Systems and methods for generating reduced order models

Abstract

Systems and methods for generating reduced order models are provided herein. In embodiments, a set of learning points is identified in a parametric space. A 3D physical solver may be used to perform a simulation for each learning point in the set of learning points to generate a learning data set, where the 3D physical solver is selected from a plurality of compatible 3D physical solvers for simulating different physical aspects of a product or process. The learning data set may be compressed to reduce the learning data set to a smaller set of vectors. Coefficients from the learning data set and the smaller set of vectors may then be used to interpolate a set of coefficients within a design space for the reduced order model.

What is claimed is: 
     
         1 . A computer-implemented method comprising:
 identifying a set of design points in a design space for designing a product or process;   generating simulation results as a set of learning data set by simulating a physical aspect of the product or process based on a respective model corresponding to each design point using a physics solver;   compressing the learning data set as an orthonormal set of vectors; and   generating a reduced order model based on the orthonormal set of vectors, the reduced order model to predict simulation results of the physics solver for products or processes corresponding to design points in the design space based on a linear combination of the orthonormal set of vectors.   
     
     
         2 . The computer-implemented method of  claim 1 , further comprising:
 comparing a validation solution from the learning data set with a solution approximated using the reduced order model to determine an accuracy level of the reduced order model.   
     
     
         3 . The computer-implemented method of  claim 2 , further comprising:
 in response to the accuracy level below a desired value, increasing the number of design points, and repeating the operations of generating simulation results, compressing the learning data set, and generating a reduced order model.   
     
     
         4 . The computer-implemented method of  claim 2 , further comprising:
 in response to the accuracy level below a desired value, increasing the number of vectors in the orthonormal set of vectors, and repeating the operations of generating simulation results, compressing the learning data set, and generating a reduced order model.   
     
     
         5 . The computer-implemented method of  claim 1 , wherein the identifying the set of design points comprises using a design of experiments (DoE) sampling operation. 
     
     
         6 . The computer-implemented method of  claim 1 , wherein the physics solver comprises a three-dimensional physical solver. 
     
     
         7 . The computer-implemented method of  claim 1 , wherein the compressing the learning data set comprises using a truncated singular value decomposition (SVD) process. 
     
     
         8 . The computer-implemented method of  claim 1 , wherein the linear combination comprises an interpolation using a genetic aggregation response surface process. 
     
     
         9 . The computer-implemented method of  claim 1 , wherein the generating a reduced order model comprises using mode coefficients from the learning data set and the orthonormal set of vectors. 
     
     
         10 . The computer-implemented method of  claim 1 , wherein the design space is defined by two or more different parameters having respective ranges. 
     
     
         11 . A system comprising:
 a memory storing instructions;   one or more processors coupled to the memory, the one or more processors executing the instructions from the memory to perform a method comprises:   identifying a set of design points in a design space for designing a product or process;   generating simulation results as a set of learning data set by simulating a physical aspect of the product or process based on a respective model corresponding to each design point using a physics solver;   compressing the learning data set as an orthonormal set of vectors; and   generating a reduced order model based on the orthonormal set of vectors, the reduced order model to predict simulation results of the physics solver for products or processes corresponding to design points in the design space based on a linear combination of the orthonormal set of vectors.   
     
     
         12 . The system of  claim 11 , wherein the identifying the set of design points comprises using a design of experiments (DoE) sampling operation. 
     
     
         13 . The system of  claim 11 , wherein the compressing the learning data set comprises using a truncated singular value decomposition (SVD) process. 
     
     
         14 . The system of  claim 11 , wherein the linear combination comprises an interpolation using a genetic aggregation response surface process. 
     
     
         15 . The system of  claim 11 , wherein the generating a reduced order model comprises using mode coefficients from the learning data set and the orthonormal set of vectors. 
     
     
         16 . A non-transitory computer-readable medium storing instructions for commanding one or more processors to perform a method comprising:
 identifying a set of design points in a design space for designing a product or process;   generating simulation results as a set of learning data set by simulating a physical aspect of the product or process based on a respective model corresponding to each design point using a physics solver;   compressing the learning data set as an orthonormal set of vectors; and   generating a reduced order model based on the orthonormal set of vectors, the reduced order model to predict simulation results of the physics solver for products or processes corresponding to design points in the design space based on a linear combination of the orthonormal set of vectors.   
     
     
         17 . The non-transitory computer-readable medium of  claim 16 , wherein the identifying the set of design points comprises using a design of experiments (DoE) sampling operation. 
     
     
         18 . The non-transitory computer-readable medium of  claim 16 , wherein the compressing the learning data set comprises using a truncated singular value decomposition (SVD) process. 
     
     
         19 . The non-transitory computer-readable medium of  claim 16 , wherein the linear combination comprises an interpolation using a genetic aggregation response surface process. 
     
     
         20 . The non-transitory computer-readable medium of  claim 16 , wherein the generating a reduced order model comprises using mode coefficients from the learning data set and the orthonormal set of vectors.