{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "924b1faf",
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "from tqdm import tqdm\n",
    "\n",
    "import torch\n",
    "import torch.nn as nn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "95ae2b01",
   "metadata": {},
   "outputs": [],
   "source": [
    "class NN(nn.Module):\n",
    "    def __init__(self):\n",
    "        super(NN, self).__init__()\n",
    "        self.net = torch.nn.Sequential(\n",
    "            nn.Linear(2,20),\n",
    "            nn.Tanh(),\n",
    "            nn.Linear(20,30),\n",
    "            nn.Tanh(),\n",
    "            nn.Linear(30,30),\n",
    "            nn.Tanh(),\n",
    "            nn.Linear(30,20),\n",
    "            nn.Tanh(),\n",
    "            nn.Linear(20,20),\n",
    "            nn.Tanh(),\n",
    "            nn.Linear(20,1)\n",
    "        )\n",
    "    \n",
    "    def forward(self, x):\n",
    "        out = self.net(x)\n",
    "        return out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f47c45a0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'\\nx_test = torch.arange(-1,1+0.1, 0.1)\\n#print(x_test)\\nt_test = torch.arange(0,1+0.1, 0.1)\\n#print(t_test)\\n\\nX = torch.stack(torch.meshgrid(x_test,t_test)).reshape(2,-1).T\\n#print(X)\\n\\nbc1_test = torch.stack(torch.meshgrid(x_test[-1],t_test)).reshape(2,-1).T\\n#print(bc1_test)\\n#print(torch.meshgrid(x_test,t_test))\\n\\ny_train_test = torch.tensor([1,2,3,4])\\nprint(y_train_test)\\ny_train_test = y_train_test.unsqueeze(1)\\nprint(y_train_test)\\n'"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'''\n",
    "x_test = torch.arange(-1,1+0.1, 0.1)\n",
    "#print(x_test)\n",
    "t_test = torch.arange(0,1+0.1, 0.1)\n",
    "#print(t_test)\n",
    "\n",
    "X = torch.stack(torch.meshgrid(x_test,t_test)).reshape(2,-1).T\n",
    "#print(X)\n",
    "\n",
    "bc1_test = torch.stack(torch.meshgrid(x_test[-1],t_test)).reshape(2,-1).T\n",
    "#print(bc1_test)\n",
    "#print(torch.meshgrid(x_test,t_test))\n",
    "\n",
    "y_train_test = torch.tensor([1,2,3,4])\n",
    "print(y_train_test)\n",
    "y_train_test = y_train_test.unsqueeze(1)\n",
    "print(y_train_test)\n",
    "'''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b8cf0e91",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Net:\n",
    "    def __init__(self):\n",
    "        device = torch.device(\"cuda\") if torch.cuda.is_available() else torch.device(\"cpu\")\n",
    "        \n",
    "        self.model = NN().to(device)\n",
    "        \n",
    "        # comp. domain \n",
    "        self.h = 0.1\n",
    "        self.k = 0.1\n",
    "        x = torch.arange(-1,1+self.h, self.h)\n",
    "        t = torch.arange(0,1+self.k, self.k)\n",
    "        \n",
    "        self.X = torch.stack(torch.meshgrid(x,t)).reshape(2,-1).T\n",
    "        \n",
    "        # train data\n",
    "        bc1 = torch.stack(torch.meshgrid(x[0],t)).reshape(2,-1).T\n",
    "        bc2 = torch.stack(torch.meshgrid(x[-1],t)).reshape(2,-1).T\n",
    "        ic  = torch.stack(torch.meshgrid(x,t[0])).reshape(2,-1).T\n",
    "        self.X_train = torch.cat([bc1, bc2, ic])\n",
    "        \n",
    "        y_bc1 = torch.zeros(len(bc1))\n",
    "        y_bc2 = torch.zeros(len(bc2))\n",
    "        y_ic  = -torch.sin(math.pi * ic[:,0])\n",
    "        self.y_train = torch.cat([y_bc1, y_bc2, y_ic])\n",
    "        self.y_train = self.y_train.unsqueeze(1)\n",
    "        \n",
    "        self.X = self.X.to(device)\n",
    "        self.y_train = self.y_train.to(device)\n",
    "        self.X_train = self.X_train.to(device)\n",
    "        self.X.requires_grad = True\n",
    "        \n",
    "        # optimizer setting\n",
    "        self.adam =  torch.optim.Adam(self.model.parameters())\n",
    "        #Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS)\n",
    "        self.optimizer = torch.optim.LBFGS(\n",
    "            self.model.parameters(),\n",
    "            lr=1.0,\n",
    "            max_iter = 50000,\n",
    "            max_eval = 50000,\n",
