Details
| Translated title of the contribution | The Application of Deep Collocation Method and Deep Energy Method with a Two-step Optimizer in the Bending Analysis of Kirchhoff Thin Plate |
|---|---|
| Original language | Chinese |
| Pages (from-to) | 249-266 |
| Number of pages | 18 |
| Journal | Guti Lixue Xuebao/Acta Mechanica Solida Sinica |
| Volume | 42 |
| Issue number | 3 |
| Publication status | Published - Jun 2021 |
Abstract
With the advancement of computing power and machine learning algorithms, deep learning methods have been widely applied in a wide range of fields. In this manuscript, we develop the deep collocation method and the deep energy method fitted to engineering computation and further apply them to solve the Kirchhoff thin plate bending problems. The deep collocation method adopts the physics-informed neural networks, incorporating the strong-form governing equations into the loss function. It reduces the solving of thin plate problem into an optimization problem. On the other hand, the deep energy method utilizes 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. With the boundary conditions penalized to the loss form, the problem is reduced to an unconstrained optimization one. 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 the numerical results, it is clearly seen that both methods are suitable for solving thin plate bending problems, easy to implement, and truly "meshfree".
Keywords
- Bending, Collocation method, Deep learning, Energy method, Partial differential equations, Thin plate
ASJC Scopus subject areas
- Engineering(all)
- Mechanics of Materials
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In: Guti Lixue Xuebao/Acta Mechanica Solida Sinica, Vol. 42, No. 3, 06.2021, p. 249-266.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - 采用两步优化器的深度配点法与深度能量法求解薄板弯曲问题
AU - Guo, Hongwei
AU - Zhuang, Xiaoying
PY - 2021/6
Y1 - 2021/6
N2 - With the advancement of computing power and machine learning algorithms, deep learning methods have been widely applied in a wide range of fields. In this manuscript, we develop the deep collocation method and the deep energy method fitted to engineering computation and further apply them to solve the Kirchhoff thin plate bending problems. The deep collocation method adopts the physics-informed neural networks, incorporating the strong-form governing equations into the loss function. It reduces the solving of thin plate problem into an optimization problem. On the other hand, the deep energy method utilizes 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. With the boundary conditions penalized to the loss form, the problem is reduced to an unconstrained optimization one. 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 the numerical results, it is clearly seen that both methods are suitable for solving thin plate bending problems, easy to implement, and truly "meshfree".
AB - With the advancement of computing power and machine learning algorithms, deep learning methods have been widely applied in a wide range of fields. In this manuscript, we develop the deep collocation method and the deep energy method fitted to engineering computation and further apply them to solve the Kirchhoff thin plate bending problems. The deep collocation method adopts the physics-informed neural networks, incorporating the strong-form governing equations into the loss function. It reduces the solving of thin plate problem into an optimization problem. On the other hand, the deep energy method utilizes 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. With the boundary conditions penalized to the loss form, the problem is reduced to an unconstrained optimization one. 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 the numerical results, it is clearly seen that both methods are suitable for solving thin plate bending problems, easy to implement, and truly "meshfree".
KW - Bending
KW - Collocation method
KW - Deep learning
KW - Energy method
KW - Partial differential equations
KW - Thin plate
UR - http://www.scopus.com/inward/record.url?scp=85108833991&partnerID=8YFLogxK
U2 - 10.19636/j.cnki.cjsm42-1250/o3.2021.029
DO - 10.19636/j.cnki.cjsm42-1250/o3.2021.029
M3 - Article
AN - SCOPUS:85108833991
VL - 42
SP - 249
EP - 266
JO - Guti Lixue Xuebao/Acta Mechanica Solida Sinica
JF - Guti Lixue Xuebao/Acta Mechanica Solida Sinica
SN - 0254-7805
IS - 3
ER -