NUMERICAL SOLUTION OF SIMULTANEOUS IDENTIFICATION OF COEFFICIENT AND COEFFICIENT AND INITIAL VALUE FOR ONE DIMENSIONAL HEAT CONDUCTION EQUATION BASED ON LOCAL OBSERVATION DATA
NUMERICAL SOLUTION OF SIMULTANEOUS IDENTIFICATION OF COEFFICIENT AND COEFFICIENT AND INITIAL VALUE FOR ONE DIMENSIONAL HEAT CONDUCTION EQUATION BASED ON LOCAL OBSERVATION DATA
The simultaneous inversion of coefficient and initial values for one-dimensional heat conduction equation is studied using local observation data.Firstly,the uniqueness of the simultaneous identification of coefficient and initial values is proved by using function substitution and analytic continuation technique of the solutions of parabolic equation based on the local observation data.Then,based on deep neural network,the inversion algorithm of simultaneous inversion problem is constructed.Finally,numerical examples with and without analytical solutions are constructed to verify the effectiveness of the inversion algorithm.
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