CBMS Conference: Research at the Interface of Applied Mathematics and Machine Learning

The Conference Board of the Mathematical Sciences (CBMS), formally incorporated in 1960, is a consortium of 19 professional societies, each dedicated to advancing and disseminating knowledge in one or more areas of the mathematical sciences.

In December 2025, the department of mathematics at the University of Houston (UH) hosted the annual CBMS Conference, titled “Research at the Interface of Applied Mathematics and Machine Learning” (CBMS-AMML). The conference—supported by the National Science Foundation (NSF) and the UH Department of Mathematics—was designed to expose early-career researchers to foundational and emerging directions at the intersection of mathematics and artificial intelligence (AI). The assembly attracted over 100 participants, including graduate students, postdoctoral researchers, faculty from universities, researchers from national laboratories, the medical sector, and industry. 

Bridging Computational Mathematics and Machine Learning

Machine learning (ML) has rapidly become a central tool across science and engineering, yet its most effective methods rely heavily on ideas long familiar to mathematicians: mathematical optimization, approximation theory, numerical linear algebra, and probability. Conversely, ML techniques increasingly influence how mathematicians approach high-dimensional data-analysis, simulations, inverse problems, and uncertainty quantification. The CBMS-AMML conference highlighted this two-way exchange through a structured lecture course combined with contributed talks, posters, and panel discussions.

A central feature of the program was a ten-lecture short course on computational mathematics and AI delivered by Lars Ruthotto of Emory University. The course provided a cohesive introduction to ML from a mathematical perspective, emphasizing optimization, regularization, and continuous viewpoints inspired by dynamical systems and partial differential equations (PDEs). The course progressed from foundational concepts, such as neural network architectures and loss functions, to advanced topics including scientific ML, neural approaches to inverse problems, and data-driven methods for high-dimensional PDEs. The course concluded with perspectives on AI for algorithmic discovery and theorem proving. Throughout, the lectures emphasized how mathematical structure improves interpretability, robustness, and efficiency in modern AI systems.

In addition to the lecture course, the conference featured 12 invited presentations by leading researchers from academia and various national laboratories. Speakers addressed topics ranging from optimization theory and approximation to operator learning and scientific applications of ML, highlighting ongoing research at the interface of computational mathematics and AI.

A poster session showcased research by more than 40 graduate students and postdoctoral scholars on various topics aligned with the principal theme of the conference. The program further included panel discussions on interdisciplinary research and career pathways, with panelists from industry, the medical sector, and academic institutions providing perspectives on emerging opportunities and challenges.

Open Resources and Impact

To extend the reach of the conference, all lectures were recorded and posted on YouTube. Furthermore, Ruthotto curated a public GitHub repository containing lecture slides, example code, and computational notebooks. These materials allow researchers and educators to build upon the course content and incorporate mathematical perspectives on AI into their own work.

The CBMS-AMML conference exemplifies a growing emphasis within the applied mathematics community on interdisciplinary training and collaboration. By combining rigorous mathematical foundations with hands-on exposure to ML methods and applications, the event helped prepare early-career researchers to contribute to a rapidly evolving research landscape where mathematics and AI are increasingly inseparable.