effectively filters noisy data. This insight explains why a weak form loss function is analogous to fitting a model to filtered data and provides a practical way to parameterize the weak form. Subsequently, we demonstrate how this approach overcomes the instability and inaccuracy of standard Neural ODE (NODE) in modeling chaotic systems. Through numerical examples, we show that our proposed training strategy, the Weak Penalty NODE, is computationally efficient, solver-agnostic, and yields accurate and robust forecasts across benchmark chaotic systems and a real-world climate dataset.

Momentum

Related topics

Latest papers 67