Simulating the behavior of poorly understood continua using neural networks

Abstract

This paper proposes and evaluates an artificial neural network based method of modeling the dynamic behavior of spatially distributed continuous engineering processes. The technique is applicable to situations where the differential equations governing the behavior of a system are nonlinear and poorly understood, such as is the case for frost-heave and thaw-settlement processes in soils. A description is first provided of a means of modeling the unknown component of governing differential equations. A range of levels of understanding of these equations is considered. A method of discretizing the resultant neural models of these equations is then illustrated, and the way in which these can be used to simulate the behavior of a process is described. The performance of the proposed neural network approach is then assessed in a series of experiments simulating the nonlinear thermal behavior of translucent solid materials. The system is proven capable of providing highly accurate simulations of system behavior sustained over many thousands of simulation time steps. The paper concludes with an identification of several ongoing areas of further development and application of the proposed tool.