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We show that a neural network whose output is obtained as the difference ofthe outputs of two feedforward networks with exponential activation function inthe hidden layer and logarithmic activation function in the output node (LSEnetworks) is a smooth universal approximator of continuous functions overconvex, compact sets. By using a logarithmic transform, this class of networksmaps to a family of subtraction-free ratios of generalized posynomials, whichwe also show to be universal approximators of positive functions overlog-convex, compact subsets of the positive orthant. The main advantage ofDifference-LSE networks with respect to classical feedforward neural networksis that, after a standard training phase, they provide surrogate models fordesign that possess a specific difference-of-convex-functions form, which makesthem optimizable via relatively efficient numerical methods. In particular, byadapting an existing difference-of-convex algorithm to these models, we obtainan algorithm for performing effective optimization-based design. We illustratethe proposed approach by applying it to data-driven design of a diet for apatient with type-2 diabetes.

A Universal Approximation Result for Difference of log-sum-exp Neural Networks