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Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

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Published on: October 28, 2022

Automated partial differential equation identification.

Ruixian Liu¹, Michael J Bianco², Peter Gerstoft²

¹Department of Electrical and Computer Engineering, University of California, San Diego, California 92161, USA.

The Journal of the Acoustical Society of America

|October 31, 2021

Summary

This summary is machine-generated.

This study introduces a novel method for automatically identifying partial differential equations (PDEs) from data using sparse modeling. The technique requires no prior assumptions about the governing physical phenomena, enabling accurate PDE estimation from complex datasets.

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A Modeling and Simulation Method for Preliminary Design of an Electro-Variable Displacement Pump

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Published on: June 1, 2022

Area of Science:

Applied Mathematics
Data Science
Scientific Computing

Background:

Data-driven methods are increasingly vital for scientific discovery.
Estimating partial differential equations (PDEs) from observational data is a key challenge.
Existing PDE identification methods often require prior knowledge of potential terms.

Purpose of the Study:

To develop an automated, data-driven approach for PDE estimation.
To leverage sparse modeling for parsimonious representation of physical laws.
To identify PDEs without pre-supposing the relevant physical terms.

Main Methods:

Constructing a comprehensive dictionary of potential PDE terms via numerical differentiation.
Employing sparse modeling with sparsity constraints to select relevant terms from the dictionary.
Applying the method to both synthetic and real-world video data.

Main Results:

Successfully identified PDEs governing wave, Burgers, and Helmholtz equations from data.
Demonstrated robustness on diverse datasets, including real video recordings.
The automated approach requires no a priori assumptions about the PDE structure.

Conclusions:

Sparse modeling offers a powerful, automated framework for PDE discovery from data.
This method advances the field of scientific machine learning and automated scientific discovery.
The open-source code facilitates broader adoption and further research in PDE identification.