The Performance of Approximating Ordinary Differential Equations by Neural Nets

—The dynamics of many systems are described by ordinary differential equations (ODE). Solving ODEs with standard methods (i.e. numerical integration) needs a high amount of computing time but only a small amount of storage memory. For some applications, e.g. short time weather forecast or real time robot control, long computation times are prohibitive. Is there a method which uses less computing time (but has drawbacks in other aspects, e.g. memory), so that the computation of ODEs gets faster? We will try to discuss this question for the assumption that the alternative computation method is a neural network which was trained on ODE dynamics and compare both methods using the same approximation error. This comparison is done with two different errors. First, we use the standard error that measures the difference between the approximation and the solution of the ODE which is hard to characterize. But in many cases, as for physics engines used in computer games, the shape of the approx...

• Type: Conference
• Year: 2008
• Where: ICTAI
• Authors: Josef Fojdl, Rüdiger W. Brause
• Keywords: Approximation, Artificial Intelligence, Computing Time, ICTAI 2008, Neural Network