Enhancing Spectroscopic Experiment Calibration through Differentiable Programming
Abstract
:1. Introduction
2. Methods
2.1. Differentiable Programming
2.2. Toy Setup
- Use the calibration constants: From known spectroscopic lines, the calibration constants , are derived in the calibration runs. These are then applied to the subsequent physics runs, until a new calibration is performed.
- Calibrating detector data: Using and , we apply the calibration to the entire dataset. This process corrects the recorded detector ADCs for each batch, ensuring that they are accurately aligned with the true energy values of the emitted lines.
- Combining the data: Finally, we combine the calibrated data from each batch together. This results in a fully calibrated dataset where the detector signals are corrected to reflect the actual energy values of the emitted lines.
2.3. Gradient-Based Optimization
3. Results
4. Discussion
5. Conclusions
- The previous unbinned likelihood-based loss function, , which was suited to rare event searches in underground laboratories, is now replaced by a global -based loss function. This allows for a wealth of different shapes to be taken into account, and the method can be applied to a broader range of spectroscopic experiments.
- Unlike previous methods, the -based loss function allows the use of KDE as a representation of the underlying PDF, providing a fully differentiable model, which can be used in gradient-based optimization. The KDE can be trivially implemented as a binned KDE, reducing the computational overhead, and allowing the method to be used with high statistics data.
- In the case of precision measurements or characterization of spectroscopic lines, the global loss function ensures a much more contained degree of distortion of the calibration parameters, making the calibration more robust and reliable, and enabling a more accurate estimation of the associated systematic uncertainties.
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Napolitano, F. Enhancing Spectroscopic Experiment Calibration through Differentiable Programming. Condens. Matter 2024, 9, 26. https://doi.org/10.3390/condmat9020026
Napolitano F. Enhancing Spectroscopic Experiment Calibration through Differentiable Programming. Condensed Matter. 2024; 9(2):26. https://doi.org/10.3390/condmat9020026
Chicago/Turabian StyleNapolitano, Fabrizio. 2024. "Enhancing Spectroscopic Experiment Calibration through Differentiable Programming" Condensed Matter 9, no. 2: 26. https://doi.org/10.3390/condmat9020026