arXiv Machine Learning July 17, 2026 By Xuyang Li, John Harlim, Dibyajyoti Chakraborty, Romit Maulik

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

Read the original on arXiv Machine Learning →

arXiv:2511. 06609v4 Announce Type: replace Abstract: The accurate forecasting of complex, high-dimensional dynamical systems from observational data is a fundamental task across numerous scientific and engineering disciplines.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

benchmarks

arXiv AI

Aug 18

PhyxMamba: Chaotic System Reconstruction from Short Context Observations with Generative State-Space Models

arXiv:2505. 23863v3 Announce Type: replace-cross Abstract: Understanding chaotic dynamics is a fundamental problem across scientific disciplines, including climate science, neuroscience, and fluid dynamics, yet direct experimentation and intervention in such systems are often infeasible.

By Chang Liu, Bohao Zhao, Jingtao Ding, Huandong Wang, Yong Li

rag

arXiv Statistics ML

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Symbolic Neural ODEs: Learning interpretable models from time-series data

arXiv:2608.22112v1 Announce Type: cross Abstract: We present a machine learning framework for identifying sparse, interpretable models of dynamical systems directly from time-series data. Our approac...

By Nibodh Boddupalli, Jeff Moehlis

efficiency

arXiv Machine Learning

Jul 2

Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression

arXiv:2607. 00257v1 Announce Type: new Abstract: Accurate prediction of complex dynamical systems from noisy measurements remains a significant challenge in scientific computing.

By Max Kreider, John Harlim, Daning Huang

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arXiv Machine Learning

Jun 19

Learning to Emulate Chaos: Adversarial Optimal Transport Regularization

arXiv:2604. 21097v2 Announce Type: replace-cross Abstract: Chaos arises in many complex dynamical systems, from weather to power grids, but is difficult to accurately model with data-driven methods such as machine learning emulators.

By Gabriel Melo, Leonardo Santiago, Peter Y. Lu

safety

arXiv AI

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A neural operator framework for data-driven discovery of stability and receptivity in physical systems

arXiv:2604. 19465v3 Announce Type: replace-cross Abstract: Understanding how complex systems respond to perturbations, such as whether they will remain stable or what their most sensitive patterns are, is a fundamental challenge across science and engineering.

By Chengyun Wang, Liwei Chen, Nils Thuerey

arXiv AI

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Adaptive Nonlinear Vector Autoregression: Robust Forecasting for Noisy Chaotic Time Series

The paper introduces a data‑adaptive nonlinear vector autoregression (NVAR) model that replaces fixed polynomial or random feature maps with a shallow, trainable multilayer perceptron (MLP). By jointly training the MLP and a linear readout via gradient‑based optimization, the model learns data‑driven nonlinearities while maintaining a simple readout structure, improving scalability in high‑dimensional settings. Experiments on several chaotic systems, both noise‑free and synthetically noisy, show that this adaptive NVAR outperforms standard NVAR, a leaky echo state network (ESN), and a hybrid ESN in predictive accuracy, demonstrating robust forecasting under noisy conditions.

By Sherkhon Azimov, Susana Lopez-Moreno, Eric Dolores-Cuenca, Sieun Lee, Jae-Il Kwon, Sangil Kim

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