Symbolic Model Discovery via Optimal Experimental Design

The patent performs preliminary analysis of existing data to identify which functional forms are plausible before conducting additional experiments. By pre-assessing the data to determine whether linear, quadratic, or other functional forms are supported, the method avoids conducting experiments that would not contribute to model discovery, thereby reducing unnecessary experimental cost and effort while maintaining reliability.

The patent implements an iterative feedback loop where experimental results are continuously analyzed to update the set of plausible functional forms. After each experiment, the method reassesses which functional forms remain consistent with the accumulated data and adjusts subsequent experimental design accordingly. This feedback mechanism ensures that experiments are directed toward resolving specific ambiguities in model structure, improving reliability while minimizing redundant experiments.

The patent employs a dynamic approach where the set of considered functional forms is not fixed but evolves iteratively based on experimental results. The method maintains a plurality of candidate functional forms (e.g., linear, quadratic, exponential) and dynamically updates which forms remain plausible as new data becomes available. This dynamic adaptation allows the system to maintain low initial complexity while progressively discovering the true model structure without requiring all functional forms to be predetermined.

The patent changes the parameter of functional form selection based on experimental evidence. Rather than committing to a single pre-defined functional form, the method treats the functional form itself as a parameter that can be updated as experiments proceed. By analyzing whether data supports linear, quadratic, or other relationships and adjusting the set of plausible functional forms accordingly, the system achieves both simplicity in individual experimental designs and adaptability in overall model discovery.

The patent segments the model discovery process into distinct phases: (1) identifying plausible functional forms from existing data, (2) determining parameter values for selected functional forms, and (3) validating models against new experimental data. This segmentation allows the method to efficiently use data-driven approaches for initial model identification while maintaining the ability to interpret and validate models structurally, thereby preserving both scalability and predictive power.

The patent introduces experimental design as an intermediary between raw data and final model selection. Rather than directly deriving models from large datasets, the method uses carefully designed experiments as intermediaries to probe specific aspects of system behavior. This intermediary approach enables efficient model derivation while ensuring that discovered models have predictive power by explicitly testing them against targeted experimental results rather than relying solely on training data patterns.