Physical Fields Determination Using Continuous Boltzmann Machines

Introduces the concept of a continuous Boltzmann machine and details an application to solve a class of partial differential equations. The digital Boltzmann machine is briefly presented at a conceptual level. Its basic ideas are then taken to another level, and a fresh concept is introduced; `continuous Boltzmann machines', with the differences discussed in some detail. Because Boltzmann machines have proven useful for hard (NP-complete) optimization problems, the continuous Boltzmann machine has been used to solve a difficult problem: large systems of elliptic partial differential equations which arise in the case of steady-state physical fields. Numerical results of computer simulations demonstrate the characteristic features of the continuous Boltzmann machine.