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 computational expense of simulating complex relationships between numerous variables, often requiring significant computational power and resulting in reduced accuracy or increased resource consumption.
Innovation Solution
A computer-implemented method that determines an approximated value of a parameter by identifying anchor points, evaluating functions at these points, and generating an approximation function using orthogonal functions or their approximations to reduce computational burden while maintaining accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If the number of approximation calculations is reduced to decrease computational effort, then computational time and resource requirements are reduced, but forecasting accuracy deteriorates
Solution Approach 1:
The patent divides the complex forecasting problem into multiple scenarios, each representing different future states. By segmenting the parameter space and using scenario-based approximation, the system can evaluate fewer points while maintaining accuracy through strategic selection of anchor points that represent entire scenario ranges rather than individual calculations.
Solution Approach 2:
The patent performs preliminary action by pre-calculating and storing approximation functions at anchor points before actual forecasting is needed. These pre-computed approximation functions capture the essential behavior of complex models, allowing rapid forecasting without repeating full calculations while preserving accuracy through the use of these pre-characterized scenarios.
2Measurement precision
If the number of approximation calculations is increased to improve forecasting accuracy, then prediction precision is improved, but computational effort and electrical power consumption increase
Solution Approach 1:
By segmenting the computational domain into discrete scenarios and using anchor points to represent groups of calculations, the patent reduces the total number of individual approximation calculations needed. This segmentation allows accurate forecasting through strategic sampling rather than exhaustive computation, directly reducing energy consumption while maintaining precision.
Solution Approach 2:
The patent creates simplified copies of complex models in the form of approximation functions that are stored and reused. These approximation copies capture the essential behavior of full complex models but require minimal computational resources to evaluate, enabling accurate forecasting with fraction of the original computational and energy requirements.
3Measurement precision
If complex simulation methods are used to model molecular interactions and protein folding, then prediction accuracy is improved, but computational resource requirements increase significantly
Solution Approach 1:
The patent applies segmentation by dividing molecular simulation problems into distinct scenarios representing different molecular configurations, interaction types, or environmental conditions. By creating scenario-based approximation functions for different molecular states, the system achieves accurate predictions of molecular behavior without requiring exhaustive simulation of all possible interactions, thus reducing computational complexity while maintaining scientific accuracy.
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.