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Abstract With the advancement of the computing power and machine learning algorithms, deep learning method has been widely applied in a wide range of fields. In this manuscript, we have developed the deep collocation and energy method fitted to engineering computation and further applied to solve Kirchhoff thin plate bending problems. The deep collocation method, which adopted the physics-informed neural networks, incorporating the strong form governing equations into the loss function, which reduces the solving of thin plate problem into an optimization problem. On the other hand, the deep energy method adopted an energy driven neural networks based on the Principle of Minimum Potential Energy, indicating that of all displacements satisfying given boundary and Equilibrium conditions, the actual displacement is the one that minimizes the total potential energy at stable Equilibrium. Thus, we can build a loss function from the total potential energy. Boundary conditions are penalized to the loss form, which reduced to an unconstrained optimization problem. The physics-informed and energy driven neural networks are based on the universal approximation theorem. Due to the introduction of physical and energy information, the neural networks become difficult to train, an improved two-step optimization algorithm is presented to train the neural network. From numerical results, it is clearly the both models are suitable to solve thin plate bending problems and contributes to they are easy in implementation and is truly “Meshfree”.
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Received: 25 December 2020
Published: 17 June 2021
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2021, Vol. 42 
