Nonlinear Function Mixing for Physical Phenomenon Modeling Accuracy
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Solution Overview
Problem
Conventional technologies face challenges in improving the accuracy of generating physical phenomenon models from time-series data due to errors in long-term future prediction, multicollinearity issues, and difficulties in optimizing basis function thresholds for each equation, leading to unstable and inaccurate models.
Innovation Solution
An information processing device that generates nonlinear functions based on dependent and independent variables, mixes them to form a linear regression equation, estimates coefficients, calculates the degree of influence, and corrects coefficients to improve model accuracy by targeting the short-term component as the representative value for basis function selection.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional function identification methods are used to generate physical phenomenon models from time-series data, then the modeling process can be completed, but the accuracy of long-term future prediction deteriorates and prediction errors increase
Solution Approach 1:
The patent segments the time-series data into multiple intervals and performs function identification separately for each interval. By dividing the modeling process into segments rather than treating it as a single global model, the method captures local variations in system behavior more accurately, thereby improving both modeling accuracy and long-term prediction reliability without requiring a single complex global model
Solution Approach 2:
The patent performs preliminary selection of candidate basis functions and pre-processing of time-series data before the actual function identification. This preliminary action includes selecting appropriate basis functions that capture essential system characteristics and pre-processing data to remove noise and artifacts, which sets a solid foundation for accurate modeling and reduces prediction errors in long-term forecasts
2Adaptability or versatility
If multiple nonlinear functions are mixed to generate basis functions, then the model can capture complex physical phenomena, but multicollinearity issues arise and model stability deteriorates
Solution Approach 1:
The patent implements feedback mechanisms through iterative optimization processes that monitor model performance and adjust basis function selection accordingly. The method uses feedback from prediction errors and model fit statistics to refine the set of basis functions, removing redundant functions that cause multicollinearity while retaining those that capture essential physical phenomena, thus maintaining both flexibility and stability
Solution Approach 2:
The patent changes parameters such as the number of basis functions, their types, and combination weights to optimize model performance. By systematically varying these parameters and selecting the optimal configuration based on validation criteria, the method achieves a balance between model flexibility for capturing complex phenomena and stability for avoiding multicollinearity issues
3Measurement precision
If basis function thresholds are optimized for each equation, then the model accuracy improves, but the complexity of the modeling process increases and optimization becomes difficult
Solution Approach 1:
The patent develops a universal threshold selection criterion that can be applied across different equations and modeling scenarios. This universal approach uses general principles such as information criteria or cross-validation thresholds that work consistently across multiple equations, eliminating the need to develop and optimize separate thresholding methods for each equation, thus reducing overall process complexity while maintaining accuracy
4Ease of manufacture
If conventional modeling approaches are used, then the process is simple, but the generated models exhibit large prediction errors and reduced accuracy
Solution Approach 1:
The patent implements self-service mechanisms where the modeling process automatically selects appropriate basis functions, determines optimal parameters, and refines the model without requiring extensive manual intervention. The method uses automated algorithms for basis function selection, parameter optimization, and model validation, making the enhanced modeling process as easy to execute as conventional methods while achieving superior accuracy through systematic self-optimization
Data Source
AI summary
According to one embodiment, an information processing device includes a memory and one or more processors. The memory stores time-series data including at least one of dependent and independent variables. The one or more processors are configured to: generate a plurality of nonlinear functions by a plurality of methods based on at least one of the dependent and independent variables; mix the plurality of nonlinear functions to generate a linear regression equation used as a basis function; estimate a coefficient of the linear regression equation; calculate, for a nonlinear function generated by one of the plurality of methods among the plurality of nonlinear functions, a product of the coefficient and a maximum value of the basis function corresponding to the coefficient as a degree of influence; correct the coefficient based on the degree of influence; and output the linear regression equation represented by the corrected coefficient.