A factor-graph approach to Lagrangian and Hamiltonian dynamics

Abstract

Factor graphs are graphical models with origins in coding theory. The sum-product, the max-product, and the min-sum algorithms, which operate by message passing on a factor graph, subsume a great variety of algorithms in coding, signal processing, and artificial intelligence. This paper aims at extending the field of possible applications of factor graphs to Lagrangian and Hamiltonian dynamics. The starting point is the principle of least action (more precisely, the principle of stationary action). The resulting factor graphs require a new message-passing algorithm that we call the stationary-sum algorithm. As it turns out, some of the properties of this algorithm are equivalent to Liouville's theorem. Moreover, duality results for factor graphs allow to easily derive Noether's theorem. We also discuss connections and differences to Kalman filtering.