Inferring properties of microscopic disorder potential from macroscopic transport measurements is a formidable challenging inverse problem in the low-dimensional nanostructures, particularly when the disorder is dynamic and experimentally uncontrolled. In this work, we investigate the inverse problem using the conventional quantum point contact (QPC) devices, modeling the impurity (its concentration can be expressed as $n$) induced disorder potential as an ensemble of randomly distributed two-dimensional circular Gaussian barriers, characterized by amplitude $A$ and spatial width $\delta$. By averaging the conductance over a large number of disorder configurations and comparing it with target data via a misfit function, we search for optimal parameter combinations that best reproduce the transport response. Our results reveal that at low impurity concentrations, the inversion uniquely identifies the correct $(n,$ $\delta )$ pair. However, at high concentrations, multiple distinct combinations yield nearly identical average conductance, indicating that the optimal solution is not a single point but a finite-width region in $(n,$ $\delta )$ parameter space. To resolve this degeneracy, we employ two complementary approaches: statistical analysis of the spatial dispersion of disorder potentials using a centroid-based standard deviation, and angular-resolved analysis of the partial local density of states after coordinate transformation to polar coordinates. The methods show that while both parameters influence transport, $\delta$ plays a dominant role in shaping the location, morphology, and extent of the optimal solution region. The significance of this study lies in revealing that the inverse problem for disordered mesoscopic systems inherently admits a continuum of equivalent solutions, highlighting the need for statistical and scattering-path analyses to distinguish microscopic configurations that are otherwise indistinguishable from conductance alone, together with providing critical insight for interpreting experimental transport data and guiding the design of quantum devices with reliable performance.

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• Quantum transport
• Two-dimensional electron system
• S-matrix method in transport