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An outlier is an observation of data that does not fit the rest of the data. It is sometimes called an extreme value. When you graph an outlier, it will appear not to fit the pattern of the graph. Some outliers are due to mistakes (for example, writing down 50 instead of 500), while others may indicate that something unusual is happening. Outliers are present far from the least squares line in the vertical direction. They have large "errors," where the "error" or residual is the...
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The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
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Outlier-resistant physics-informed neural network.

D H G Duarte1,2, P D S de Lima1,3, J M de Araújo1

  • 1Universidade Federal do Rio Grande do Norte, Departamento de Física Teórica e Experimental, 59078-970 Natal-RN, Brazil.

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|March 19, 2025
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Summary
This summary is machine-generated.

We developed an outlier-resistant physics-informed neural network (OrPINN) using Tsallis statistics. This robust OrPINN improves solution accuracy for dynamics problems, even with significant data corruption from outliers.

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Area of Science:

  • Computational physics
  • Machine learning applications
  • Data science

Background:

  • Physics-informed neural networks (PINN) are advanced machine learning tools for solving dynamics problems using physical laws and data.
  • Measurement outliers can severely degrade the accuracy of PINN solutions.
  • Robustness against noisy data is crucial for reliable scientific machine learning models.

Purpose of the Study:

  • To develop a novel physics-informed neural network resistant to outliers in measurement data.
  • To enhance the accuracy and reliability of PINN solutions in the presence of corrupted data.
  • To evaluate the performance of the proposed method on wave dynamics problems.

Main Methods:

  • Construction of an outlier-resistant PINN (OrPINN) framework.
  • Integration of Tsallis statistics into the PINN loss function to down-weight outliers.
  • Testing OrPINN on acoustic and linear elastic wave propagation dynamics.
  • Systematic investigation under varying levels of data outlier corruption.

Main Results:

  • The OrPINN demonstrates significant robustness against data outliers.
  • Improved accuracy in solutions for acoustic and linear elastic wave dynamics compared to standard PINNs.
  • Effective performance maintained even with highly corrupted input datasets.
  • Validation of the Tsallis statistics approach for outlier mitigation in physics-informed learning.

Conclusions:

  • The proposed OrPINN effectively handles outliers in observational data.
  • Tsallis statistics provide a robust statistical foundation for outlier-resistant scientific machine learning.
  • OrPINN offers a reliable approach for dynamics modeling with real-world, noisy experimental data.