Automated Model Discovery via Expression Tree Optimization
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Solution Overview
Problem
Existing mathematical modeling approaches face challenges in accurately representing complex phenomena with limited data, as first-principles methods rely heavily on human intuition and data-driven methods require large datasets, limiting generalizability and extrapolation capabilities.
Innovation Solution
A method that combines data-driven and first-principles-based modeling using stochastic programming and mixed integer non-linear programming to automatically discover both the model functional form and parameters, allowing for a more universal and compact representation of mathematical models through expression trees and optimization of objective functions with constraints.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If first-principles formulations are used to model complex phenomena, then model generality is improved, but model formulation difficulty increases and relies heavily on human intuition
Solution Approach 1:
The system performs automated model discovery by formulating mathematical models autonomously from observational data without requiring human intuition or manual formulation. The algorithm automatically identifies governing equations and parameters, making the modeling process self-service and eliminating dependency on human expertise for model formulation.
Solution Approach 2:
The patent replaces the manual, intuition-based mechanical process of model formulation with an automated computational algorithm. The system uses mathematical programming and optimization techniques to automatically discover model structures and parameters, substituting human cognitive processes with systematic computational methods.
2Ease of operation
If data-driven approaches with generic statistical models are used, then model formulation ease is improved, but model generalizability deteriorates and requires large datasets
Solution Approach 1:
The system changes the parameters of the modeling approach by using automated algorithms that can adapt to different data scenarios. The mathematical programming framework allows flexible adjustment of model complexity and data requirements, enabling the system to achieve good generalizability with limited data by optimizing the balance between model fidelity and complexity.
Solution Approach 2:
The model discovery process is dynamic and adaptive, automatically adjusting model structure and parameters based on the available observational data. The system can dynamically select appropriate model complexities and structures without requiring predetermined assumptions, enabling effective modeling with varying data quantities and qualities.
3Quantity of substance
If data-driven methods are used with limited observational data, then data requirements are reduced, but model accuracy and reliability deteriorate
Solution Approach 1:
The system applies local quality by focusing computational efforts on the most informative aspects of the limited data available. The automated model discovery algorithm identifies and utilizes key patterns and relationships in the observational data more effectively, extracting maximum information from limited samples to build accurate and reliable models.
Data Source
AI summary
Methods and systems for model discovery include forming a mathematical program based on a set of observational data to generate an objective function and one or more constraints. The mathematical program represents a model space as an expression tree comprising operators and operands. The mathematical program is solved by optimizing the objective function subject to the one or more constraints to determine a model in the model space that best fits the set of observational data.