OpenFOAM libtorch tutorial step by step

[李东岳]

@1064168551 我刚又编译了一个新的程序，没问题。你应该是版本问题。

[1064168551]

@李东岳 在 OpenFOAM外挂libtorch 中说：

http://dyfluid.com/download.html 我这面有全系列的，里面gcc也可以切换。
你用你的老版本也行，老版本要更新gcc。
不管咋的你可以试试，有问题反馈我我协助

谢谢东岳老师，我的伴随拓扑优化是用老版本of写的，我试着更新gcc后编译一下，感谢感谢

[李东岳]

更新gcc之后你openfoam就编译不了了。那你尝试安装老版本的libtorch吧

[1064168551]

@李东岳 在 OpenFOAM外挂libtorch 中说：

更新gcc之后你openfoam就编译不了了。那你尝试安装老版本的libtorch吧

好的老师，我找一下老版本的libtorch

[李东岳]

这是个我写的求解1D对流方程的代码。PINN方法。可以在openfoam下执行。

#include <torch/torch.h>
#include "net.H"

int main()
{
    int iter = 1;
    int IterationNum = 1000;

    // Computational domain
    double dx = 0.1;
    double dt = 0.1;

    torch::Tensor x = torch::arange(-1, 1 + dx, dx);
    torch::Tensor t = torch::arange(0, 1 + dt, dt);
    torch::Tensor meshAndTime = torch::stack(torch::meshgrid({x, t})).reshape({2, -1}).transpose(0, 1);

    torch::DeviceType device = torch::kCPU;
    torch::nn::MSELoss criterion = torch::nn::MSELoss();
    std::shared_ptr<NN> model = std::make_shared<NN>();
    model->to(device);

    std::shared_ptr<torch::optim::Adam> adam = 
        std::make_shared<torch::optim::Adam>(model->parameters());

    torch::Tensor inlet = 
        torch::stack
        (
            torch::meshgrid({x.index({0}), t})
        ).reshape({2, -1}).transpose(0, 1);

    torch::Tensor outlet = 
        torch::stack
        (
            torch::meshgrid({x.index({-1}), t})
        ).reshape({2, -1}).transpose(0, 1);

    torch::Tensor ic = 
        torch::stack
        (
            torch::meshgrid({x, t.index({0})})
        ).reshape({2, -1}).transpose(0, 1);

    torch::Tensor icbc = torch::cat({outlet, inlet, ic});

    torch::Tensor U_inlet = torch::full({11}, 0.5);
    torch::Tensor U_outlet = torch::zeros(outlet.size(0));

    torch::Tensor UiniLeft = torch::full({11}, 0.5);
    torch::Tensor UiniRight = torch::full({10}, 0.);
    //torch::Tensor U_ic = torch::cat({UiniLeft, UiniRight});
    torch::Tensor U_ic = 
        torch::tensor
        (
            {0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.4,0.3,0.2,0.1,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.}
        );

    torch::Tensor U_icbc = torch::cat({U_outlet, U_inlet, U_ic}).unsqueeze(1);

    meshAndTime = meshAndTime.to(device);
    U_icbc = U_icbc.to(device);
    icbc = icbc.to(device);
    meshAndTime.requires_grad_(true);

    model->train();

    // Iteration
    for (int i = 0; i < IterationNum; i++) 
    {
        adam->zero_grad();

        torch::Tensor U_icbcPred = model->forward(icbc);
        torch::Tensor loss_data = criterion(U_icbcPred, U_icbc);
        torch::Tensor UIter = model->forward(meshAndTime);

        torch::Tensor dudxt = 
            torch::autograd::grad
            (
                {UIter},
                {meshAndTime},
                {torch::ones_like(UIter)},
                true,
                true
            )[0];

        torch::Tensor dudt = dudxt.index({torch::indexing::Slice(), 1});
        torch::Tensor dudx = dudxt.index({torch::indexing::Slice(), 0});

        torch::Tensor loss_pde = criterion(dudt, -0.3*dudx);
        torch::Tensor loss = loss_pde + loss_data;
        loss.backward();
        adam->step();

        if (iter % 100 == 0) 
        {
            std::cout << iter << " " << loss.item<double>() << std::endl;
        }
        iter++;
    }

