ABSTRACT
Most problems in engineering can be recast in the framework of inverse/design problems. The goal of inverse/design problems is to identify conditions, including the initial conditions, boundary conditions, or property and coefficient distribution conditions, that result in a desired behavior of the engineered system. Examples of these are everywhere in the engineering world. With the current focus on sustainable manufacturing, a good example is in the identification of tailored processing conditions that result in electronic devices with high-performance metrics. In most electronics manufacturing, it has been shown that various processing conditions can critically impact device properties, and the identification of optimal processing conditions is a key problem from financial and sustainability standpoints [1–5]. Another example is in identification of useful designs for biomedical diagnostic platforms [6,7]. In this chapter, we discuss how much rapid design iterations that result in a desired flow transformation (one that provides mixing for a rapid reaction, flow separation for disease diagnostics, etc.) are required. In both of these cases, considerable effort has been expended to construct excellent “forward” models of the engineering problem, i.e., models that map the set of input conditions, boundary conditions, and property distributions to the output quantity of interest https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315391250/36ed0def-c58f-4767-b036-87e12aaef3d7/content/inline-math7_1.tif"/> ( ℱ : i n p u t → p r o p e r t y ) . The design problem, however, calls for the reverse mapping https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315391250/36ed0def-c58f-4767-b036-87e12aaef3d7/content/inline-math7_2.tif"/> ( G = ℱ − 1 : p r o p e r t y → i n p u t ) for a desired value of the output for a set of inputs.
