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Partial differential equations in data science
Andrea L Bertozzi1, Nadejda Drenska2, Jonas Latz3
1Department of Mathematics, UCLA, Los Angeles, CA, USA.
Summary
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.
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.
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