    "            history_size = 50,\n",
    "            tolerance_grad = 1e-7,\n",
    "            tolerance_change = 1.0* np.finfo(float).eps,\n",
    "            line_search_fn =\"strong_wolfe\"\n",
    "        )\n",
    "        \n",
    "        self.criterion = torch.nn.MSELoss()\n",
    "        self.iter = 1\n",
    "    \n",
    "    def loss_func(self):\n",
    "        self.adam.zero_grad()\n",
    "        self.optimizer.zero_grad()\n",
    "        \n",
    "        y_pred = self.model(self.X_train)\n",
    "        loss_data = self.criterion(y_pred,self.y_train)\n",
    "        \n",
    "        u = self.model(self.X)\n",
    "        \n",
    "        du_dX = torch.autograd.grad(\n",
    "            u,\n",
    "            self.X,\n",
    "            grad_outputs = torch.ones_like(u),\n",
    "            create_graph = True,\n",
    "            retain_graph = True\n",
    "        )[0]\n",
    "        \n",
    "        #print(du_dX)\n",
    "        #print(\"xxxxxxxxxxxxxxxxxxxxxxxxx\")\n",
    "        #print(du_dX[0])\n",
    "        \n",
    "        du_dt = du_dX[:,1]\n",
    "        du_dx = du_dX[:,0]\n",
    "        \n",
    "        du_dXX = torch.autograd.grad(\n",
    "            du_dX,\n",
    "            self.X,\n",
    "            grad_outputs = torch.ones_like(du_dX),\n",
    "            create_graph = True,\n",
    "            retain_graph = True\n",
    "        )[0]\n",
    "        \n",
    "        du_dxx = du_dXX[:,0]\n",
    "        \n",
    "        loss_pde = self.criterion(du_dt + u.squeeze()*du_dx , (0.01/math.pi) * du_dxx)\n",
    "        \n",
    "        loss = loss_pde + loss_data\n",
    "        loss.backward()\n",
    "        \n",
    "        if self.iter % 100 == 0:\n",
    "            print(self.iter, loss.item())\n",
    "        self.iter = self.iter+1\n",
    "        \n",
    "        return loss\n",
    "    \n",
    "    def train(self):\n",
    "        self.model.train()\n",
    "        for i in range(1000):\n",
    "            self.adam.step(self.loss_func)\n",
    "        self.optimizer.step(self.loss_func)\n",
    "    \n",
    "    def eval_(self):\n",
    "        self.model.eval()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "f7b786a1",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\mecha\\anaconda3\\Lib\\site-packages\\torch\\functional.py:504: UserWarning: torch.meshgrid: in an upcoming release, it will be required to pass the indexing argument. (Triggered internally at C:\\cb\\pytorch_1000000000000\\work\\aten\\src\\ATen\\native\\TensorShape.cpp:3484.)\n",
      "  return _VF.meshgrid(tensors, **kwargs)  # type: ignore[attr-defined]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 0.17142267525196075\n",
      "200 0.09170893579721451\n",
      "300 0.08023164421319962\n",
      "400 0.07239650189876556\n",
      "500 0.062420327216386795\n",
      "600 0.04624633491039276\n",
      "700 0.04437953606247902\n",
      "800 0.027044180780649185\n",
      "900 0.026495132595300674\n",
      "1000 0.02123439311981201\n",
      "1100 0.011409871280193329\n",
      "1200 0.006951150484383106\n",
      "1300 0.004899165593087673\n",
      "1400 0.0035827099345624447\n",
      "1500 0.0022788802161812782\n",
      "1600 0.00173501530662179\n",
      "1700 0.0012664643581956625\n",
      "1800 0.0009671457228250802\n",
      "1900 0.0007982993847690523\n",
      "2000 0.0008580870926380157\n",
      "2100 0.0004991141031496227\n",
      "2200 0.0004000520857516676\n",
      "2300 0.00034320264239795506\n",
      "2400 0.0002762374933809042\n",
      "2500 0.00024084714823402464\n",
      "2600 0.00020908507576677948\n",
      "2700 0.00017261735047213733\n",
      "2800 0.00014505621220450848\n",
      "2900 0.00011912699847016484\n",
      "3000 0.00010479683987796307\n",
      "3100 9.73835849436e-05\n",
      "3200 9.187370596919209e-05\n",
      "3300 8.5382183897309e-05\n",
      "3400 8.032815821934491e-05\n",
      "3500 7.568503497168422e-05\n"
     ]
    }
   ],
   "source": [
    "# training\n",
    "net = Net()\n",
