Symbolic Model Discovery Rectification via Partial Expression Trees
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Solution Overview
Problem
Mis-specified symbolic models often lead to erroneous predictions and suboptimal decisions due to noise factors, including epistemic and aleatory errors, which are not effectively addressed by existing technologies.
Innovation Solution
The method involves generating partial expression trees from a mis-specified symbolic model, solving optimization problems for each tree, and determining a refined model that minimizes prediction error while maintaining bounded complexity, numerical parameters, and functional form differences, adhering to symbolic grammatic constraints, resulting in a higher fidelity model.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If a mis-specified symbolic model is used, then model complexity is reduced, but prediction accuracy deteriorates due to noise factors
Solution Approach 1:
The patent introduces an intermediary refinement process that takes a mis-specified symbolic model and transforms it into a refined model. This intermediary process uses optimization algorithms to adjust the model's parameters and structure, mediating between the simplicity of the original model and the accuracy requirements of the target system.
Solution Approach 2:
The patent systematically changes model parameters through optimization techniques. By adjusting parameters within bounded complexity distances and maintaining constrained functional forms, the method improves prediction accuracy while preserving the underlying simplicity of the original mis-specified model structure.
2Measurement precision
If model refinement is performed to reduce prediction error, then prediction accuracy improves, but model complexity increases
Solution Approach 1:
The patent applies partial refinement by performing optimization within bounded complexity distances from the original model. Rather than completely re-specifying the model, the method performs partial adjustments to parameters and structure, achieving sufficient accuracy improvement without excessive complexity increase.
Solution Approach 2:
The optimization process uses feedback from prediction errors to iteratively refine the model. By continuously measuring prediction accuracy and adjusting parameters accordingly within constrained boundaries, the method achieves improved accuracy while preventing unbounded complexity growth through the bounded complexity distance constraint.
3Ease of operation
If the refined model maintains bounded complexity distance from the mis-specified model, then model interpretability is preserved, but the ability to capture complex phenomena is limited
Solution Approach 1:
The patent segments the model refinement process into constrained components: bounded complexity distance constraints, numerical parameters difference constraints, and functional form difference constraints. This segmentation allows the model to maintain interpretability through structural similarity while capturing complex phenomena through parameter adjustments within each segmented constraint.
Data Source
AI summary
A method for obtaining a refined model given a mis-specified symbolic model. The method includes receiving a mis-specified symbolic model and data pertaining to a process or phenomenon corresponding to the mis-specified symbolic model; receiving one or more constraints; generating a plurality of partial expression trees based on the mis-specified symbolic model; solving an optimization problem for each of the partial expression trees; and determining a refined symbolic model of the mis-specified symbolic model based on results of the optimization problem for each partial expression tree.