CN-121981015-A - AI acceleration of pressure poisson equation in incompressible flow numerical computation

Abstract

An AI acceleration asynchronous GMRES preconditioning method of a pressure poisson equation in incompressible flow numerical calculation belongs to the field of computational fluid mechanics. Aiming at the calculation bottleneck of the traditional GMRES method in solving the pressure poisson equation, the method adopts an asynchronous parallel AI precondition framework to decouple the neural network training and the flow field solving, thereby realizing concurrent execution. The solver thread uses the current model to make real-time inference to provide high-quality initial guess, and the trainer thread background optimizes the weight and uses the flow field time coherence to tolerate hysteresis. Experimental results show that the method shortens the solving time by 67% -82% on the premise of guaranteeing the convergence accuracy, and is suitable for large-scale fluid simulation.

Inventors

• CHEN GUOSHENG

Assignees

• 西南科技大学

Dates

Publication Date

20260505

Application Date

20260319

Claims (6)

1. 1. An AI acceleration method of a pressure poisson equation in incompressible flow numerical calculation, which is characterized by comprising the following steps: step one, constructing a neural network model for capturing flow field characteristics in real time and generating an initial guess solution of a pressure poisson equation; decoupling a training process of the neural network and a time stepping solving process of the flow field by adopting an asynchronous parallel architecture, so as to realize concurrent execution of calculation and learning; step three, in the solver thread, performing non-blocking inference by utilizing the current neural network parameters, and providing initial guessing for GMRES solving; step four, in the training device thread, continuously optimizing the weight of the neural network by using the historical flow field data; and fifthly, based on flow field time coherence, tolerating time delay of model parameter updating, and ensuring improvement of GMRES convergence efficiency.
2. 2. The AI acceleration method of pressure poisson's equation in incompressible flow numerical computation of claim 1, wherein in the first step, the neural network model is a lightweight convolutional neural network, the input is a source term of the pressure poisson's equation, and the output is an initial pressure field guess generated by approximate inverse mapping.
3. 3. The AI acceleration method of pressure poisson's equation in incompressible flow numerical computation of claim 1, wherein in the second step, the asynchronous parallel architecture includes two independent threads, a solver thread is responsible for solving a navy-stokes equation and GMRES iteration by a projection method, and a trainer thread performs back propagation optimization in the background, avoiding waiting delay of the solver.
4. 4. The AI acceleration method of pressure poisson's equation in incompressible flow numerical computation of claim 1, wherein in the third step, the non-blocking inference uses the current available latest model parameters to reduce GMRES iteration times, and the initial residual is reduced by 2-3 orders of magnitude by AI preconditions.
5. 5. The AI acceleration method of pressure poisson's equation in incompressible flow numerical computation of claim 1, wherein in the fourth step, the historical flow field data includes source term-pressure pairs, the training process uses an online learning framework, and the cumulative training amount is increased by 15-40 times than that of the serial method.
6. 6. The AI acceleration method of the pressure poisson equation in the incompressible flow numerical computation of claim 1, wherein in the fifth step, the time delay is several to tens steps, and the method is suitable for flow scenes such as high reynolds number turbulence, cap driving square cavity flow, taylor-Green vortex and the like, and ensures the numerical stability.

Description

AI acceleration of pressure poisson equation in incompressible flow numerical computation Technical Field The invention belongs to the field of Computational Fluid Dynamics (CFD), and particularly relates to an incompressible flow numerical calculation acceleration method based on artificial intelligence, in particular to solving and optimizing a pressure poisson equation. Background Numerical simulation of incompressible fluid dynamics is widely applied to the fields of turbulence research, aero-pneumatic optimization and the like. In the solution of the Naviet-Stokes equation, the solution of the Pressure Poisson Equation (PPE) takes up a major calculation time, typically up to 80% -90%. The traditional GMRES approach relies on an initial guess and the convergence efficiency is limited by the spectral distribution and condition number. The existing online deep learning method adopts a serial blocking mode, so that the efficiency contradiction between training and solving is caused, and hardware resources cannot be fully utilized. Disclosure of Invention The invention aims to provide an asynchronous parallel AI precondition method, which eliminates training waiting delay, realizes concurrency of calculation and learning and improves PPE solving efficiency. In order to achieve the above purpose, the invention adopts the following technical scheme: An AI acceleration method of a pressure poisson equation in incompressible flow numerical computation, comprising: (1) Constructing a neural network, learning a PPE inverse mapping, and providing an initial guess; (2) Decoupling training and solving of an asynchronous framework; (3) Solving thread non-blocking inferences; (4) Continuously optimizing a training thread; (5) Hysteresis is tolerated with temporal coherence. The invention has the beneficial effects of obviously reducing the analog wall clock time and improving the practicability of the AI in CFD. Drawings In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for the description of the embodiments will be briefly described below, and it is apparent that the drawings in the following description are only some embodiments of the present application, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art. FIG. 1 is a schematic diagram of an asynchronous architecture according to the present invention; FIG. 2 is a block diagram of a neural network; FIG. 3 is a comparison of the convergence history and time consumption per iteration of the standard GMRES, serial MLGMRES and proposed parallel MLGMRES over a 2D pressure Poisson equation flow test problem (40X 40 grid); FIG. 4 is a plot of time spent per iteration as a function of iteration steps, parallel MLGMRES (green) keeps the lowest and most stable single step time spent, significantly better than serial MLGMRES (red) and standard GMRES (blue); fig. 5 is an iteration-by-iteration acceleration ratio map. Detailed Description The technical scheme of the invention is further described by the following specific examples. These examples are provided only to illustrate the present invention and not to limit the scope thereof. Various modifications and improvements of the following embodiments may be made by those skilled in the art in light of the basic teaching of the invention, and all such modifications and improvements are intended to be within the scope of the invention. Example 1 pure elliptic solution acceleration under the 2D poisson equation (2D Poisson Equation) problem The present embodiment focuses on the classical 2D poisson equation as an independent reference problem, which is a pure elliptic partial differential equation, commonly used to test the performance of linear solvers without involving the time evolution of fluid dynamics. The form of the 2D poisson equation is ∇ p=f (x, y), where p is the unknown field and f is the source term function. The boundary condition is a Dirichlet type (boundary value fixed to 0). (1) The calculation field is unit square [0,1] × [0,1]. (2) Grid Scale 50×50 structured grid (degree of freedom 2500), five-point template matrix A (sparse, symmetric positive) was generated using center-difference discretization. (3) The source term function is f (x, y) = -2pi 2 sin (pi x) sin (pi y), and p (x, y) = sin (pi y)/(2pi 2) is accurately solved for verifying the accuracy. (4) GMRES solving parameters, restart dimension m=20, convergence threshold epsilon=10-8, maximum number of iterations 500 (no time step, only single solving repetition test). (5) The neural network model is a simple multi-layer perceptron (MLP), and the structure comprises an input layer (the grid is flattened into a vector, the dimension 2500), a3 hidden layer (neurons 512-256-128) and an output layer (dimension 2500). The activation function is a leak ReLU (α=0.01), the total amount of parameters is about 1.5M, w