    "net.train()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a32f74e9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "NN(\n",
       "  (net): Sequential(\n",
       "    (0): Linear(in_features=2, out_features=20, bias=True)\n",
       "    (1): Tanh()\n",
       "    (2): Linear(in_features=20, out_features=30, bias=True)\n",
       "    (3): Tanh()\n",
       "    (4): Linear(in_features=30, out_features=30, bias=True)\n",
       "    (5): Tanh()\n",
       "    (6): Linear(in_features=30, out_features=20, bias=True)\n",
       "    (7): Tanh()\n",
       "    (8): Linear(in_features=20, out_features=20, bias=True)\n",
       "    (9): Tanh()\n",
       "    (10): Linear(in_features=20, out_features=1, bias=True)\n",
       "  )\n",
       ")"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.model.eval()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "caffd7ad",
   "metadata": {},
   "outputs": [],
   "source": [
    "h = 0.01\n",
    "k = 0.01\n",
    "\n",
    "x = torch.arange(-1,1,h)\n",
    "t = torch.arange(0,1,k)\n",
    "\n",
    "X= torch.stack(torch.meshgrid(x,t)).reshape(2,-1).T\n",
    "X= X.to(net.X.device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "324530ea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[-1.0000,  0.0000],\n",
       "        [-1.0000,  0.0100],\n",
       "        [-1.0000,  0.0200],\n",
       "        ...,\n",
       "        [ 0.9900,  0.9700],\n",
       "        [ 0.9900,  0.9800],\n",
       "        [ 0.9900,  0.9900]], device='cuda:0')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "7cb0d485",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([20000, 2])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b8618120",
   "metadata": {},
   "outputs": [],
   "source": [
    "model = net.model\n",
    "model.eval()\n",
    "with torch.no_grad():\n",
    "    y_pred = model(X)\n",
    "    y_pred = y_pred.reshape(len(x),len(t)).cpu().numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "8aeebe42",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(200, 100)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "2d8544b1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.00251437,  0.00211867,  0.00188104, ..., -0.00078454,\n",
       "        -0.00077557, -0.00076252],\n",
       "       [ 0.03291537,  0.03159838,  0.03048771, ...,  0.00669334,\n",
       "         0.00664395,  0.0065986 ],\n",
       "       [ 0.06330501,  0.06107554,  0.05909846, ...,  0.01418952,\n",
       "         0.01408086,  0.01397699],\n",
       "       ...,\n",
       "       [-0.09238189, -0.08987071, -0.08762251, ..., -0.02535262,\n",
       "        -0.02522626, -0.02510789],\n",
       "       [-0.06131541, -0.05973559, -0.05836456, ..., -0.01742845,\n",
       "        -0.01736608, -0.01731017],\n",
       "       [-0.03012968, -0.02948872, -0.02900073, ..., -0.00947988,\n",
       "        -0.00948113, -0.00948909]], dtype=float32)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "805a4290",
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
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     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
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      "text/plain": [
       "<Figure size 15000x9000 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.set_style(\"white\")\n",
    "plt.figure(figsize=(5,3), dpi=3000)\n",
    "sns.heatmap(y_pred, cmap='jet')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "5f6298ef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2b31b39a790>]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(y_pred[:,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "79e43b83",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2b323e21c50>]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(y_pred[:,-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "7ef2dfb6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2b368a9bfd0>]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(y_pred[:,30])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8b409850",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
