This work proposes to train an attention graph neural network by minimizing the finite-volume method (FVM) residuals of the governing equations to provide a practical training signal for neural surrogates and reduce the model development cost.
Abstract
Neural surrogates are widely used in scientific machine learning for fast prediction of three-dimensional (3D) thermo-fluid fields. However, generating training data using conventional numerical solvers often incurs substantial computational and storage costs. We propose to train an attention graph neural network by minimizing the finite-volume method (FVM) residuals of the governing equations. These residuals are evaluated directly on the mesh, requiring no labeled data. We evaluate the trained surrogates against computational fluid dynamics (CFD) references and a data-supervised baseline across four scenarios. On the two steady-state benchmarks, the FVM-loss model achieves an all-field normalized root-mean-square error (nRMSE) of 2.3-2.8%. It demonstrates close agreement with the CFD references, including the buoyancy-energy coupling. On the two parametric transient cases, the FVM-loss model outperforms the supervised baseline in terms of accuracy, while avoiding the data-generation cost entirely. These results indicate that the FVM loss can provide a practical training signal for neural surrogates and reduce the model development cost.
The growing application of physics-informed neural networks (PINNs) for solving parametric partial differential equations (PDEs) in fluid dynamics has demonstrated their potential for modeling complex multiscale flows; however, conventional PINNs often exhibit spectral bias and slow, unstable convergence, limiting accuracy in boundary layers and wakes. This research presents novel physics-informed feature decomposition in residual dense block neural networks (PI-RDB-NN), which embeds physical constraints directly into the network architecture rather than relying solely on soft constraints. PI-RDB-NN uses hierarchical residual dense blocks for multi-scale feature extraction, allocates feature channels to velocity and pressure in a 2:1 ratio consistent with two-dimensional incompressible Navier–Stokes physics, and enforces mass conservation via a learnable divergence-aware projection applied at the feature level. The model is evaluated on National Advisory Committee for Aeronautics (NACA) 0012 airfoil flow at Reynolds numbers (Re)=5000 and Re=1000 using a hybrid loss combining PDE residuals, boundary conditions, and sparse computational fluid dynamics (CFD) data. PI-RDB-NN reduces PDE residual and divergence error by 91.2% and 71.7% vs traditional PINNs (Re=5000) and by 85.5% and 85.4% vs a physics-informed Deep Operator Network (DeepONet) baseline (Re=1000). These physics consistency gains improve aerodynamic force predictions and CFD agreement, confirmed by velocity, wake, and pressure coefficient (Cp) distributions. Consistent accuracy across both Reynolds regimes supports the framework's generality, with three-dimensional and unsteady extensions identified as future work.
Sarmad Iftikhar, Ishfaq Ahmad, Diltaj Ali et al.· The Physics of Fluids· 0 citations
Physics-informed neural networks (PINNs) have emerged as a compelling pathway toward trustworthy artificial-intelligence-based computational fluid dynamics (CFD) by embedding governing equations directly into the learning process. Many existing AI flow models require large simulation or experimental datasets and often remain problem-specific, limiting their generalization and physical reliability. Data-free PINN frameworks offer an alternative by learning flow solutions from the Navier-Stokes equations and prescribed boundary conditions, potentially reducing dependence on expensive CFD datasets while retaining physical consistency. However, traditional PINN frameworks have struggled at high Reynolds numbers, limiting their application in CFD. In this work, we present NeuralFlowNet, a data-free, physics-informed proof-of-concept framework designed to solve steady Navier-Stokes problems across low- to high-Reynolds-number conditions. We describe the proposed methodological framework and demonstrate its applicability using benchmark problems with increasing physical and geometric complexity. The results demonstrate that NeuralFlowNet can accurately recover steady flow fields across a broad Reynolds-number range, including cases with strong pressure gradients, without training on external flow-field data and while maintaining good agreement with reference numerical solutions. These findings establish NeuralFlowNet as a reliable framework for future testing of unsteady and more complex simulations and could provide a basis for developing trustworthy and efficient AI solvers for high-Reynolds-number fluid dynamics.
