How does physics-informed deep learning improve the accuracy of incompressible laminar flow simulations compared to traditional methods?
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Physics-informed deep learning, such as Physics-Informed Neural Networks (PINNs), enhances the accuracy of incompressible laminar flow simulations compared to traditional methods by leveraging deep neural networks and incorporating physical laws as constraints . PINNs utilize the Navier-Stokes equation and boundary conditions as losses in the neural network training, eliminating the need for extensive simulation or experimental data. Additionally, the adaptive gradient descent algorithm (AGDA) optimizes the training process by balancing loss function gradients and resolving gradient direction conflicts, leading to more efficient and robust solutions for partial differential equations of flow problems. This approach not only improves accuracy but also reduces computational costs, memory usage, and training time compared to traditional computational fluid dynamics methods .
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| Papers (5) | Insight |
|---|---|
1 Citations | Physics-informed neural networks (PINNs) enhance accuracy in incompressible laminar flow simulations by utilizing Navier-Stokes equations as losses, requiring no simulation data, and showing improved performance with increased network complexity. |
| Physics-informed deep learning, specifically the AV-augmented PINN, enhances accuracy in incompressible flow simulations by stabilizing high Reynolds number flows, as shown in cavity flow and film boiling cases. | |
| Physics-informed deep learning enhances traffic flow model calibration, yielding comparable or superior results to optimization-based methods, as demonstrated in the study on I-210 E in California. | |
| Physics-informed neural networks with adaptive gradient descent enhance accuracy in incompressible laminar flow simulations by reducing training time and iterations compared to traditional methods like Adam optimizer. | |
| Physics-informed deep learning enhances accuracy in incompressible laminar flow simulations by incorporating physics constraints into neural networks, as demonstrated in the melting heat transfer analysis with transfer learning. |
Related Questions
How does physics-informed deep learning compare to traditional methods for modeling flow and transport in porous media?5 answersPhysics-informed deep learning, exemplified by models like PI-DeepONets and P-PINN, offers significant advantages over traditional numerical methods for simulating flow and transport in porous media. These deep learning models learn the mapping between flux functions and solutions accurately, predict 3D velocity fields efficiently, and handle uncertainty quantification effectively. Compared to traditional methods, physics-informed deep learning eliminates the need for expensive data generation processes, achieves up to four orders of magnitude faster solutions, and demonstrates excellent generalization qualities. Additionally, these models can predict pressure variations in subsurface flows without relying on numerical schemes, outperforming various machine learning methods. Overall, physics-informed deep learning stands out for its speed, accuracy, and robustness in modeling flow and transport in porous media.
How does physics-informed deep learning for CFD?5 answersPhysics-informed deep learning is a powerful tool in computational fluid dynamics (CFD) for solving nonlinear differential equations. By incorporating physics constraints into neural networks, such as in the presented adaptive deep collocation method (DCM), the accuracy and efficiency of models can be significantly improved. This approach eliminates the need to convert nonlinear differential equations into initial value problems, addressing convergence issues seen in conventional methods. Additionally, physics-informed neural networks can be used to solve both forward and inverse problems by integrating partial differential equations into loss functions, as demonstrated in modeling coseismic crustal deformation. These methods showcase the potential of deep learning in accurately capturing complex fluid dynamics phenomena while maintaining computational efficiency.
What is the first paper on physics-informed neural networks?5 answersThe first paper on physics-informed neural networks (PINNs) was proposed by Raissi et al. in 2019. PINNs aim to address the challenge of missing data in complex systems by incorporating physical knowledge into neural network training, enabling the approximation of differential equations through unsupervised learning. PINNs differ from traditional neural networks by integrating physical information directly into the activation functions, allowing for training with only boundary/initial data. This innovative approach has paved the way for solving various partial differential equations (PDEs) efficiently and accurately, demonstrating the potential of AI strategies in tackling problems where classical methods fall short.
Can physics-informed neural networks be used to solve fluid dynamics problems?5 answersPhysics-informed neural networks (PINNs) can be used to solve fluid dynamics problems. PINNs are deep neural networks that use the Navier-Stokes equation and boundary conditions as losses, eliminating the need for simulation or experimental data in training. PINNs have been successfully applied to solve forward and inverse problems in fluid mechanics, including problems with large spatiotemporal domains and high Reynolds numbers. PINNs have also been explored for unsteady flows past moving bodies, such as flapping wings, using an immersed boundary aware framework. Additionally, PINNs have been used to solve free-surface flow problems governed by the shallow water equations, providing accurate predictions with a better trade-off between computational speed and accuracy compared to finite volume models.
How can physics-informed neural networks be useful in computational geomechanics?5 answersPhysics-informed neural networks (PINNs) have shown promise in computational geomechanics. PINNs can adapt to changes in geometry and mesh definitions, allowing for generalization across different shapes. They have been used to simulate fluid flows in complex geometries, such as 3D Y-shaped mixers, resulting in higher accuracy compared to classical neural networks. PINNs have also been applied to solve the partial differential equation governing the thermo-poro-mechanical behavior of shear bands in deep-seated landslides. By training a deep neural network with synthetic data, PINNs can estimate the temperature inside the shear band and forecast the stability of landslides in real-time. PINNs, along with other neural operators like Deep Operator Networks, Fourier neural operators, and graph neural operators, have been used as surrogates in design problems, uncertainty quantification, and autonomous systems in computational mechanics, including geomechanics.
How can physics-informed neural networks be used to minimize worst-case violations in DC optimal power flow?3 answersPhysics-informed neural networks can be used to minimize worst-case violations in DC optimal power flow by integrating the AC power flow equations into neural network training and implementing methods to rigorously determine and reduce constraint violations across the entire input domain while maintaining prediction optimality. These networks exploit the existing models of the underlying physical systems to generate higher accuracy results with fewer data, reducing computation time and building trust among power system operators. By formulating mixed-integer linear programs, worst-case guarantees for neural network predictions related to constraint violations, distances between predicted and optimal decision variables, and sub-optimality can be obtained. Training on a larger input domain than the evaluation domain can systematically reduce worst-case guarantees. Physics-informed neural networks offer high accuracy and faster determination of dynamic states in power systems compared to conventional methods.