Symbolic Model Discovery Using Generative Reasoning
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current automated model discovery methods fail to derive mathematical models from data, even when the functional form is explicitly extracted and not embedded in the model, leading to issues with correctness, robustness, generalizability, insight, and scalability.
Innovation Solution
Integrate generative reasoning with symbolic discovery by using a computerized generative reasoner to produce provable conjectures based on background theory, fitting training data to obtain candidate symbolic models, and reducing the search space for prediction using a computerized prediction module.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If symbolic regression approaches are used to infer both the functional form and underlying parameterization, then model discovery capability is improved, but the search space becomes excessively large and computationally intractable
Solution Approach 1:
The patent segments the model discovery process into distinct modules: a generative reasoner that produces candidate symbolic expressions based on background theory, a model inference engine that fits data to these candidates, and a prediction module. This segmentation allows each component to specialize, with the generative reasoner leveraging domain knowledge to produce only physically plausible candidates, thereby dramatically reducing the effective search space while maintaining comprehensive model discovery capability.
2Productivity
If parametric regression methods with predetermined functional form are used, then computational efficiency is improved, but the ability to discover novel functional forms is lost
Solution Approach 1:
The patent applies preliminary action by having the generative reasoner pre-generate candidate symbolic expressions based on background physical theory before the model fitting process. This preliminary generation of theoretically-grounded candidates enables the subsequent fitting process to be computationally efficient, as it only needs to evaluate a limited set of pre-filtered, physically plausible functional forms rather than searching the entire space of possible functions.
3Productivity
If the search space is reduced by providing candidate symbolic models to the prediction module, then productivity is improved, but the risk of missing the correct model increases
Solution Approach 1:
The patent implements feedback through the model inference engine, which systematically evaluates candidate symbolic models by fitting training data to each candidate and assessing the quality of fit. This feedback mechanism ensures that only models with sufficient empirical support are selected, maintaining reliability. Simultaneously, the generative reasoner incorporates domain theory to ensure candidates are physically plausible, creating a dual-filter system that balances speed and correctness.
Data Source
AI summary
Provide a background theory applicable to a scientific problem as input to a computerized generative reasoner, which in turn produces a plurality of provable conjectures applicable to the problem, based on the input. Provide the plurality of provable conjectures and a set of input training data to a computerized model inference engine, which fits the input training data to the plurality of provable conjectures to obtain at least one candidate symbolic model reflecting scientific laws associated with the problem. Reduce a search space of a computerized prediction module by providing to the computerized prediction module at least one candidate symbolic model. Provide new data to the computerized prediction module, which searches in the reduced search space to make a prediction related to the problem based on the new data and the at least one candidate symbolic model.