    // output results
    torch::Tensor Ufinal = model->forward(meshAndTime);
    Ufinal = Ufinal.reshape({(int)(2/dx) + 1, (int)(1/dt) + 1});
    std::ofstream file("U");
    for (int i = 0; i < Ufinal.size(0); i++) 
    {
        for (int j = 0; j < Ufinal.size(1); j++) 
        {
            file << Ufinal[i][j].item<float>() << " ";
        }
        file << "\n";
    }
    file.close();

    std::cout<< "Done!" << std::endl;
    return 0;
}

上面给的是光滑的数据。在纯的黎曼问题的时候，有震荡如下图。感觉需要附加监督点

[xiezhuoyu]

@李东岳 在 OpenFOAM外挂libtorch 中说：

#include "net.H"

李老师，不知道是否方便贴一下net.H？
感谢！

[李东岳]

net.H

#include <torch/torch.h>

class NN
:
    public torch::nn::Module 
{
    torch::nn::Sequential net_;

public:

    NN();

    torch::Tensor forward(torch::Tensor x);
};

net.C

/*---------------------------------------------------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Copyright (C) 2022-2023 OpenFOAM Foundation
     \\/     M anipulation  |
-------------------------------------------------------------------------------
License
    This file is part of OpenFOAM.

    OpenFOAM is free software: you can redistribute it and/or modify it
    under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.

    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
    for more details.

    You should have received a copy of the GNU General Public License
    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.

Class

See also

SourceFiles

\*---------------------------------------------------------------------------*/
#include "net.H"

NN::NN()
{
    net_ = register_module
    (
        "net", 
        torch::nn::Sequential
        (
            torch::nn::Linear(2,20),
            torch::nn::ReLU(),
            torch::nn::Linear(20,30),
            torch::nn::ReLU(),
            torch::nn::Linear(30,30),
            torch::nn::ReLU(),
            torch::nn::Linear(30,20),
            torch::nn::ReLU(),
            torch::nn::Linear(20,20),
            torch::nn::ReLU(),
            torch::nn::Linear(20,1)
        )
    );
};

torch::Tensor NN::forward(torch::Tensor x) 
{
    return net_->forward(x);
}

这个要编译成库，挂到PINNFoam上面

[xiezhuoyu]

@李东岳 可运行，👍👍👍谢谢李老师！

[李东岳]

@xiezhuoyu 老铁可以试试求解黎曼问题，这个结果不太好，有spike。

[李东岳]

更新一段代码，简单的做个一维拟合。蓝线是训练数据。黄点灰点是预测值。

#include <torch/torch.h>

typedef torch::Tensor TT;

class NN
:
    public torch::nn::Module 
{
    torch::nn::Sequential net_;
public:
    NN()
    {
        net_ = register_module
        (
            "net", 
            torch::nn::Sequential
            (
                torch::nn::Linear(1,20),
                torch::nn::ReLU(),
                torch::nn::Linear(20,30),
                torch::nn::ReLU(),
                torch::nn::Linear(30,30),
                torch::nn::ReLU(),
                torch::nn::Linear(30,30),
                torch::nn::ReLU(),
                torch::nn::Linear(30,1)
            )
        );
    }
    torch::Tensor forward(torch::Tensor x)
    {
        return net_->forward(x);
    }   
};


int main() 
{
    torch::manual_seed(30);

    TT X = torch::tensor({1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0}).reshape({-1, 1});
    TT Y = torch::tensor({1.0, 0.5, 1.5, 2.0, 2.5, 2.0, 2.5, 3.0, 3.1}).reshape({-1, 1});

    std::shared_ptr<NN> model = std::make_shared<NN>();
    torch::nn::MSELoss criterion = torch::nn::MSELoss();
    torch::optim::Adam adam(model->parameters(), torch::optim::AdamOptions(0.01));

    const size_t num_epochs = 1000;
    for (size_t epoch = 0; epoch < num_epochs; ++epoch) 
    {
        TT output = model->forward(X);
        TT loss = criterion(output, Y);

        adam.zero_grad();
        loss.backward();
        adam.step();

        if ((epoch + 1) % 100 == 0) 
        {
            std::cout << "Loss: " << loss.item<float>() << std::endl;
        }
    }

