Forecasting Systems Using Orthogonal Function Approximation
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Solution Overview
Problem
Current forecasting systems face challenges in achieving accurate and timely predictions due to the high computational effort required for complex simulations, often necessitating reduced accuracy or increased resource usage, particularly in fields like molecular biology, structural engineering, and financial modeling.
Innovation Solution
A computer-implemented method determines an approximated value of a parameter by identifying anchor points in the variable domain, evaluating the function at these points, and generating an approximation function using orthogonal functions or their approximations to reduce computational time without sacrificing accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of time
If the number of approximation calculations is reduced to decrease computational effort, then the computational time is reduced, but the accuracy of the forecast deteriorates
Solution Approach 1:
The system performs preliminary approximation calculations at selected anchor points to generate an approximation function (such as a polynomial or orthogonal polynomial) that represents the complex relationship between input variables and output parameters. This pre-computed approximation function can then be evaluated rapidly for any input scenario without requiring full complex calculations, thus reducing computational time while maintaining forecast accuracy.
Solution Approach 2:
The invention creates a simplified copy of the complex simulation model in the form of an approximation function. Instead of running the full complex simulation for every scenario, the system uses the approximation function (which captures the essential behavior of the complex model) to generate forecasts. This copying approach dramatically reduces computational effort while preserving the accuracy characteristics of the original complex model.
2Measurement precision
If the number of approximation calculations is increased to improve accuracy, then the forecast accuracy is improved, but the computational effort and resource requirements increase
Solution Approach 1:
The system segments the computational work into two distinct phases: (1) an offline phase where approximation calculations are performed at a limited number of strategically selected anchor points to build the approximation function, and (2) an online phase where the pre-built approximation function is evaluated rapidly for forecasting. This segmentation allows accurate forecasts to be generated with minimal computational effort during the online phase, while the computationally intensive work is confined to the offline setup phase.
3Measurement precision
If complex simulation methods are used to maintain accuracy, then the forecast accuracy is maintained, but the electrical power and resource requirements increase
Solution Approach 1:
The invention replaces expensive, computationally intensive complex simulation calculations with a cheap, lightweight approximation function that can be evaluated rapidly with minimal computational resources. The approximation function serves as a disposable, low-cost alternative to the expensive complex model, providing sufficient accuracy for forecasting while consuming significantly less electrical power and computational resources.
Data Source
AI summary
A computer-implemented method of determining an approximated value of a parameter in a first domain is described. The parameter is dependent on one or more variables which vary in a second domain, and the parameter is determined by a function which relates sets of values of the one or more variables in the second domain to corresponding values in the first domain. The method is implemented on a computer system including a processor, and the method comprises: determining a plurality of anchor points in the second domain, wherein each anchor point comprises a set of values of the one or more variables in the second domain; evaluating, at each anchor point, the function to generate corresponding values of the parameter in the first domain; generating an approximation function to the function by fitting a series of orthogonal functions or an approximation to a series of orthogonal functions to the corresponding values of the parameter in the first domain; and using the approximation function to generate the approximated value of the parameter in the first domain.