Free-form discovery of differential equations

Abstract

Free-form discovery of differential equations for modeling a physical system or process under investigation that includes defining a formal language sentence grammar that describes admissible relationships between quantities, and incorporating the use of such grammar for free-(functional) form, automatic discovery of differential equations. The method requires minimum knowledge of the desired differential equation and is universally applicable to ordinary and partial differential equations. From received training set data representing inputs to the physical system and measured outputs, a numerical error bound data, primitive operators, differential equation operators, variables, coefficients and grammatical rules that define the syntax of valid expressions, the system finds a model characterized by sources of error to find a simplest (minimum complexity) mathematical expression comprising differential operators such that a discrepancy between the observed data and the value of the mathematical expression is bounded, and the mathematical expression is consistent with valid syntax constraints.