Mesh generation remains a key technology in many areas where numerical simulations are required. As numerical algorithms become more efficient and computers become more powerful, the percentage of time devoted to mesh generation becomes higher. In this paper, we present an improved structured mesh generation method. The method formulates the meshing problem as a global optimization problem related to a physics-informed neural network. The mesh is obtained by intelligently solving the physical boundary-constrained partial differential equations. To improve the prediction accuracy of the neural network, we also introduce a novel auxiliary line strategy and an efficient network model during meshing. The strategy first employs a priori auxiliary lines to provide ground truth data and then uses these data to construct a loss term to better constrain the convergence of the subsequent training. The experimental results indicate that the proposed method is effective and robust. It can accurately approximate the mapping (transformation) from the computational domain to the physical domain and enable fast high-quality structured mesh generation.

Computational fluid dynamics (CFD) plays a critical role in many scientific and engineering applications, with aerodynamic design optimization being a primary area of interest. Recently, there has been much interest in using artificial intelligence approaches to accelerate this process. One promising method is the graph convolutional neural network (GCN), a deep learning method based on artificial neural networks (ANNs). In this paper, we propose a novel GCN-based aerodynamic design optimization acceleration framework, GCN-based aerodynamic design optimization acceleration framework. The framework significantly improves processing efficiency by optimizing data flow and data representation. We also introduce a network model called GCN4CFD that uses the GCF framework to create a compact data representation of the flow field and an encoder–decoder structure to extract features. This approach enables the model to learn underlying physical laws in a space-time efficient manner. We then evaluate the proposed method on an airfoil aerodynamic design optimization task and show that GCN4CFD provides a significant speedup compared to traditional CFD solvers while maintaining accuracy. Our experimental results demonstrate the robustness of the proposed framework and network model, achieving a speedup average of [Formula: see text].

Computational Fluid Dynamics (CFD) plays a crucial role in investigating new physical phenomena and exploring the principles of fluid mechanics. However, CFD numerical methods often face the challenges of long research cycles, high costs, and extensive human-computer interactions due to the growing complexity of computational tasks. To meet the burgeoning requirements of contemporary physical sciences, in recent years, the coupling of traditional scientific computing techniques with promising deep learning techniques well-known from computer science have emerged as a new research paradigm. This paradigm aims to create automated, intelligent tools for obtaining valuable insights as well as being able to categorize, predict, and make evidence-based decisions in novel ways. These tools can be used to reduce the reliance on expert experience and laborious computations inherent in existing numerical theories and methods. In this paper, we delve into the essence of science paradigms, the evolution of computing intelligence, and provide a comprehensive overview of the key applications driving the development of a new intelligence paradigm in CFD simulations. In addition, we outline a prototype platform for CFD simulations within this new paradigm. Based on this platform, three intelligent workflows are proposed, anticipating to serve as a reference source for future research and foster the emergence of innovative applications in the field of CFD.Highlights Deep learning techniques emerged as a new method to create automated, intelligent tools for CFD simulations.A review of deep learning methods for mesh pre-processing.A review of deep learning methods for numerical solving.A review of deep learning methods for post-processing visualization.A prototype platform for CFD simulations within the new paradigm.Perspectives on challenges and future directions.

Physics-informed neural networks (PINNs) have emerged as promising surrogate modes for solving partial differential equations (PDEs). Their effectiveness lies in the ability to capture solution-related features through neural networks. However, original PINNs often suffer from bottlenecks, such as low accuracy and non-convergence, limiting their applicability in complex physical contexts. To alleviate these issues, we proposed auxiliary-task learning-based physics-informed neural networks (ATL-PINNs), which provide four different auxiliary-task learning modes and investigate their performance compared with original PINNs. We also employ the gradient cosine similarity algorithm to integrate auxiliary problem loss with the primary problem loss in ATL-PINNs, which aims to enhance the effectiveness of the auxiliary-task learning modes. To the best of our knowledge, this is the first study to introduce auxiliary-task learning modes in the context of physics-informed learning. We conduct experiments on three PDE problems across different fields and scenarios. Our findings demonstrate that the proposed auxiliary-task learning modes can significantly improve solution accuracy, achieving a maximum performance boost of 96.62% (averaging 28.23%) compared to the original single-task PINNs. The code and dataset are open source at https://github.com/junjun-yan/ATL-PINN.

Partial differential equations (PDEs) are an essential computational kernel in physics and engineering. With the advance of deep learning, physics-informed neural networks (PINNs), as a mesh-free method, have shown great potential for fast PDE solving in various applications. To address the issue of low accuracy and convergence problems of existing PINNs, we propose a self-training physics-informed neural network, ST-PINN. Specifically, ST-PINN introduces a pseudo label based self-learning algorithm during training. It employs governing equation as the pseudo-labeled evaluation index and selects the highest confidence examples from the sample points to attach the pseudo labels. To our best knowledge, we are the first to incorporate a self-training mechanism into physics-informed learning. We conduct experiments on five PDE problems in different fields and scenarios. The results demonstrate that the proposed method allows the network to learn more physical information and benefit convergence. The ST-PINN outperforms existing physics-informed neural network methods and improves the accuracy by a factor of 1.33x-2.54x.

In CFD, mesh smoothing methods are commonly utilized to refine the mesh quality to achieve high-precision numerical simulations. Specifically, optimization-based smoothing is used for high-quality mesh smoothing, but it incurs significant computational overhead. Pioneer works improve its smoothing efficiency by adopting supervised learning to learn smoothing methods from high-quality meshes. However, they pose difficulty in smoothing the mesh nodes with varying degrees and also need data augmentation to address the node input sequence problem. Additionally, the required labeled high-quality meshes further limit the applicability of the proposed method. In this paper, we present GMSNet, a lightweight neural network model for intelligent mesh smoothing. GMSNet adopts graph neural networks to extract features of the node's neighbors and output the optimal node position. During smoothing, we also introduce a fault-tolerance mechanism to prevent GMSNet from generating negative volume elements. With a lightweight model, GMSNet can effectively smoothing mesh nodes with varying degrees and remain unaffected by the order of input data. A novel loss function, MetricLoss, is also developed to eliminate the need for high-quality meshes, which provides a stable and rapid convergence during training. We compare GMSNet with commonly used mesh smoothing methods on two-dimensional triangle meshes. The experimental results show that GMSNet achieves outstanding mesh smoothing performances with 5% model parameters of the previous model, and attains 13.56 times faster than optimization-based smoothing.

Sparse Matrix-Vector Multiplication (SpMV) plays a critical role in many areas of science and engineering applications. The storage space of value array in general real sparse matrices accounts for costly. However, the existing compressed formats cannot balance the compressed rate and computational speed. To address this issue, we propose an efficient value compression format implemented by AVX512 instructions called Compressed Sparse Row and Repetition Value (CSR RV). This format stores each different value once and uses the indexes array to store the position of values, which reduces the storage space by compressing the value array. We conduct a series of experiments on an Intel Xeon processor and compare it with five other formats in 30 real-world matrices. Experimental results show that CSR RV can achieve a speedup up to 3.86 × (1.66 × on average) and a speedup up to 12.42 × (3.12 × on average) for single-core and multi-core throughput, respectively. Meanwhile, our format can reduce the memory space by 48.57