**Title: **Digital models, scientific machine learning, and digital twins: a virtuous interplay between data-driven algorithms and physics-inspired numerical models.

**When:** Spring 2024 ; Wednesdays from 12 till 2pm in MATH 3206

**Instructor:** Alfio Quarteroni

**Abstract: **Problem setting is a critical precursor to problem solving. It involves the art of formulating the right problem statement. The importance of this phase is underscored by the fact that without a well-defined problem, finding the right tools and techniques for problem solution becomes a cumbersome and often futile endeavor. This transition from problem setting to problem solving is integral to the larger paradigm of knowledge development. While AI tools have made tremendous strides in recent years, they remain dependent on the foundation laid by human intelligence. Mathematicians, with their ability to discern patterns and relationships, data, and variables, play a vital role in this stage.

In this course, I will introduce basic mathematical concepts from both traditional machine learning and scientific machine learning. Scientific machine learning, which integrates data-driven machine learning algorithms with physics-based digital models, provides an ideal platform for the virtuous merging of problem setting and problem solving, facilitated by a profound domain knowledge. During the course, the reference application will focus on the development of a mathematical simulator for the cardiac function.

Dr. Alfio Quarternori will join the UMD Math Department for two months in Spring 24 as a visiting professor. Alfio is a distinguished mathematician, working in the area of mathematical modeling, numerical analysis, scientific computing, and applications to fluid mechanics, geophysics, biomechanics, medicine, and structural analysis. Alfio is the author of 24 books and author of more than 400 papers. Throughout his career, he has received many awards, including membership in 9 Academies, a plenary speaker at the ICM (2006), and the Lagrange Prize (2023) – awarded to one mathematician every four years.