Sparse Gaussian Process Model for Engine Control Unit
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Solution Overview
Problem
Conventional Gaussian process models require large amounts of training data for efficient regression analysis, leading to high computational costs and memory inefficiencies, particularly in engine control units where resource optimization is crucial.
Innovation Solution
A method for determining a sparse Gaussian process model using a hardware-based model calculation unit, where virtual supporting point data points are generated and a parameter vector is calculated via Cholesky decomposition of covariance matrices, reducing the number of required data points and enabling more efficient storage and analysis.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional Gaussian process models use large amounts of training data for regression analysis, then measurement precision is improved, but device complexity and memory requirements increase
Solution Approach 1:
The patent extracts only the essential supporting point data from the complete training data set. By identifying and retaining only the critical data points needed for accurate regression analysis, the method reduces the data volume from N training points to M supporting points (where M << N), thereby reducing computational complexity while preserving measurement precision
Solution Approach 2:
The patent segments the training data into two distinct components: supporting point data (M points) and virtual supporting point data (generated via pseudo-inputs). This segmentation allows the model to use only the essential supporting points for computation while deriving virtual points to maintain accuracy, effectively separating critical information from redundant data
2Measurement precision
If conventional Gaussian process models store large training data sets, then measurement precision is improved, but memory efficiency deteriorates
Solution Approach 1:
The patent extracts and stores only the M supporting point data points from the N training data points. This extraction reduces the storage requirement from O(N) to O(M) where M is much smaller than N, while the model accuracy is maintained through the use of these critical supporting points combined with virtual supporting points generated during inference
Solution Approach 2:
The patent generates virtual supporting point data through pseudo-inputs that copy the essential characteristics of the full training data distribution. These virtual points are synthesized during the prediction phase to represent the information contained in the full training set without requiring storage of the actual training data, enabling accurate predictions with minimal storage
3Measurement precision
If conventional Gaussian process models process large training data sets, then measurement precision is improved, but processing speed decreases
Solution Approach 1:
The patent extracts only the M supporting point data points from N training points for the computation of the covariance matrix and its decomposition. This reduces the computational complexity from O(N³) to O(M³) for the matrix operations, significantly accelerating processing speed while maintaining prediction accuracy through the careful selection of supporting points and use of virtual supporting points
Solution Approach 2:
The patent performs preliminary computation of the covariance matrix QM and its Cholesky decomposition Lm using only the M supporting points during the offline training phase. This preliminary action prepares the model for fast online predictions, avoiding the need to process the full N training points during real-time inference, thus improving computational speed while maintaining precision
Data Source
AI summary
A method for determining a sparse Gaussian process model to be carried out in a solely hardware-based model calculation unit includes: providing supporting point data points, a parameter vector based thereon, and corresponding hyperparameters; determining or providing virtual supporting point data points for the sparse Gaussian process model; and determining a parameter vector Qy* for the sparse Gaussian process model with the aid of a Cholesky decomposition of a covariant matrix KM between the virtual supporting point data points and as a function of the supporting point data points, the parameter vector based thereon, and the corresponding hyperparameters, which define the sparse Gaussian process model.