Rapid Digital Nuclear Reactor Design Using Machine Learning

Abstract

A method designs nuclear reactors using design variables and metric variables. A user specifies ranges for the design variables and threshold values for the metric variables and selects design parameter samples. For each sample, the method runs three processes, which compute metric variables for thermal-hydraulics, neutronics, and stress. The method applies a cost function to compute an aggregate residual of the metric variables compared to the threshold values. The method deploys optimization methods, either training a machine learning model using the samples and computed aggregate residuals, or using genetic algorithms, simulated annealing, or differential evolution. When using Bayesian optimization, the method shrinks the range for each design variable according to correlation between the respective design variable and estimated residuals using the machine learning model. These steps are repeated until a sample having a smallest residual is unchanged for multiple iterations. The final model assesses relative importance of each design variable.

1 - 20 . (canceled) 
     
     
         21 . A method of designing a nuclear reactor, comprising:
 identifying a plurality of design variables for the nuclear reactor;   identifying a plurality of metric variables for the nuclear reactor, each of the plurality of metric variables measuring a respective thermal-hydraulic property, neutronics property, or stress property;   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 threshold value for each of the plurality of metric variables;   (i) constructing a Latin hypercube comprising N samples of values for the plurality of design parameters within the initial trust region, wherein N is an integer greater than 1;   (ii) computing each of the plurality of metric variables for each of the N samples in the Latin hypercube and applying a cost function to compute a respective residual of the respective metric variable compared to the respective threshold value;   (iii) training a machine learning model according to the N samples and the corresponding computed residuals;   shrinking the trust region, wherein the respective range for each of the plurality of design variables is shrunk according to a correlation between the respective design variable and estimated residuals using the machine learning model;   repeating the (i) constructing, (ii) computing, and (iii) training until a sample having a smallest residual is unchanged for a predetermined number of iterations;   using the machine learning model from the final iteration to assess relative importance of each of the plurality of design variables; and   providing the assessment visually in a report.   
     
     
         22 . The method of  claim 21 , wherein the machine learning model is a random forest of decision trees or a neural network for Bayesian optimization. 
     
     
         23 . The method of  claim 21 , wherein the machine learning model uses one or more evolutionary methods, including genetic algorithms, coupled simulated anneal algorithms, and/or differential evolutionary algorithms. 
     
     
         24 . The method of  claim 21 , wherein computing each of the plurality of metric variables is performed concurrently 
     
     
         25 . The method of  claim 21 , wherein computing each of the plurality of metric variables is performed serially. 
     
     
         26 . The method of  claim 21 , wherein computing each of the plurality of metric variables includes a thermal-hydraulics analysis process, a neutronics analysis process, and a stress analysis process, and each of the thermal-hydraulics analysis process, the neutronics analysis process, and the stress analysis process is performed at a respective distinct computing subsystem 
     
     
         27 . The method of  claim 21 , further comprising during repeating of the (i) constructing, (ii) computing, and (iii) training:
 determining a sample having a smallest aggregate residual;   determining that the sample has a value for a first design variable of the plurality of the design variables on a boundary of the trust region; and   in response to the determination, expanding the trust region to include a range for the first design variable that was not previously in the trust region.   
     
     
         28 . The method of  claim 21 , wherein one of the plurality of metric variables is the effective neutron multiplication factor (K eff ). 
     
     
         29 . The method of  claim 21 , wherein the shrinking uses a learning rate multiplier specified by user input 
     
     
         30 . The method of  claim 21 , wherein the initial Latin hypercube is centered at average values for the user-specified ranges of the design variables. 
     
     
         31 . The method of  claim 21 , wherein the plurality of design variables includes a first design variable that has discrete categorical values, the method further comprising:
 encoding each distinct categorical value as a numeric value in a continuous range to form a first replacement design variable; and   substituting the first replacement design variable for the first design variable.   
     
     
         32 . The method of  claim 31 , further comprising, during each repeating of the (i) constructing, (ii) computing, and (iii) training:
 for a sample having a smallest residual, estimating probabilities that switching to different categorical values would produce a smaller residual according to the cost function; and   for an immediately subsequent repeating of the (i) constructing, (ii) computing, and (iii) training, using sampling rates for the Latin hypercube that are proportional to the estimated probabilities.   
     
     
         33 . The method of  claim 31 , wherein the first design variable is fluid type or material type 
     
     
         34 . The method of  claim 33 , wherein the categorical values for fluid type or material type are selected from a database of materials including single phase gases, liquids, and solids 
     
     
         35 . 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 metric variables for a nuclear reactor, each of the plurality of metric variables measuring a respective thermal-hydraulic property, neutronics property, or stress property; 
 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 threshold value for each of the plurality of metric variables; 
 (i) constructing a Latin hypercube comprising N samples of values for the plurality of design parameters within the initial trust region, wherein N is an integer greater than 1; 
 (ii) computing each of the plurality of metric variables for each of the N samples in the Latin hypercube and applying a cost function to compute a respective residual of the respective metric variable compared to the respective threshold value; 
 (iii) training a machine learning model according to the N samples and the corresponding computed residuals; 
 shrinking the trust region, wherein the respective range for each of the plurality of design variable is shrunk according to a correlation between the respective design variable and estimated residuals using the machine learning model; 
 repeating the (i) constructing, (ii) computing, and (iii) training until a sample having a smallest residual is unchanged for a predetermined number of iterations; 
 using the machine learning model from the final iteration to assess relative importance of each of the plurality of design variables; and 
 providing the assessment visually in a report. 
   
     
     
         36 . The computing system of  claim 35 , wherein the machine learning model is a random forest of decision trees or a neural network for Bayesian optimization. 
     
     
         37 . The computing system of  claim 35 , wherein the machine learning model uses one or more evolutionary methods, including genetic algorithms, coupled simulated anneal algorithms, and/or differential evolutionary algorithms. 
     
     
         38 . The computing system of  claim 35 , wherein one of the plurality of metric variables is the effective neutron multiplication factor (K eff ) 
     
     
         39 . The computing system of  claim 35 , wherein the plurality of design variables includes a first design variable that has discrete categorical values, the method further comprising:
 encoding each distinct categorical value as a numeric value in a continuous range to form a first replacement design variable; and   substituting the first replacement design variable for the first design variable.   
     
     
         40 . The computing system of  claim 39 , further comprising, during each repeating of the (i) constructing, (ii) computing, and (iii) training:
 for a sample having a smallest residual, estimating probabilities that switching to different categorical values would produce a smaller residual according to the cost function; and   for an immediately subsequent repeating of the (i) constructing, (ii) computing, and (iii) training, using sampling rates for the Latin hypercube that are proportional to the estimated probabilities.