Continuous Boltzmann Machines: Theoretical Aspects and Applications Extended Abstract
Valeriu C. Beiu, Daniel Ioan, M. C. DumbravaSS · 1992
The paper introduces the concept of a continuous Boltzmann machine (CBM), and details an application to solve a class of partial differential equations (PDE). Afier briejly stating the problems, the BM is presented at a conceptual level. The basic ideas are taken to another level, andafresh concept is introduced: CBM, with the differences discussed in some detail. As Boltzmann machines (BMs) have solved hard (NP-complete) optimiuctionproblems, the CBM has been used to solve large systems of elliptic PDE arising in steady state physical fwlds. Numerical results of simulations prove the characteristic features of the CBM. stochastic function of the states of the units it is connected to and the associated connection strengths. Simulated annealing [ 101 is based on the Metropolis algorithm: (1) given a current estimate zS (2) accept the pointy as the new estimate with probability mid 1, P CP l$ (X ) 3, where the probabilities are Gibb (i.e., with form p@) a exp[-H @&I), and t is the temperature parameter. This formula emphasizes that the decision to accept or rejecty is based ona probability. It is implemented by “accept y if exd- [H(x)-H(y)]Ak r”, where r is a