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.