Gaussian Process Model Calculation Acceleration
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Solution Overview
Problem
Current data-based function models, particularly Gaussian process models, face challenges in efficiently calculating multiple output values when only one or a few input variables are varied, as they require repetitive calculations for each input value, leading to increased computation time and difficulty in inversion.
Innovation Solution
A method that calculates the sum of terms dependent on non-varying input variables only once, allowing for simultaneous determination of multiple output values by varying one or a few input variables, and enables interpolation for efficient inversion, reducing computational effort and enabling faster calculation of output values.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If multiple output values are calculated by varying one or a few input variables using current data-based function models, then the corresponding variation in the output variable can be ascertained, but the computation time increases significantly due to repetitive calculations for each input value
Solution Approach 1:
The calculation process is segmented into two distinct phases: a first phase that computes common terms independent of the varying input variable(s), and a second phase that computes terms specific to each input variable value. This segmentation allows the common computational work to be performed only once, while the variable-specific computations are performed efficiently for each case, thereby reducing overall computation time while maintaining accuracy.
Solution Approach 2:
The patent applies preliminary action by pre-calculating the sum of terms that do not depend on the varying input variable(s) before the actual variation analysis is performed. This preliminary calculation result is then reused for all subsequent calculations when different values of the varying input variable are tested, eliminating redundant computations and significantly accelerating the process of ascertaining output variable variations.
2Adaptability or versatility
If current data-based function models calculate multiple output values for varying input variables, then inversion of the model becomes possible, but the repetitive calculation operations make the inversion process computationally expensive
Solution Approach 1:
The calculation process is segmented into two distinct phases: a first phase that computes common terms independent of the varying input variable(s), and a second phase that computes terms specific to each input variable value. This segmentation allows the common computational work to be performed only once, while the variable-specific computations are performed efficiently for each case, thereby reducing overall computation time while maintaining accuracy.
Solution Approach 2:
The patent applies preliminary action by pre-calculating the sum of terms that do not depend on the varying input variable(s) before the actual variation analysis is performed. This preliminary calculation result is then reused for all subsequent calculations when different values of the varying input variable are tested, eliminating redundant computations and significantly accelerating the process of ascertaining output variable variations.
Data Source
AI summary
A method for carrying out a calculation of a data-based function model, in particular a Gaussian process model, the data-based function model being defined by predefined hyperparameters and node data, multiple input variables being assigned to one output variable and having a sum of terms, each of which depend on one of the input variables, including the following: determining at least one input variable to be varied, for which multiple output values of a corresponding output variable are to be determined; calculating the sum of the terms, which depend on the input variables not to be varied; providing multiple input values for each of the determined at least one input variable to be varied; and ascertaining multiple output values of the output variable for the provided multiple input values, each based on the calculated sum of the terms, which depend on the input variables not to be varied.