Neural operator modeling method based on differential homeomorphic mapping network and application thereof

Abstract

The invention discloses a neural operator modeling method based on a differential homeomorphic mapping network and application of the neural operator modeling method, belongs to the technical field of artificial intelligence and computational mechanics, is used for describing rapid solution of a partial differential equation of a physical relationship in a part machining deformation process in different complex part geometric domains, and comprises the following steps: inputting an original geometric domain # imgabs0 # of an input function into a model; the # imgabs 1 # is geometrically characterized as # imgabs 2 #; the # imgabs3 # in different geometric domains is mapped to a reference domain # imgabs4 # through a differential homeomorphic neural network, and a # imgabs5 # is obtained; constructing a neural operator in a reference geometric domain # imgabs6 #, establishing a mapping relation between an input function and an output function of a partial differential equation, and solving the partial differential equation under different geometric domains; according to the method and the application thereof provided by the invention, the neural operator fits the relationship between the partial differential equation input function and the solution function, and is applied to scenes such as a part residual stress field prediction deformation field.

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