    //model->eval();
    TT test = torch::tensor({4.4, 5.5}).reshape({-1, 1});    
    TT predic = model->forward(test);
    std::cout<< "prediction is " << predic << std::endl;

    return 0;
}

单变量对多变量变种：

#include <torch/torch.h>

typedef torch::Tensor TT;

class NN
:
    public torch::nn::Module 
{
    torch::nn::Sequential net_;
public:
    NN()
    {
        net_ = register_module
        (
            "net", 
            torch::nn::Sequential
            (
                torch::nn::Linear(1,20),
                torch::nn::ReLU(),
                torch::nn::Linear(20,30),
                torch::nn::ReLU(),
                torch::nn::Linear(30,30),
                torch::nn::ReLU(),
                torch::nn::Linear(30,30),
                torch::nn::ReLU(),
                torch::nn::Linear(30,2)
            )
        );
    }
    torch::Tensor forward(torch::Tensor x)
    {
        return net_->forward(x);
    }   
};


int main() 
{
    torch::manual_seed(30);

    TT X = torch::tensor({1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0}).reshape({-1, 1});
    TT Y = torch::tensor({{1.0, 1.0}, {0.5, 0.5}, {1.5, 1.5}, {2.0, 2.0}, {2.5, 2.5}, {2.0, 2.0}, {2.5, 2.5}, {3.0, 3.0}, {3.1, 3.1}}).reshape({-1, 2});

    std::shared_ptr<NN> model = std::make_shared<NN>();
    torch::nn::MSELoss criterion = torch::nn::MSELoss();
    torch::optim::Adam adam(model->parameters(), torch::optim::AdamOptions(0.01));

    const size_t num_epochs = 1000;
    for (size_t epoch = 0; epoch < num_epochs; ++epoch) 
    {
        TT output = model->forward(X);
        TT loss = criterion(output, Y);

        adam.zero_grad();
        loss.backward();
        adam.step();

        if ((epoch + 1) % 100 == 0) 
        {
            std::cout << "Loss: " << loss.item<float>() << std::endl;
        }
    }

    //model->eval();
    TT test = torch::tensor({4.4, 5.5}).reshape({-1, 1});    
    TT predic = model->forward(test);
    std::cout<< "prediction is " << predic << std::endl;

    return 0;
}

[李东岳]

下面这个代码是个正儿八经的监督学习。下图左边是OpenFOAM算的，右边是OpenFOAM环境下libtorch训练的。

#include <torch/torch.h>
#include "argList.H"
#include "solver.H"

#define SIZE 64
typedef torch::Tensor TT;

class NN
:
    public torch::nn::Module 
{
    torch::nn::Sequential net_;
public:
    NN()
    {
        net_ = register_module
        (
            "net", 
            torch::nn::Sequential
            (
                torch::nn::Linear(1,20),
                torch::nn::ReLU(),
                torch::nn::Linear(20,30),
                torch::nn::ReLU(),
                torch::nn::Linear(30,30),
                torch::nn::ReLU(),
                torch::nn::Linear(30,30),
                torch::nn::ReLU(),
                torch::nn::Linear(30,SIZE)
            )
        );
    }
    torch::Tensor forward(torch::Tensor x)
    {
        return net_->forward(x);
    }   
};

using namespace Foam;

int main(int argc, char *argv[])
{
    #include "setRootCase.H" 
    #include "createTime.H"
    #include "createMesh.H"
    #include "createFields.H"

    scalarField P0internal = P[0].primitiveField();
    scalarField P1internal = P[1].primitiveField();

    float* P0array = new float[SIZE];
    float* P1array = new float[SIZE];

    for (int i = 0; i < SIZE; i++)
    {
        P0array[i] = P0internal[i];
        P1array[i] = P1internal[i];
    }

    TT P0label = torch::from_blob(P0array, SIZE, torch::kFloat32).clone();
    TT P1label = torch::from_blob(P1array, SIZE, torch::kFloat32).clone();

    delete [] P0array;
    delete [] P1array;

    TT X = torch::tensor({1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8}).reshape({-1, 1});
    torch::Tensor Y = 
        torch::cat
        (
            {
                P0label.unsqueeze(0),
                P1label.unsqueeze(0)
            }
        );
    //std::cout<< "Y = " << Y << std::endl;

    std::shared_ptr<NN> model = std::make_shared<NN>();
    torch::nn::MSELoss criterion = torch::nn::MSELoss();
    torch::optim::Adam adam(model->parameters(), torch::optim::AdamOptions(0.001));

    for (int epoch = 0; epoch < 1500; epoch++) 
    {
        //Info<< "epoch = " << epoch << nl;
        TT output = model->forward(X);
        TT loss = criterion(output, Y);
        adam.zero_grad();
        loss.backward();
        adam.step();

        if ((epoch + 1) % 100 == 0) 
        {
            std::cout << "Loss: " << loss.item<float>() << std::endl;
        }
    }

