Confidence bounds of petrophysical predictions from conventional neural networks

Neural networks are powerful tools for solving the complex regression problems which abound in geosciences. Estimation of prediction confidence from neural networks is an important area. Many procedures are available to date, but it is often tedious for practitioners to implement such procedures without significant modification of the existing learning algorithms. In many cases, the procedures are also computationally intensive. This paper presents a practical solution using conventional backpropagation networks with simple data pre-processing and post-processing algorithms. The methodology involves conversions of the target outputs into linguistic variables (classes) prior to learning. When the classification network converges, minimum and maximum predictions are derived from the output activations using a simple averaging algorithm. Two examples from petroleum reservoirs are used to demonstrate the proposed methodology. The results show that the confidence bounds of the petrophysical predictions are realistic in both cases. The proposed methodology is generally useful, and can be implemented in simple spreadsheets without altering any existing neural network code.