Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
The time dimension of neural network models
ACM SIGART Bulletin
Machine Learning
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This paper advocates integrating two decades-old tools, namely, input-space bisection and backpropagation, in support of design decision making. Either technique independently could offer some improvements in efficiency and reduced computational costs; however, taken in concert their effects could be greatly amplified. Traditional design decisions have often relied too heavily upon expensive, time-consuming HPC runs. This paper demonstrates from three disparate cases that a carefully chosen input space serving as training instances for a backpropagation algorithm can often perform within acceptable error bounds for the test cases, while providing a much quicker response to decision makers. First, we introduce the problem domain, stressing the inadequacies and the inefficiencies of using too highly resolved parameter variations in batch HPC runs. We then provide a step-by-step overview of our surrogate model approach. We describe the similarities of the requirements for running both numerical solvers and artificial neural networks. Our method entails using an input-space bisection to reduce (in both the spatial and temporal domains) the output of the numerical solver, the results of which will serve as training cases for the backpropagation algorithm. The technique is demonstrated in three test cases, two of which are built to predict behavior at a fixed point in time, while the other, more ambitiously, tackles contaminant trace in hydraulic flow over multiple timesteps. Finally, we summarize some of the benefits this approach offers and outline directions for future research.