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Restoring a smooth function from its noisy integrals.

Olga Goulko1, Nikolay Prokof'ev2, Boris Svistunov3

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Summary
This summary is machine-generated.

We developed a bin hierarchy method to reconstruct smooth functions from binned integral data. This approach maximizes data utilization for accurate function restoration, even with challenging datasets.

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Area of Science:

  • Computational Physics
  • Data Analysis
  • Numerical Methods

Background:

  • Scientific data analysis often involves reconstructing smooth functions from discrete, binned integral measurements.
  • Existing methods may not fully leverage all available information in the data.

Purpose of the Study:

  • To introduce an efficient method for restoring maximally smooth functions from sampled integrals.
  • To utilize all information contained within binned data for improved accuracy.

Main Methods:

  • The proposed bin hierarchy method.
  • Application to various function classes and data qualities.
  • Testing with Monte Carlo data (sign problem) and physical data (Fröhlich polaron Green's function).

Main Results:

  • The bin hierarchy method efficiently computes maximally smooth functions.
  • Successful application across diverse data types and quality levels.
  • Demonstrated effectiveness on challenging datasets like those with a sign problem.

Conclusions:

  • The bin hierarchy method is a robust and efficient technique for function restoration from binned integrals.
  • It offers significant advantages in handling noisy and complex datasets.
  • The method preserves and utilizes the maximum information from the input data.