A comprehensive review of advances in physics-informed neural networks and their applications in complex fluid dynamics

Physics of Fluids, Journal Year: 2024, Volume and Issue: 36(10)

Published: Oct. 1, 2024

Physics-informed neural networks (PINNs) represent an emerging computational paradigm that incorporates observed data patterns and the fundamental physical laws of a given problem domain. This approach provides significant advantages in addressing diverse difficulties field complex fluid dynamics. We thoroughly investigated design model architecture, optimization convergence rate, development modules for PINNs. However, efficiently accurately utilizing PINNs to resolve dynamics problems remain enormous barrier. For instance, rapidly deriving surrogate models turbulence from known characterizing flow details multiphase fields present substantial difficulties. Additionally, prediction parameters multi-physics coupled models, achieving balance across all scales multiscale modeling, developing standardized test sets encompassing dynamic are urgent technical breakthroughs needed. paper discusses latest advancements their potential applications dynamics, including turbulence, flows, multi-field flows. Furthermore, we analyze challenges face these outline future trends growth. Our objective is enhance integration deep learning facilitating resolution more realistic problems.

Language: Английский

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A deep learning approach: physics-informed neural networks for solving a nonlinear telegraph equation with different boundary conditions

BMC Research Notes, Journal Year: 2025, Volume and Issue: 18(1)

Published: Feb. 19, 2025

The nonlinear Telegraph equation appears in a variety of engineering and science problems. This paper presents deep learning algorithm termed physics-informed neural networks to resolve hyperbolic telegraph with Dirichlet, Neumann, Periodic boundary conditions. To include physical information about the issue, multi-objective loss function consisting residual governing partial differential initial conditions is defined. Using multiple densely connected networks, feedforward proposed scheme has been trained minimize total results from function. Three computational examples are provided demonstrate efficacy applications our suggested method. Python software package, we conducted several tests for various model optimizations, activation functions, network architectures, hidden layers choose best hyper-parameters representing problem's optimal solution. Furthermore, using graphs tables, approach contrasted analytical solution literature based on relative error analyses statistical performance measure analyses. According results, method effective resolving difficult non-linear issues

Language: Английский

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A pseudo-time stepping and parameterized physics-informed neural network framework for Navier–Stokes equations

Physics of Fluids, Journal Year: 2025, Volume and Issue: 37(3)

Published: March 1, 2025

Physics-informed neural networks (PINNs) have emerged as a popular approach in scientific machine learning for solving both forward and inverse problems of partial differential equations (PDEs). However, complex physical systems are often characterized by parameters, such viscosity Reynolds number fluid dynamics, which pose significant challenges parameterized PDE solutions. The inherent limitations PINNs include the need repeated time-consuming training under varying parameter conditions, minimization residuals with PDE-based soft constraints, makes “ill-conditioned” problem. To address these issues, this paper proposes an innovative framework: pseudo-time stepping physics-informed network (P2PINN). P2PINN leverages explicit encoding only two parameters' latent representations to enable efficient interpolation extrapolation across wide range parameters. By integrating method deep learning, framework significantly alleviates ill-conditioned We validated our context Navier–Stokes equations, experimental results demonstrate that achieves solution speedups up 2–4 orders magnitude compared baseline their variants, while also surpassing them accuracy.

Language: Английский

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Forward to the Special Topic on “Solving Differential Equations with Deep Learning”

Journal of Systems Science and Complexity, Journal Year: 2024, Volume and Issue: 37(2), P. 389 - 390

Published: March 25, 2024

Language: Английский

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