Adaptive Sampling: an improvement on conventional strategies

omet
omet
Altair Employee
edited December 2021 in Other Discussion & Knowledge

One of the purposes of Design Space Exploration is to generate high-fidelity mathematical(predictive) models to be later used in lieu of actual solver for approaches like optimization or quick trade-off studies. The exploration is performed by sampling design points which are nothing but different combinations of design variables. In general, the variables in engineering are continuous which makes design combinations infinite and for that reason, it is crucial to have a smart design space sampling strategy.

In conventional sampling methods such as Latin HyperCube and Hammersley, sample selection does not depend on observations. In other words, the size of samples is fixed and must be defined by design explorers in advance. Having to define the number of samples in advance leads to two undesirable consequences: burden of specifying the exact number of samples to build accurate predictive models and potential waste of samples when each evaluation is costly.

To remedy the burden of defining number of samples in advance, HyperStudy employs adaptive sampling (also called response-adaptive sampling) strategy which samples the design space and stops when desired accuracy is reached. The algorithm, at user-defined intervals, builds a response surface to check if desired cross-validation r-squared value is achieved and this periodic process requires an extensible sampling scheme. At each interval, the sampling sequence stops, and after cross-validation r-squared is calculated, the sampling must continue without discarding samples accrued thus far. Hence, conventional methods like Latin HyperCube (LH) are not suitable due to their non-extensibility. There are two images to illustrate the inextensibility of LH; Figure 1 shows initial sequence of ten samples and Figure 2 shows the next sequence of ten samples plus the ten samples of that initial sequence. When LH generates a new sequence, the previous sequence is discarded which causes non-uniform distribution of samples in design space as shown in Figure 2.

    image         image

    Figure 1. Latin HyperCube, initial sequence of 10 samples                   Figure 2. Latin HyperCube, subsequent sequence of 10 samples plus initial  ten samples.

The adaptive sampling method in HyperStudy is called Modified Extensible Lattice Sequence (MELS). MELS's extensibility comes from its capability of including the existing samples by offsetting the subsequent ones.

If you are struggling with choosing the right number of samples to build a representative predictive model, adaptive sampling would be a great option to use.