Estimating aquifer properties in heterogeneous formations from hydraulic head data is a critical aspect of inverse modeling for groundwater flow in subsurface porous media. Unlike traditional pumping test analysis, which often involves deducing the bulk-average hydraulic conductivity value around the pumping or injection well, multiple-well flow tests provide a more spatially detailed characterization of aquifer heterogeneity. In this work, we represent the pressure front propagating from the vertical pumping well using the diffusive time of flight (DTOF), computed by solving the Eikonal equation derived from the high-frequency limit of the diffusion equation. Taking advantage of the high computational speed of the Fast Marching Method (FMM) to obtain the DTOF and the drainage volume within it, we establish a robust and highly efficient 1D flow simulator capable of modeling drawdown tests in heterogeneous confined aquifers. To inversely estimate hydraulic conductivity, drawdown derivative data incorporating slight boundary effects (BEs) are collected at sparse monitoring points in the aquifer model and treated as input variables within a deep neural network (DNN), previously known as the inversion neural network (INN) and now upgraded as the BE-INN. Flow tests with single and multiple pumping wells are designed to validate the effectiveness of the BE-INN for predicting heterogeneous hydraulic conductivity fields. Comparison analysis shows that the BE-INN demonstrates excellent parameter estimation accuracy when 37 sparse monitoring points are placed in a 2D confined aquifer model discretized into a 48 × 48 grid system with a no-flow outer boundary for both the one-well and five-well flow tests. By inverting the “field” observational drawdown derivative data generated by a conventional groundwater flow simulator, the BE-INN achieves an estimation accuracy of approximately 90 % for logarithmic values of hydraulic conductivity fields with smoothly varying heterogeneity and about 70 % accuracy for those hydraulic conductivity fields with channelized geological features.