• Corpus ID: 235829771

# Error Processing of Sparse Identification of Nonlinear Dynamical Systems via $L_\infty$ Approximation

@inproceedings{Wu2021ErrorPO,
title={Error Processing of Sparse Identification of Nonlinear Dynamical Systems via \$L\_\infty\$ Approximation},
author={Yuqiang Wu},
year={2021}
}
• Yuqiang Wu
• Published 12 July 2021
• Engineering, Computer Science, Physics
Sparse identification of nonlinear dynamical systems(SINDy) is a recently presented framework in the reverse engineering field. It soon gains general interests due to its interpretability and efficiency. Error processing, as an important issue in the SINDy framework, yet remains to be an open problem. To date, literature about error processing focuses on data processing methods which aim to improve the accuracy of data. However, the relationship between data and the identification framework is…

## References

SHOWING 1-10 OF 21 REFERENCES
Sparse identification of nonlinear dynamics for rapid model recovery.
• Computer Science, Medicine
Chaos
• 2018
The proposed abrupt-SINDy architecture provides a new paradigm for the rapid and efficient recovery of a system model after abrupt changes, and shows that sparse updates to a previously identified model perform better with less data, have lower runtime complexity, and are less sensitive to noise than identifying an entirely new model.
Automatic Differentiation to Simultaneously Identify Nonlinear Dynamics and Extract Noise Probability Distributions from Data
• Computer Science, Engineering
ArXiv
• 2020
A variant of the SINDy algorithm that integrates automatic differentiation and recent time-stepping constrained motivated by Rudy et al. is developed, resulting in an architecture that is approximately twice as robust to noise as state-of-the-art methods.
Sparse learning of stochastic dynamical equations.
• Computer Science, Mathematics
The Journal of chemical physics
• 2018
It is proved the asymptotic correctness of stochastic SINDy in the infinite data limit, both in the original and projected variables.
Numerical Differentiation of Noisy Data: A Unifying Multi-Objective Optimization Framework
• Mathematics, Computer Science
IEEE Access
• 2020
This work takes a principled approach and proposes a multi-objective optimization framework for choosing parameters that minimize a loss function to balance the faithfulness and smoothness of the derivative estimate.
Discovering governing equations from data by sparse identification of nonlinear dynamical systems
• Mathematics, Medicine
Proceedings of the National Academy of Sciences
• 2016
This work develops a novel framework to discover governing equations underlying a dynamical system simply from data measurements, leveraging advances in sparsity techniques and machine learning and using sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data.
Automated reverse engineering of nonlinear dynamical systems
• Computer Science, Medicine
Proceedings of the National Academy of Sciences
• 2007
This work introduces for the first time a method that can automatically generate symbolic equations for a nonlinear coupled dynamical system directly from time series data, applicable to any system that can be described using sets of ordinary nonlinear differential equations.
Statistical Learning with Sparsity: The Lasso and Generalizations
• Computer Science
• 2015
Statistical Learning with Sparsity: The Lasso and Generalizations presents methods that exploit sparsity to help recover the underlying signal in a set of data and extract useful and reproducible patterns from big datasets.
Sparse identification of a predator-prey system from simulation data of a convection model
• Physics
• 2017
The use of low-dimensional dynamical systems as reduced models for plasma dynamics is useful as solving an initial value problem requires much less computational resources than fluid simulations. We
Deep learning in fluid dynamics
• J. Kutz
• Computer Science
Journal of Fluid Mechanics
• 2017
Although neural networks have been applied previously to complex fluid flows, the article featured here is the first to apply a true DNN architecture, specifically to Reynolds averaged Navier Stokes turbulence models, suggesting that DNNs may play a critically enabling role in the future of modelling complex flows.
Reverse Engineering Cellular Networks with Information Theoretic Methods
• Computer Science, Medicine
Cells
• 2013
This work attempts to review some of the existing information theoretic methodologies for network inference, and clarify their differences.