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Response Surface Modeling, and Optimization
using Process and Device Simulation
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Experimental design and optimization fundamentally require a way to express the response of the system under study. Conceptually, a generic representation of a model of that system is needed, independent of whether analytic, numeric, or experimental execution of the model produces the response. In this way, many of the same experimental design, execution, and optimization mechanisms can be applied to real systems, to extensive numerical simulations, or to fast analytic models.
In DOE/Opt, a block is the embodiment of some model, and maps
inputs to outputs. A block has several tabular and script components
as pictured in Fig. 3. The key computational component
is the block body. The block body is often a script that chains
together process simulation, device simulation, and output data
extraction. In other cases, a response surface model (or RSM
block) contains a block body which is an analytic polynomial function
to calculate response and gradient information. Similar to the
block body is the block context, which is another script that
is run only once when the block is first loaded. The context is useful
for defining utility procedures that will be called repetitively
within the block body.
The block input table defines the possible inputs to the block. For each input, the name, default value, units, minimum, and maximum values may be specified. A toggle for each input indicates whether or not that input will vary in an experimental design or optimization. The block coefficient table is very much like the input table, except that it defines the values of any internal model coefficients inside the block. For example, automatically generated response surface models have coefficient values determined by the regression fit to run data. The block output table defines the possible outputs that the block is able to compute. Each output has a name, and may have an associated ``RSM'' giving the filename of an external response surface model that may be used in place of the block body to calculate the outputs. Desired transformations of output values may also be specified. For optimization, additional information about each output may be specified in the output table: each output may have a target value, and/or may have upper and lower constraint values. Finally, each row in the run and optimization tables presents specific input values and resulting outputs (or the initial starting point and resulting optima in the case of the optimization table).