Experimental design for symbolic model discovery

An apparatus for selecting at least one new data point through optimal experimental design, the apparatus comprising:

• memory;
• and
• at least one processor operably coupled with the memory, the at least one processor configured:
• to obtain a set of input values in a model discovery process relating to a system under investigation;
• to generate prediction values for a for a set of output values for a given inquiry data point, functional forms along with their respective parameterizations for conducting one or more experiments relating to said system under investigation, wherein said one or more experiments are selected to provide maximum information gained among a plurality of experiments to provide accurate prediction of said output values, the prediction values being used to:
• determine a sequence of action for performing said at least one experiment and selecting one or more instrumentation to perform said at least one experiment and collect data, wherein said instrumentation generates, one or more input parameter inquiry values for a next sequence of experiments;
• and
• determine a plurality of underlying regression models and select at least one of said underlying regression models using data collected from said one or more experiments;
• select an optimal symbolic regression model from the plurality of underlying regression models, wherein the selected optimal symbolic regression model minimizes complexity for a bounded misfit, or minimizes a misfit measure, subject to bounded complexity based on said output values;
• and
• determine a new data point by using said selected optimal symbolic regression model and updating a posterior distribution, given results and data collected from aid one or more experiments relating to the system under investigation to provide informed assessment among a plurality of functional forms and parameterizations to generate said predicted accurate output values.