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Underground duct banks carrying power cables dissipate heat to thesurrounding soil. The amount of heat dissipated determines the current ratingof cables, which in turn affects the sizing of the cables. The dissipation ofheat through the surrounding soils happens through conduction and convection.The mode of heat transfer depends on the soil's thermal and hydraulicproperties like diffusivity and permeability. The soil surrounding the cablescould be designed to have maximum heat dissipation to have an improved currentrating of cables. Differentiable programming is a novel technique that combinesautomatic differentiation with gradient-based optimization to minimize a lossfunction. Hence, differentiable programming can be used to evaluate inputparameters based on output results. Given a desired heat distribution in thesoil and a temperature source, we use differentiable programming to solve theinverse problem of estimating the soil permeability. In the present study, weemploy differentiable programming to optimize the design of the buried duckbank and the backfill soil to improve heat dissipation. The design involvesoptimizing the permeability and size of the fill material compared to thesurrounding natural soil. To implement automatic differentiation, we develop aninverse finite difference code in the Julia programming language andForwardDiff package. We demonstrate the design capabilities of thedifferentiable programming technique to obtain the optimum permeability of thebackfill material from the norm of the temperature distribution in thesurrounding soil.

Differentiable programming for inverse estimation of soil permeability and design of duct banks