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Summary
This summary is machine-generated.

This study introduces a principled framework for computing derivatives from noisy data, simplifying parameter selection for better accuracy and smoothness. An open-source Python library, pynumdiff, is provided for easy application.

Keywords:
Numerical differentiationdata-driven modelingderivativesoptimization

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Area of Science:

  • Numerical analysis
  • Data processing
  • Scientific computing

Background:

  • Numerical differentiation of noisy data is crucial in science and engineering.
  • Existing methods often involve arbitrary parameter choices, leading to suboptimal results.
  • Developing dynamic models and control systems relies heavily on accurate derivative estimation.

Purpose of the Study:

  • To propose a principled multi-objective optimization framework for selecting parameters in numerical differentiation.
  • To reduce the complexity of parameter selection to a single hyper-parameter.
  • To unify and facilitate unbiased comparison of different numerical differentiation methods.

Main Methods:

  • A multi-objective optimization framework is developed to balance derivative estimate faithfulness and smoothness.
  • A heuristic is proposed for selecting the hyper-parameter based on data's power spectrum and temporal resolution when ground-truth is unknown.
  • The framework's consistency across different differentiation methods is demonstrated.

Main Results:

  • Parameter selection is simplified to choosing a single hyper-parameter.
  • A heuristic provides data-driven guidance for hyper-parameter selection.
  • The approach unifies various numerical differentiation techniques, enabling consistent and unbiased comparisons.
  • An open-source Python library, pynumdiff, is released to aid practical implementation.

Conclusions:

  • The proposed framework offers a robust and unified approach to numerical differentiation of noisy data.
  • It simplifies complex parameter tuning, improving the reliability of derivative estimates.
  • The open-source library promotes wider adoption and facilitates reproducible research in scientific computing.