    TT test = torch::tensor({2.0}).reshape({-1, 1});    
    TT predic = model->forward(test);
    std::cout<< "prediction is " << predic.reshape({-1,1}) << std::endl;
    return 0;
}

[xiezhuoyu]

@李东岳 在 OpenFOAM外挂libtorch 中说：

scalarField P0internal = P[0].primitiveField();
scalarField P1internal = P[1].primitiveField();

李老师，这个P[0]和P[1]分别是什么物理量？怎么得到呢？

[李东岳]

@xiezhuoyu 你训练的场，比如温度场压力场

[李东岳]

这是一个顶盖驱动流动的PINN代码。写了一天，最开始的版本植入的是守恒的形式，边界条件除了顶盖都给的零梯度，导致导数特别多。

下面这个版本我还植入的非守恒形式，然后边界条件都变成了固定值0。不过结果还是不太对。做个记录吧。整了一天这个导数

我目前怀疑边界的导数应该也是从mesh计算，而不能单独计算边界的导数。这需要大改。

#include <torch/torch.h>

using namespace std;

class NN
:
    public torch::nn::Module 
{
    torch::nn::Sequential net_;

public:

    NN()
    {
        net_ = register_module
        (
            "net", 
            torch::nn::Sequential
            (
                torch::nn::Linear(2,20),
                torch::nn::Tanh(),
                torch::nn::Linear(20,20),
                torch::nn::Tanh(),
                torch::nn::Linear(20,20),
                torch::nn::Tanh(),
                torch::nn::Linear(20,20),
                torch::nn::Tanh(),
                torch::nn::Linear(20,3)
            )
        );
    }

    auto forward(torch::Tensor x)
    {
        return net_->forward(x);
    }
};

int main()
{
    torch::manual_seed(30); 
    int iter = 1;
    int IterationNum = 200;
    auto crit = torch::nn::MSELoss();
    auto model = std::make_shared<NN>();
    auto adam = std::make_shared<torch::optim::Adam>(model->parameters());

    // Computational domain
    double dx = 0.2;
    double dy = 0.2;

    auto x = torch::arange(0, 1 + dx, dx);
    auto y = torch::arange(10, 11 + dy, dy);
    auto mesh = 
        torch::stack(torch::meshgrid({x, y})).reshape({2, -1}).transpose(0, 1);
    mesh.requires_grad_(true);
    auto leftWall = 
        torch::stack
        (
            torch::meshgrid({x.index({0}), y})
        ).reshape({2, -1}).transpose(0, 1);
    auto rightWall = 
        torch::stack
        (
            torch::meshgrid({x.index({-1}), y})
        ).reshape({2, -1}).transpose(0, 1);
    auto bottom = 
        torch::stack
        (
            torch::meshgrid({x, y.index({0})})
        ).reshape({2, -1}).transpose(0, 1);
    bottom.requires_grad_(true);
    auto top = 
        torch::stack
        (
            torch::meshgrid({x, y.index({-1})})
        ).reshape({2, -1}).transpose(0, 1);
    top.requires_grad_(true);
    auto fixedWalls = torch::cat({leftWall, rightWall, bottom});
    auto u_top = torch::full({x.size(0)}, 1.0);
    auto v_top = torch::full({x.size(0)}, 0.0);

    //cout<< "mesh = \n" << mesh << endl;
    //cout<< "leftWall = \n" << leftWall << endl;
    //cout<< "rightWall = \n" << rightWall << endl;
    //cout<< "bottom = \n" << bottom << endl;
    //cout<< "top = \n" << top << endl;
    //cout<< "fixedWalls = \n" << fixedWalls << endl;

    // Iteration
    for (int i = 0; i < IterationNum; i++) 
    {
        adam->zero_grad();

