Outlier-resistant physics-informed neural network

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.