
Variational PhysicsInformed Neural Networks For Solving Partial Differential Equations
Physicsinformed neural networks (PINNs) [31] use automatic differentiat...
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Transfer learning based multifidelity physics informed deep neural network
For many systems in science and engineering, the governing differential ...
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Physics informed deep learning for computational elastodynamics without labeled data
Numerical methods such as finite element have been flourishing in the pa...
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Simulation free reliability analysis: A physicsinformed deep learning based approach
This paper presents a simulation free framework for solving reliability ...
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Plasticity without phenomenology: a first step
A novel, concurrent multiscale approach to meso/macroscale plasticity is...
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An energybased error bound of physicsinformed neural network solutions in elasticity
An energybased a posteriori error bound is proposed for the physicsinf...
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Entropyguided Retinex anisotropic diffusion algorithm based on partial differential equations (PDE) for illumination correction
This report describes the experimental results obtained using a proposed...
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Transfer learning enhanced physics informed neural network for phasefield modeling of fracture
We present a new physics informed neural network (PINN) algorithm for solving brittle fracture problems. While most of the PINN algorithms available in the literature minimize the residual of the governing partial differential equation, the proposed approach takes a different path by minimizing the variational energy of the system. Additionally, we modify the neural network output such that the boundary conditions associated with the problem are exactly satisfied. Compared to conventional residual based PINN, the proposed approach has two major advantages. First, the imposition of boundary conditions is relatively simpler and more robust. Second, the order of derivatives present in the functional form of the variational energy is of lower order than in the residual form. Hence, training the network is faster. To compute the total variational energy of the system, an efficient scheme that takes as input a geometry described by spline based CAD model and employs Gauss quadrature rules for numerical integration has been proposed. Moreover, we utilize the concept of transfer learning to obtain the crack path in an efficient manner. The proposed approach is used to solve four fracture mechanics problems. For all the examples, results obtained using the proposed approach match closely with the results available in the literature. For the first two examples, we compare the results obtained using the proposed approach with the conventional residual based neural network results. For both the problems, the proposed approach is found to yield better accuracy compared to conventional residual based PINN algorithms.
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