        // Top boundary
        auto top_pred = model->forward(top);
        auto u_top_pred = top_pred.index({torch::indexing::Slice(), 0});
        auto v_top_pred = top_pred.index({torch::indexing::Slice(), 1});
        auto p_top_pred = top_pred.index({torch::indexing::Slice(), 2});
        auto loss_top = 
            crit(v_top_pred, v_top) + crit(u_top_pred, u_top);
        auto dpdTop = 
            torch::autograd::grad
            (
                {p_top_pred},
                {top},
                {torch::ones_like(p_top_pred)},
                true,
                true
            )[0];
        auto dpdyTop = dpdTop.index({torch::indexing::Slice(), 1});
        loss_top += crit(dpdyTop, torch::zeros({dpdyTop.size(0)}));
        //cout << "loss_top\n" << loss_top << endl;

        // Bottom boundary
        auto bot_pred = model->forward(bottom);
        auto u_bot_pred = bot_pred.index({torch::indexing::Slice(), 0});
        auto v_bot_pred = bot_pred.index({torch::indexing::Slice(), 1});
        auto p_bot_pred = bot_pred.index({torch::indexing::Slice(), 2});
        auto dpdBot = 
            torch::autograd::grad
            (
                {p_bot_pred},
                {bottom},
                {torch::ones_like(p_bot_pred)},
                true,
                true
            )[0];
        auto dpdyBot = dpdBot.index({torch::indexing::Slice(), 1});
        
        auto loss_bot = crit(dpdyBot, torch::zeros({dpdyBot.size(0)})) 
          + crit(u_bot_pred, torch::zeros({dpdyBot.size(0)})) 
          + crit(v_bot_pred, torch::zeros({dpdyBot.size(0)}));


        // Field 
        auto UP = model->forward(mesh);
        auto u_pred = UP.index({torch::indexing::Slice(), 0});
        auto v_pred = UP.index({torch::indexing::Slice(), 1});
        auto p_pred = UP.index({torch::indexing::Slice(), 2});

        auto dpdMesh = 
            torch::autograd::grad
            (
                {p_pred},
                {mesh},
                {torch::ones_like(u_pred)},
                true,
                true
            )[0];
        auto dpdx = dpdMesh.index({torch::indexing::Slice(), 0});
        auto dpdy = dpdMesh.index({torch::indexing::Slice(), 1});

        auto dudMesh = 
            torch::autograd::grad
            (
                {u_pred},
                {mesh},
                {torch::ones_like(u_pred)},
                true,
                true
            )[0];
        auto dudx = dudMesh.index({torch::indexing::Slice(), 0});
        auto dudy = dudMesh.index({torch::indexing::Slice(), 1});
 
        auto dudxMesh = 
            torch::autograd::grad
            (
                {dudx},
                {mesh},
                {torch::ones_like(u_pred)},
                true,
                true
            )[0];
        auto dudyMesh = 
            torch::autograd::grad
            (
                {dudy},
                {mesh},
                {torch::ones_like(u_pred)},
                true,
                true
            )[0];
        auto dudxx = dudxMesh.index({torch::indexing::Slice(), 0});
        auto dudyy = dudyMesh.index({torch::indexing::Slice(), 1});

        //cout << "dudxx\n" << dudxx << endl;
        auto dvdMesh = 
            torch::autograd::grad
            (
                {v_pred},
                {mesh},
                {torch::ones_like(u_pred)},
                true,
                true
            )[0];
        auto dvdx = dvdMesh.index({torch::indexing::Slice(), 0});
        auto dvdy = dvdMesh.index({torch::indexing::Slice(), 1});

        auto dvdxMesh = 
            torch::autograd::grad
            (
                {dvdx},
                {mesh},
                {torch::ones_like(u_pred)},
                true,
                true
            )[0];
        auto dvdyMesh = 
            torch::autograd::grad
            (
                {dvdy},
                {mesh},
                {torch::ones_like(u_pred)},
                true,
                true
            )[0];
        auto dvdxx = dvdxMesh.index({torch::indexing::Slice(), 0});
        auto dvdyy = dvdyMesh.index({torch::indexing::Slice(), 1});

        auto loss_cont = crit(dudx, -dvdy);
        auto loss_mom1 = crit(u_pred*dudx + v_pred*dudy - 0.001*(dudxx + dudyy), -dpdx);
        auto loss_mom2 = crit(u_pred*dvdx + v_pred*dvdy - 0.001*(dvdxx + dvdyy), -dpdy);
        auto loss_pde = loss_cont + loss_mom1 + loss_mom2; 
        //cout<< "loss_cont\n" << loss_cont << endl;
        //cout<< "loss_mom1\n" << loss_mom1 << endl;
        //cout<< "loss_mom2\n" << loss_mom2 << endl;
        //cout<< "loss_pde\n" << loss_pde << endl;

