Correcting systematic errors by hybrid 2D correlation loss functions in nonlinear inverse modelling.

Area of Science:

• Data analysis
• Statistical modeling
• Machine learning

Background:

• Smart error sums are a new class of loss functions designed to handle correlations in experimental data.
• These functions are based on 2D correlation analysis, a technique widely used in spectroscopic data analysis.
• Current applications primarily focus on spectroscopic modeling, with potential for broader use.

Purpose of the Study:

• To mathematically generalize and simplify the methodology of smart error sums and 2D correlation analysis.
• To explore the mathematical foundations of these techniques.
• To establish a general tool applicable beyond spectroscopic modeling and discuss its potential in deep learning.

Main Methods:

• Mathematical generalization and breakdown of 2D correlation analysis and smart error sums.
• Analysis of the underlying mathematical principles.
• Development of a generalized framework for error correction and data modeling.

Main Results:

• A simplified and generalized mathematical framework for smart error sums and 2D correlation analysis.
• Demonstration of the method's ability to reveal and correct multiplicative systematic errors.
• Identification of potential applications in deep learning as a sophisticated loss function.

Conclusions:

• The generalized smart error sums offer a versatile tool for analyzing experimental data and improving model accuracy.
• The method's mathematical roots are clarified, enabling wider adoption and further development.
• Future prospects include sophisticated loss functions for deep learning models, enhancing their ability to handle systematic errors.