Bilateral Sensitivity Analysis for Understandable Neural Networks and its application to Reservoir Engineering

Abstract

In this paper, a model-independent sensitivity analysis for (deep) neural network, Bilateral Sensitivity Analysis (BiSA), is proposed to measure the relationship between neurons and layers. Both the BiSA between pair of layers and the BiSA between any pair neurons in different layers are defined for (deep) neural networks. This sensitivity can measure the influence or contribution from any layer to another layer behind this layer in the (deep) neural networks. It provides a helpful tool to interpret the learned model. The BiSA can also measure the influence or contribution from any neuron to another neuron in a subsequent layer and is critical to analyze the relationship between neurons in different layers. Then the BiSA from any input to any output of a network is easily defined to assess the connections between the inputs and outputs. The proposed BiSA of (deep) neural networks is then applied to characterize the well connectivity in reservoir engineering. Given a network trained by Water Injection Rates (WIRs) and Liquid Production Rates (LPRs) data, the well connectivity can be efficiently described through BiSA. The empirical results verify the effectiveness of the proposed method. The comparisons with the exiting methods demonstrate the robustness and the superior performance of the proposed method.