        // leftWall and rightWall
        auto dpdxLeft = dpdx.index({torch::indexing::Slice(0, 6)});
        auto u_pred_left = u_pred.index({torch::indexing::Slice(0, 6)});
        auto v_pred_left = v_pred.index({torch::indexing::Slice(0, 6)});
        auto dpdxRight = dpdx.index({torch::indexing::Slice(-6, torch::indexing::None)});
        auto u_pred_right = u_pred.index({torch::indexing::Slice(-6, torch::indexing::None)});
        auto v_pred_right = v_pred.index({torch::indexing::Slice(-6, torch::indexing::None)});

        auto loss_leftRight = crit(u_pred_left, torch::zeros({6})) 
          + crit(v_pred_left, torch::zeros({6})) 
          + crit(dpdxLeft, torch::zeros({6})) 
          + crit(v_pred_right, torch::zeros({6})) 
          + crit(u_pred_right, torch::zeros({6})) 
          + crit(dpdxRight, torch::zeros({6}));
        //cout<< "loss_leftRight\n" << loss_leftRight << endl;

        auto loss = loss_top + loss_bot + loss_leftRight + loss_pde;
        //cout<< "loss\n" << loss << endl;

        loss.backward();
        adam->step();

        std::cout << iter << " " << loss.item<double>() << std::endl;
        iter++;
    }

    model->eval();//neglect
    auto results = model->forward(mesh);
    cout << "results\n" << results << endl;
    return 0;
}

都是在OpeNFOAM环境下，左边是我的PINN算的，下面是OpenFOAM自带的simpleFoam算的。

[tiankai]

@xiezhuoyu 我是小白，想要请教一下，怎么才能运行呢

[xiezhuoyu]

@tiankai

1. 查看/修改OpenFOAM执行wmake时采用的Gcc版本，OpenFOAM/wmake/rules/General/Gcc/c++

   CC          = g++$(COMPILER_VERSION) -std=c++14
   

2. pytorch官网下载libtorch
   
   2.3.0版本依赖C++17
   
   
   2.0.0版本依赖C++14
   
   
   1.10.0版本依赖C++14
3. 修改/home/***/.bashrc，设置环境变量

   export LD_LIBRARY_PATH=/home/***/OpenFOAM/libtorch/lib:$LD_LIBRARY_PATH
   

4. wmake你的库（比如李老师贴的代码）PINNFoam
5. 最后调用PINNFoam

[tiankai]

@xiezhuoyu 多谢回复，我查看了g++版本，确实是14，而且我已经成功编译了libtorch库，但是在编译一维对流方程时报错了

提示指针变量有错误

[xiezhuoyu]

@tiankai 看不出来什么问题？问问李老师@李东岳

[李东岳]

我已经成功编译了libtorch库

@tiankai 我这个路子不需要编译libtorch。 你看楼上总结那个也不需要编译。我这面没有编译。就跟OpenFOAM安装一样。OpenFOAM可以直接下载装（apt install那种），也可以编译安装。你不要编译，你按照我1楼的方法用现成的，跟openfoam捆绑起来能跑起来。回头再研究编译libtorch

[tiankai]

@李东岳 在 OpenFOAM外挂libtorch 中说：

我已经成功编译了libtorch库

@tiankai 我这个路子不需要编译libtorch。 你看楼上总结那个也不需要编译。我这面没有编译。就跟OpenFOAM安装一样。OpenFOAM可以直接下载装（apt install那种），也可以编译安装。你不要编译，你按照我1楼的方法用现成的，跟openfoam捆绑起来能跑起来。回头再研究编译libtorch

不好意思李老师，是我没有表述清楚，我是将libtorch解压了，用wmake了torchFoam，添加了路径。输入torchFoam，输出了上文中一样的信息，这表明libtorch库挂载成功了。

所以我想要运行PiNNFoam的代码，需要创建一个制作make文件夹，然后将PiNNFoam（一维对流方程），net.h，net.H添加到PiNNFoam的文件夹下，然后使用wmake文件夹PiNNFoam，最后调用PiNNFoam即可吧。现在使用wmake执行PiNNFoam报错了图中内容