Optimization is the process of improving a system to better meet some objective. There are a variety of optimization paradigms, each of which can make use of numerous methods and algorithms. Most of the methods in SmartUQ fall under the umbrella of Parametric Optimization in which a set of input parameters are modified in order to improve some result metric or output objective function.
Using a combination of proprietary adaptive DOEs and our breakthrough emulators, SmartUQ can rapidly evaluate the entire design space and make predictions about promising regions.
This emulator-based optimization works well with both low and high-dimensional problems. Our software minimizes the number of simulation runs required to get optimal results for a wide variety of problems and can handle a large number of input and output types including binary and discrete, multiple constraints, and optimization with multiple goals.
As an added benefit, significant savings can be achieved by using the same system evaluations for finding optimums as well as for analytics and UQ analysis of the optimization results. Not only can you explore optimal regions of the design space, you can also determine how sensitive optimums are to changes in input parameters and whether variations around optimal points might lead to unexpected or undesirable behavior such as constraint violations.
Figure: Statistical Optimization Flow Chart SmartUQ features dedicated tools for carrying out a number of optimization types:
Figure: 2d Projection of optimization Pareto front 
Figure: 3d Projection of optimization Pareto front Optimization problems often require testing enormous numbers of candidate input parameter points. While some simulations are fast enough to run optimizations directly and SmartUQ has some very efficient methods, for many systems using surrogate models/emulators is the only practical approach. Emulator based optimization applies optimization algorithms to an emulator which mimics the underlying system, taking advantage of the extremely fast prediction speeds to exhaustively cover the design space. Emulators do require training data but with SmartUQ’s advanced sampling methods and high accuracy machine learning tools, using emulators as stand-ins for complex systems can result in significant decreases in both the number of system evaluations and the clock time required to get solutions. Even better, once an emulator has been created it can be used for all sorts of optimization problems and other applications. Hence building an emulator multiplies the utility gained from the initial simulation/sampling effort.
Methods for optimization under uncertainty go a step further and integrate analysis and UQ directly into the optimization process. When some or all of a system's inputs are uncertain it is necessary to focus on identifying points that do well under a range of conditions, rather than optimizing to find the best point for a single set of conditions. Without investigating the behavior around the optimal design point, it is difficult to avoid unstable optima that can result in undesirable behavior given normal variation in the final product.
For example, when optimizing the efficiency of a jet engine, it is necessary to consider the uncertainty in material properties, manufactured dimensions, and operating conditions of the actual system. Because of the uncertainty in the actual engine, it will likely operate near but not at the optimal design point. If the goal is to optimize for maximum efficiency while ensuring that the engine doesn’t violate pollution emission requirements, it is necessary to understand the engine behavior around the optimal design point. This helps ensure that, for the known uncertainties in the design inputs, engine efficiency is always acceptable and the pollution requirements are never violated.
SmartUQ has three main approaches for optimization under uncertainty:
SmartUQ has machine learning tools such as functional and spatial-temporal emulation which can directly predict a field of response values. Field optimization allows users to optimize properties over the full set of response values. As an example, this allows users to target specific response profiles or to simultaneously maximize all the response values while minimizing the differences between responses over the entire field.
SmartUQ has multiple optimization approaches for simulations, tests, and machine learning models, each of which has even more options for constraints, objectives, algorithms, and visualization. All of these are dramatically accelerated by SmartUQ’s highly efficient design of experiments, cutting edge machine learning models, and advanced Bayesian sampling techniques.