Machine Learning for Science - Mathematics at the Interface of Data-driven and Mechanistic Modelling - Oberwolfach Report 26/2023

Aug 2, 2026

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Rapid progress in machine learning is expanding scientific capabilities, yet transforming data-derived insights into new explanations of why system dynamics emerge remains limited by the gap between data-driven learning and traditional physical modelling. Mathematics is presented as the bridge linking these paradigms, enabling formal foundations for machine-learning methods that support scientific discovery. The workshop brought together researchers to discuss applications, foundational methods, and approaches for Earth and climate science.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages32

Reading Time1 h 21 min

AccessFree to download

Introduction

Workshop goals and themes

Mathematics as an interface

Applications and current limitations

Open mathematical questions and foundational methods

Future directions in mathematics and machine learning

Mathematisches Forschungsinstitut Oberwolfach Report No. 26/2023 DOI: 10.4171/OWR/2023/26 Machine Learning for Science: Mathematics at the Interface of Data-driven and Mechanistic Modelling Organized by Neil Lawrence, Cambridge UK Jessica Montgomery, Cambridge UK Bernhard Sch¨olkopf, T¨ubingen 11 June – 16 June 2023 Abstract. Rapid progress in machine learning is enabling scienti􀀌c advances across a range of disciplines. However, the utility of machine learning for science remains constrained by its current inability to translate insights from data about the dynamics of a system to new scienti􀀌c knowledge about why those dynamics emerge, as traditionally represented by physical modelling. Mathematics is the interface that bridges data-driven and physical models of the world and can provide a foundation for delivering such knowledge. This workshop convened researchers working across domains with a shared interest in mathematics, machine learning, and their application in the sciences, to explore how tools of mathematics can help build machine learning tools for scienti􀀌c discovery. Mathematics Subject Classi􀀌cation (2020): 60XX, 62XX, 68XX, 85XX, 86A08, 92XX. Introduction by the Organizers The workshop Machine Learning for Science: Mathematics at the Interface of Data-driven and Mechanistic Modelling, co-organised by Neil Lawrence, Jessica Montgomery, and Bernhard Sch¨olkopf was attended by 40 participants from 11 to 16 June 2023 . It set out to consider how mathematical innovations can help produce machine learning tools that can be deployed in support of scienti􀀌c discovery, creating new interfaces between physical and data-driven modelling approaches. In support of this objective, the workshop convened three discussion themes —Lessons from the application of machine learning in science; Foundational conceptsand emerging methods; Machine learning for Earth and climate sciences—which 1454 Oberwolfach Report 26/2023 between them included 19 talks. This workshop report presents a summary of discussion points and insights from the workshop. The machine learning for science community is a rendezvous point for diverse disciplinary perspectives. E􀀋ective research, development, and deployment of machine learning in science requires insights from computer science, domains of application, and software engineering, amongst other areas. Across these domains, mathematics acts as the interface between machine learning and the world, providing a foundation for theories, methods, and tools that enable its safe and e􀀋ective use for scienti􀀌c discovery. Mathematics provides means of formalizing structure. In the context of machine learning for science, it allows researchers to: 􀀏 Represent pre-existing domain knowledge, embedding this in machine learning systems to deliver more reliable results; 􀀏 Formalize desiderata such as fairness, interpretability, or uncertainty, which are vital to ensure machine learning models align with user needs; 􀀏 Model users, and the interactions between the user’s model of the machine learning system and machine learning’s model of the user. Opening this workshop, a series of talks focussing on di􀀋erent applications of machine learning in the sciences explored the capabilities of today’s machine learning tools [B¨uttner; Igel; Machuve; Mishra; M¨uller] . These demonstrated how machine learning can be deployed to: stitch together di􀀋erent data types, allowing researchers to gain a more nuanced view of a system; extract insights from data— and speed up analysis of complex datasets—to gain a more accurate understanding of how the system works, inferring properties of the physical world; and identify areas for experimentation and theorising, showing researchers where they should focus their investigations. Across scienti􀀌c domains, today’s machine learning systems share a fundamental limitation: the 􀀌eld is not yet at the stage where these systems are directly enabling re

FAQs

Why is machine learning for science still limited today?

Advanced analysis can uncover dynamics, but systems are not yet able to translate these data back into new scientific knowledge explaining why the dynamics emerge.

How does mathematics bridge data-driven and physical modelling?

Mathematics formalizes structure and enables embedding domain knowledge, specifying properties like fairness and uncertainty, and modelling user–system interaction within learning pipelines.

What were the main discussion themes of the workshop?

The workshop organized three themes: lessons from machine learning applications in science, foundational concepts and emerging methods, and machine learning for Earth and climate sciences.

Aug 2, 2026

Upload by Oliver