Statistical Forces in Equation Learning and Ship Design

by Prof. Andrei Klishin (Mech. Engr. UH Manoa)

Thursday Oct 3, 2024, 3:00 PM → 4:00 PM Pacific/Honolulu

The idea of a force is so pervasive in physics that we insist on teaching it even to non-physics majors. Most interesting physics phenomena result from an interplay of opposing forces, whether they have fundamental or effective origins. In this talk I present two case studies of statistical physics inspired analysis applied to other systems. The first study concerns learning interpretable dynamical equations from observed trajectories with tension between data fit and model sparsity. I show that the large data limit, much like the thermodynamic limit, enables the sharp noise- and sparsity-induced phase transitions between different models. The second study concerns the design of large complex systems like those found in Naval Engineering where cost minimization trades off with solution flexibility. These ill-defined design objectives and combinatorial solution spaces defeat the conventional optimization techniques, but make the problem amenable to statistical mechanics. I show how the formalism of tensor networks allows us to detangle the solution ensembles and identify the familiar physics phenomena of symmetry breaking and emergent localization.

Klishin_UH_Physics_static.pdf

Video - Prof. A. Klishin