ML Solver Prediction for CFD Matrix Equations
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Solution Overview
Problem
Existing numerical simulation methods for solving matrix equations in computational fluid dynamics (CFD) are inefficient due to their dependency on computationally expensive and time-consuming matrix property calculations, which complicates the selection of optimal solver combinations and increases simulation time.
Innovation Solution
A Machine Learning (ML) based method and system that trains ML models using CFD model parameters to predict the fastest solver combination by eliminating the need for matrix property calculations, utilizing a self-learning mode to continuously update and optimize the model for improved prediction accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If ML models are trained using matrix property calculations, then solver combination prediction is enabled, but computation time and cost increase
Solution Approach 1:
The patent extracts and eliminates the dependency on matrix property calculations from the ML training process. Instead of using matrix properties as input features, the model directly uses CFD problem parameters (geometry, boundary conditions, physical models) to predict solver combinations, removing the time-consuming intermediate step while maintaining prediction accuracy
Solution Approach 2:
The patent performs preliminary action by pre-training the ML model offline using historical CFD data. The model learns the mapping between CFD parameters and optimal solver combinations in advance, so during actual CFD simulations, only fast inference is needed without real-time matrix property calculations
2Productivity
If manual selection of solver combination is performed, then optimal performance can be achieved, but difficulty and time increase
Solution Approach 1:
The patent implements self-service by enabling the ML model to automatically select optimal solver combinations based on CFD problem parameters without human intervention. The model independently analyzes problem characteristics and recommends appropriate solver-preconditioner-smoother combinations, making the system self-sufficient in solver selection tasks
Solution Approach 2:
The patent changes the approach from manual parameter selection to automated parameter prediction. By transforming solver selection into a parameter prediction problem using ML, the system automatically determines optimal solver combinations based on learned patterns from training data, eliminating manual difficulty
3Extent of automation
If existing ML approaches are used, then automation is achieved, but dependency on matrix properties remains
Solution Approach 1:
The patent extracts and removes the dependency on matrix property calculations from the automated solver selection process. The model directly maps CFD problem parameters to solver combinations without requiring matrix properties as intermediate features, simplifying the overall methodology while maintaining automation
Data Source
AI summary
Machine Learning approaches in literature for determining optimal solver-preconditioner-smoother for solving matrix equations in computer modelling of any systems are directly dependent on matrix property calculation as an intermediate step. However, in CFD domain, this matrix system is generated from simulation input parameters. Also, part of simulation parameter's relation with the matrix equations can be derived from the theory. Embodiments of the present disclosure provide a method and system for prediction of fastest solver combination for solution of matrix equations during CFD simulations. The system trains a Machine Learning (ML) model using a set of relevant input parameters, based on domain knowledge of a CFD problem of interest, as a plurality of input features. The ML model is a multi-class classification model for the prediction of solver combination taking the CFD simulation parameters as an input.