Solving an inverse partial differential equation for a two dimensional heat conduction problem with oscillating boundary conditions using an artificial immune system

Increases in computing power have brought a renewed interest in solving inverse initial-value, boundary-value (inverse IVBV) problems, and in the development of robust, computationally efficient methods suitable for their solution. Inverse IVBV problems are prominent in science and engineering problems governed by partial differential equations where often an effect is measured and the cause is not known. In these situations scientists and engineers typically observe the response of a system and desire to know the particulars of the system that elicited such a response. In this paper, an artificial immune system (AIS) is used to monitor a physical system, to identify the need for solving an inverse IVBV problem within that system, and to solve said problem. Specifically, an AIS is used to determine the heat conducting properties of a material that elicits a measured temperature distribution response when subjected to time-varying boundary temperatures. Results indicate that the AIS provides an effective mechanism for solving this particular inverse IVBV problem.