Optimization of expensive cost functions subject to complex multidimensional constraints

A computing system, comprising:

• one or more computers, each having one or more processors and memory, wherein the memory stores one or more programs configured for execution by the one or more processors, the one or more programs comprising instructions for:
• identifying a plurality of design variables for a nuclear reactor;
• identifying a plurality of metric variables for the nuclear reactor, wherein the plurality of metric variables for the nuclear reactor include a plurality of metric variables to measure thermal-hydraulic properties of the nuclear reactor, a plurality of metric variables to measure neutronics properties of the nuclear reactor, and a plurality of metric variables to measure stress properties of the nuclear reactor;
• receiving user input to specify a respective range of values for each of the plurality of design variables, thereby forming an initial trust region;
• receiving user input to specify a respective target value for each of the plurality of metric variables;
• obtaining N samples of values for the design parameters within the initial trust region that minimizes a multivariate correlation between the plurality of design variables, wherein N is an integer greater than 1;
• for each of the N samples:
• executing a thermal-hydraulics analysis process to compute the plurality of metric variables to measure thermal-hydraulic properties;
• executing a neutronics analysis process to compute the plurality of neutronics metrics corresponding metric variables to measure neutronics properties;
• executing a stress analysis process to compute the plurality of metric variables to measure stress properties;
• and
• applying a cost function to compute a respective aggregate residual of the plurality of metric variables compared to target values for the plurality of metric variables;
• training an optimization model according to the N samples and the corresponding computed aggregate residuals;
• shrinking the initial trust region, centered at a sample of the N samples having a smallest residual, wherein the respective range for each design variable of the plurality of design variables is shrunk according to correlation between the respective design variable and estimated residuals using the optimization model;
• repeating the constructing, executing the thermal-hydraulic analysis processes, executing the neutronics analysis processes, executing the stress analysis processes, computing, and training until a sample of the N samples having a smallest residual is unchanged for a predetermined number of iterations;
• using the optimization model from a final iteration to assess importance of each design variable of the plurality of design variables;
• and
• providing the assessment visually in a report.

A method of optimizing design constraints for manufacturing, which is performed in a system including one or more processors and a non-transitory memory coupled to the one or more processors and storing software instructions executed by the one or more processors, the method comprising:

• receiving user input to specify design optimization constraints for a plurality of design variables, and to specify a cost function for evaluating designs for the plurality of design variables;
• (i) applying stochastic sampling to obtain a plurality of data samples for the plurality of design variables;
• (ii) training a first machine learning model to generate a subset of data samples based on the plurality of data samples and the design optimization constraints;
• (iii) training a Gaussian mixture model to classify the subset of data samples to obtain Gaussian distributions for a predetermined number of groups;
• (iv) training a second machine learning model to rank the Gaussian distributions, based on the cost function, to obtain a candidate design;
• (v) generating a new plurality of data samples based on the candidate design using a Markov Chain Monte Carlo algorithm;
• repeating steps of (i) applying the stochastic sampling, (ii) training the first machine learning model, (iii) training the Gaussian mixture model, (iv) training the second machine learning model, and (v) generating the new plurality of data samples, until design criteria are unchanged for a predetermined number of iterations;
• using the first machine learning model, the Gaussian mixture model, and the second machine learning model from a final iteration to assess importance of each design variable of the plurality of design variables;
• and
• providing the assessment visually in a report.

A computing system, comprising:

• one or more computers, each having one or more processors and memory, wherein the memory stores one or more programs configured for execution by the one or more processors, the one or more programs comprising instructions for:
• receiving user input to specify design optimization constraints for a plurality of design variables and a cost function for evaluating designs for the plurality of design variables;
• (i) applying stochastic sampling to obtain a plurality of data samples for the plurality of design variables;
• (ii) training a first machine learning model to generate a subset of data samples based on the plurality of data samples and the design optimization constraints;
• (iii) training a Gaussian mixture model to classify the subset of data samples to obtain Gaussian distributions for a predetermined number of groups;
• (iv) training a second machine learning model to rank the Gaussian distributions, based on the cost function, to obtain a candidate design;
• (v) generating a new plurality of data samples based on the candidate design using a Markov Chain Monte Carlo algorithm;
• iterating steps of (i) applying the stochastic sampling, (ii) training the first machine learning model, (iii) training the Gaussian mixture model, (iv) training the second machine learning model, and (v) generating the new plurality of data samples, until design criteria are unchanged for a predetermined number of iterations;
• using the first machine learning model, the Gaussian mixture model, and the second machine learning model from a final iteration to assess importance of each design variable of the plurality of design variables;
• and
• providing the assessment visually in a report.