Topic 5

11:00-: Taxi pickup (at hotels)

12:00-13:00: Lunch

13:15-14:00: Talk: John Molina

14:00-14:30: Break

14:30-15:15: Talk: Paul Francois

15:15-15:45: Break

15:45-16:30: Talk; Ayaka Sakata

16:30-17:30: General discussion

18:00-21:00: Dinner (taxi leave at 18:00 from Lab5 Parking Lot)

Title: Physics-Informed Machine Learning for the Physical and Social Sciences

Lecturer: John Molina

In this presentation I will describe ways to develop Physics-Informed Machine Learning  (PIML) methods, i.e., how to incorporate governing equations and/or constraints into standard Machine Learning frameworks.

Because of these additional inductive biases, such PIML methods generally require less training data and offer more robust predictions compared to "Naive" ML approaches.

I will introduce the basics of PIML (e.g., automatic-differentiation, physics-informed neural networks / operators) and present some examples in the physical, biological, and social sciences.

In particular, I will focus on the use of PIML to solve-inverse problems,  e.g. discovering hidden Hamiltonians (mechanical systems) or utility functions (optimal control & game theory).

If machine learning is the answer, what is the question?

Lecturer: Paul François

In this talk, I will describe how machine learning approaches can be used not only as analysis tools, but also as inspiration for setting and studying biological problems. I will show how Generalized Hopfield Networks present 'biology-like' learning dynamics, reminiscent of the Waddington landscape caricature. One can then build new learning rules, inspired by biology, to better model specific biological processes. This connects machine learning to current advances in geometric modeling of biological systems, and I will discuss specific examples.

Understanding Generalization in Statistical Models: Insights from Statistical Physics

Lecturer: Ayaka Sakata

Generalization is a key concept in statistics and machine learning, and its evaluation can be viewed as a form of perturbation analysis, such as cross-validation. In this talk, I will demonstrate how statistical physics provides powerful tools that can be applied to perturbation analysis in statistics. Concepts from statistical physics, such as fluctuation-response relationship, enable us to quantitatively understand the generalization performance of statistical models.

I will briefly discuss how these considerations may have potential applications in biological systems, particularly from the perspective of the similarity between generalization in statistical models and robustness in biological systems.