Computational optimal transport for molecular spectra: The fully discrete case

Area of Science:

• Computational chemistry
• Spectroscopy
• Data analysis

Background:

• Molecular spectra analysis is crucial for identifying and characterizing chemical compounds.
• Traditional spectral comparison methods, like Euclidean distances, often rely on line-by-line matching and can be sensitive to spectral resolution.
• A need exists for robust methods that capture broader spectral features and handle variations in resolution.

Purpose of the Study:

• To investigate the application of computational optimal transport (OT) for comparing molecular spectra.
• To demonstrate that OT distances offer a superior alternative to Euclidean distances for spectral comparison.
• To provide a tutorial and illustrative examples of OT in molecular spectroscopy.

Main Methods:

• Optimal transport theory is applied to quantify the 'distance' between two molecular spectra.
• Spectra are treated as distributions of intensity over spectral features (e.g., line positions).
• Transport distances are computed, considering both the positions and intensities of spectral lines.

Main Results:

• Optimal transport distances effectively encode information from both spectral line positions and intensities simultaneously.
• Transport distances provide a more holistic comparison of spectra compared to line-by-line Euclidean distances.
• The method demonstrates robustness in comparing molecular spectra with different resolutions.

Conclusions:

• Computational optimal transport is a powerful and versatile tool for molecular spectral comparison.
• OT offers advantages over traditional methods, particularly for complex spectra or those with resolution differences.
• This approach enhances pattern recognition and data analysis in molecular spectroscopy.