The Reactive Response Surface (RRS) optimizer is a Machine Learning method that efficiently finds optimal solutions by intelligently selecting data points for evaluation. Instead of relying on a large, pre-determined dataset, RRS iteratively learns from existing data to decide where to focus the search next, minimizing the cost and time of complex optimization problems requiring high-fidelity simulation. The core components are a probabilistic Response Surface Model (RSM), a Multi-Objective Genetic Algorithm (MOGA), and a Reactive Function that balances exploring the design space with exploiting known good areas. The final verified results show the RRS surrogate model retains the accuracy of high-fidelity simulations with errors as low as 0.00% on key performance metrics.
● An Introduction to Reactive Response Surface (RRS)
● What is Response Surface Model (RSM)?
● Multi-Objective Genetic Algorithm (MOGA)
● Reactive Function
● Verification
● Reactive Function
● Key Takeaway
ADT’s Reactive Response Surface (RRS) optimizer engine is a Machine Learning (ML) method used to efficiently find an optimal solution to a set of objectives by intelligently selecting data points for evaluation. Instead of examining a large, pre-determined set of possibilities, RRS iteratively learns from the data it has already seen and uses that knowledge to decide where to look next. This reactive approach makes it ideal for reducing the overall cost (either in resource or time, or both) of performance optimization where high-fidelity simulation is required to provide accuracy and verification during the design space search.
The main components of the RRS method are a probabilistic surrogate model, a multi-objective genetic algorithm, and an reactive function that mathematically formalises the trade-off between design space exploration and exploitation.
A machine learning system should, in theory, be able to find a close to optimum design for this type of blading, especially when tailored to a unique operating requirement. However a number of obstacles must be overcome to turn this into a reality.
As the name suggests, the surrogate within the RRS system is a Response Surface Model (RSM) - essentially an n-dimensional construct that is conditioned to minimise the difference between the observed objective values to date and those predicted by a 2nd order polynomial function. The quality of the RSM is checked using Analysis of Variance (ANOVA) and refined on the basis of the ANOVA indicators of quality and fit. This results in a probability distribution for the objective function's value at any new point, conditioned on the previously observed data, with a mean (the predicted value) and a variance (the uncertainty).
At this point a Multi-Objective Genetic Algorithm (MOGA) is run over the design space, using the response surface to generate the outputs from the genetically coded inputs. Using the surrogate in this way is an extremely rapid way to identify candidates at the Pareto front - that is the front beyond which no improvement in compromise-performance between the objectives can be achieved. MOGA itself is a relatively expensive method in terms of the required number of candidates for an effective search, but using the surrogate model, rather than full-fidelity simulation, means the actual computational cost is extremely low for this step. Typically the MOGA would run for 100 generations, generating 100 children in each. So a total of 10,000 assessed points. In general this will take a matter of seconds on a standard desktop or laptop workstation.
The reactive part of the RRS interrogates the response surface model at the Pareto front, calculating the probability that evaluating a new point will result in a better value than the best one found so far, and drawing up a ‘shortlist’ (typically less than 10) of new candidate points. The simulation results of these candidates (either low- or high-fidelity, single- or multi-operating-point) are fed back to the RSM and the response surface is rebuilt using the new data. This improves the overall model accuracy and drastically reduces the error typically associated with low order models. This iterative addition of datapoints in the high performance areas of the design space, rather than a space filling plus gradient search approach, ensures higher accuracy of the overall model whilst using a small learning dataset.
Left - MOGA is a high accuracy design space search method, but very computationally expensive, requiring 1000’s of datapoints.
Centre - Surrogate models are computationally cheap but are not always accurate and can lead to false optima.
Right - Reactive Response Surface combines the accuracy of MOGA with very small datasets - typically around 50 points required.
The final optimum design, selected from the surrogate model Pareto front, can be checked using high-fidelity CFD. The table below shows the error between the RRS surrogate model predicted performance and a verification run in high-fidelity CFD for a centrifugal compressor study. Showing that the surrogate model retains the accuracy of the high-fidelity method.
Likewise, the table below shows the error between the RRS surrogate model and high-fidelity CFD for a hydraulic turbine optimization study.
The Reactive Response Surface, or if used in combination with high-fidelity simulation - RRS+CAE, method ensures that computational and resource costs are kept to a minimum, whilst comprehensively driving the design towards the global optimum with maximum efficiency and accuracy. This method lies at the heart of ADTs mission to provide Machine Learning for turbomachinery design at high-fidelity with small datasets.