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Partial differential equations in data science.

Andrea L Bertozzi1, Nadejda Drenska2, Jonas Latz3

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Artificial intelligence and machine learning advance science but pose challenges. Partial differential equations offer novel solutions in data science, enhancing machine learning models and analyzing complex processes.

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Area of Science:

  • Mathematics
  • Computer Science
  • Data Science

Background:

  • Artificial intelligence (AI) and machine learning (ML) drive scientific progress but introduce new complexities.
  • Partial differential equations (PDEs) are traditionally used in scientific modeling.
  • PDEs are increasingly recognized for their utility in data science applications.

Purpose of the Study:

  • To introduce a theme issue exploring the intersection of PDEs and data science.
  • To provide an overview of the synergies between PDEs and data science.
  • To serve as an editorial foreword for the theme issue.

Main Methods:

  • Reviewing existing literature on PDEs in data science.
  • Identifying key areas where PDEs intersect with data science tasks.
  • Synthesizing current research trends and future directions.

Main Results:

  • PDEs can serve as physical models for data description.
  • PDEs offer alternative or supplementary approaches to artificial neural networks.
  • PDEs provide analytical tools for stochastic processes in ML model training.

Conclusions:

  • The integration of PDEs and data science presents significant opportunities.
  • PDEs offer a powerful mathematical framework for addressing data science challenges.
  • This theme issue highlights the growing importance of this interdisciplinary field.