Alan Edelman, Professor of Applied Mathematics, MIT

Seminar Title: Scientific Machine Learning, SmartSolve, and Dyad: Applied Mathematics in the AI Era

Abstract: The Julia Lab at MIT and JuliaHub have been exploring a future in which humans and AI augment one another in scientific computing and engineering. Scientific machine learning supplies part of the mathematical foundation. Physical models remain central, but they are now differentiable programs: they can be fitted to data, coupled to learned components, and automatically transformed for modern hardware.

SmartSolve asks a deliberately provocative question: is the age of the numerical library coming to an end? Libraries arose because numerical analysts had to anticipate the needs of domain scientists and freeze their expertise into general-purpose algorithms. An AI system can instead examine the equations, the structure (sparsity, symmetry, conditioning, stiffness), the data, the accuracy requirements, and the available hardware, and then construct or adapt a solver for the problem at hand. What persists is the mathematics: stability, convergence, and error analysis become the specification against which a generated solver is judged.

Dyad carries this idea into engineering design. An engineer describes a physical system and directs the work, while an AI agent helps research formulations, derive equations, assemble components, run simulations, and diagnose or validate the resulting model. The compiler continues to enforce units, physical connections, and conservation laws, so the agent works inside guarantees it cannot violate.

Together these projects suggest a new division of labor. The human supplies scientific judgment, goals, and skepticism; AI supplies increasingly capable mathematical and computational execution; and mathematical structure is what makes the result trustworthy.

Joint work with Chris Rackauckas, the Julia Lab, JuliaHub, and the Julia community.

3:30pm - Pre-talk meet and greet teatime - 219 Prospect Street, 13th floor, there will be light snacks and beverages in the kitchen area.