Jayanga T. Samarasinghe, Luis A. de la Fuente, Laura V. Alvarez· 0 citations
We present a physics-informed, data-free neural solver for partial differential equations, built on a graph neural network architecture that utilises message passing. By relying on the weak form of the problem, we use gradients of finite-element shape functions (which are therefore polynomials) rather than automatic differentiation operators to compute the residuals of the equation from the displacements predicted by the network itself. Our approach generalises to previously unseen load cases and geometries, achieving easily convergence errors in the residuals of less than 1% and being capable of scaling up to models of considerable size and arbitrary geometries. To ensure compliance with the laws of physics and provide guarantees regarding the inference, it is possible to use the residual itself as an error indicator for the inference, and thus perform a refinement at the testing stage if the residual tolerance set in advance by the user is not met. Examples are provided to demonstrate the performance of the proposed method. This results in a method that avoids the costly process of obtaining, curating and storing high-fidelity synthetic data for training the neural network. Whilst this is not unique to our method, it is the first time it has been combined with a geometric machine learning technique capable of providing the necessary geometric bias to overcome the well-known difficulties of physics-informed neural networks.
Mikel M. Iparraguirre, Icíar Alfaro, David González et al.· arXiv.org· 0 citations
Full three-dimensional gear-contact analysis resolves localized tensor fields that simplified models cannot recover, but repeated nonlinear finite element (FE) solutions are costly. This study develops a multi-fidelity physics-informed graph surrogate combining a coarse learning graph, peak-sensitive KDTree projection, gated message passing, and a regularized least-squares finite-difference equilibrium residual. The stress-prior-conditioned benchmark uses a coarse prior derived from the same high-fidelity FE field and therefore is not label-free. Across five random seeds on the 750-case test split, it yields NMSE = (9.1 ± 0.4) × 10−5, R2 = 0.985 ± 0.001, and peak-stress error = 2.5 ± 0.2%. A geometry-only gate provides a preliminary label-free result, with 4.1% peak-stress error for seed 42; its complete multi-seed metrics were not retained. One conditioned forward pass requires 42 ms, excluding preprocessing and prior construction, and peak training memory is 47.6 GB on the reported hardware. Maximum projection outperforms distance-weighted averaging at one fixed graph resolution. All targets are simulated, so the method is presented as a numerical FE surrogate rather than an experimentally validated digital-twin replacement.
A Physics-Informed Neural Network framework for a tractable chemo-fluidic continuum model of tumor growth that couples an advection-diffusion-reaction (ADR) equation for the tumor volume fraction with a quasi-static Darcy pressure equation for the interstitial fluid pressure is introduced.
Celia Taboada, Pedro Navas, M. Molinos· 0 citations
Grid-based fluid dynamics solvers routinely struggle with exhaustive meshing demands and ill-posed inverse problems. A practical mesh-free alternative is given by Physics-informed neural networks (PINNs) but, applying them to highly elastic Oldroyd-B fluids results in many training failures. The High Weissenberg Number Problem (HWNP), driven by the exponential stress growth near stagnation points is a major issue, which causes standard PINN optimizers to diverge. To prevent the network from crashing, we apply a Cholesky decomposition to the conformation tensor. This mathematical constraint stabilizes the gradients by guaranteeing a positive-definite stress field. Beyond mathematical stability, the inherent spectral bias of deep learning models can hinder the network from accurately capturing the highly elastic wake structures. Therefore, we used sparse data assimilation to force the model toward the actual physical solution. By anchoring the physics loss with targeted CFD data points and accelerating training via transfer learning, we successfully pushed the network past non-physical local minima. We validated this Cholesky-PINN approach on flow past cylindrical geometries for Reynolds numbers (Re) between 5-25, for the single-cylinder setup. In addition, the relaxation time ({\lambda}) is increased from 0.1 to 0.5 to test the stability of the network. Finally, we scale the framework to a complex 3-cylinder array which proved our constructive solid geometry approach completely bypasses the tedious re-meshing steps of traditional CFD. The combined framework accurately captured sharp viscoelastic wakes, providing a stable computational tool for complex rheological modeling.
Midhuna Suresh, Akanksha Gupta· 0 citations
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