Solving nonlinear engineering problems with the aid of neural networks

In this paper, a technique is presented for using neural networks as an aid for solving nonlinear engineering problems, which are encountered in optimization, simulations and modeling, or complex engineering calculations. Iterative algorithms are often used to find the solutions of such problems. For many large-scale engineering problems, finding good starting points for the iterative algorithms is the key to good performance. We describe using neural networks to select starting points for the iterative algorithms for nonlinear systems. Since input/output training data are often easily obtained from the problem description or from the system equations, a neural network can be trained to serve as a rough model of the underlying problem. After the neural network is trained, it is used to select starting points for the iterative algorithms. We illustrate the method with four small nonlinear equation groups, two real applications in petroleum engineering are also given to demonstrate the method's potential application in engineering.