lnn.ipynb

{
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  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "'1.5.1'"
     },
     "metadata": {},
     "execution_count": 114
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.integrate import odeint\n",
    "import matplotlib.pyplot as plt \n",
    "\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "import torch.optim as optim\n",
    "\n",
    "from functools import partial\n",
    "from torch.autograd.functional import jacobian, hessian\n",
    "\n",
    "from torchdiffeq import odeint as tor_odeint\n",
    "from torchdiffeq import odeint_adjoint as tor_odeintadj\n",
    "torch.version.__version__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lagrangian for spring pendulum, in 2D, with $r$ spring length, $\\theta$ angle from vertical: \n",
    "\n",
    "$\\mathcal{L} = T - V = \\frac{1}{2}\\dot{r}^2 + \\frac{1}{2} r^2\\dot{\\theta}^2 - gr(1-\\cos(\\theta)) - k(r -r_0)^2$\n",
    "\n",
    "By applying Euler Lagrange equataions get:\n",
    "\n",
    "$\\ddot r = r\\dot{\\theta}^2 + g(1-\\cos(\\theta)) - 2k(r-r_0)$\n",
    "\n",
    "and \n",
    "\n",
    "$\\ddot \\theta = -\\frac{1}{r}(g\\sin(\\theta) + 2\\dot{r}\\dot{\\theta})$\n",
    "\n",
    "can use these and `odeint` to solve analytically.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lagrangian(x, g=10, k=10):\n",
    "    q, qt = torch.split(x, 2)\n",
    "    T = 0.5*(qt[0]**2 + (q[0]*qt[1])**2)\n",
    "    V = g*q[0]*(1-torch.cos(q[1])) + k*(q[0] - 1)**2\n",
    "    return T - V \n",
    "\n",
    "def E(x, g=10, k=10):\n",
    "    try:\n",
    "        q, qt = torch.split(x, 2)\n",
    "        cos = torch.cos\n",
    "    except: \n",
    "        q, qt = np.split(x, 2)\n",
    "        cos = np.cos\n",
    "    T = 0.5*(qt[0]**2 + (q[0]*qt[1])**2)\n",
    "    V = g*q[0]*(1-cos(q[1])) + k*(q[0] - 1)**2\n",
    "    return T + V \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_qdtt(q, qt, g=10, k=10):\n",
    "    '''\n",
    "    q is array of genralise coords, [r, theta]\n",
    "    qt is array of genralise coords, [rdt, thetadt]\n",
    "\n",
    "    returns time derivative of q.\n",
    "    '''\n",
    "    qdtt = np.zeros_like(q)\n",
    "\n",
    "    qdtt[:, 0] = q[:, 0]*qt[:, 1]**2 - g*(1-np.cos(q[:, 1])) - 2*k*(q[:, 0]-1) \n",
    "    qdtt[:, 1] = (-g*np.sin(q[:, 1]) -2*qt[:, 0]*qt[:, 1])/q[:, 0]\n",
    "\n",
    "    return qdtt  \n",
    "\n",
    "def get_xt_anal(x, t):\n",
    "    d = np.zeros_like(x)\n",
    "    d[:, :2] = x[:, 2:]\n",
    "    d[:, 2:] = get_qdtt(x[:, :2], x[:, 2:])\n",
    "\n",
    "    # print(x, d)\n",
    "    return d\n",
    "\n",
    "def anal_solve_ode(q0, qt0, t,):\n",
    "\n",
    "    x0 = np.append(q0, qt0)\n",
    "\n",
    "    def f_anal(x, t):\n",
    "        d = np.zeros_like(x)\n",
    "        d[:2] = x[2:]\n",
    "        d[2:] = np.squeeze(get_qdtt(np.expand_dims(x[:2], axis=0), np.expand_dims(x[2:], axis=0)))\n",
    "        # print(x, d)\n",
    "        return d\n",
    "    \n",
    "    return odeint(f_anal, x0, t, rtol=1e-10, atol=1e-10)\n",
    "    \n",
    "def q2xy(ql):\n",
    "    '''\n",
    "    Polar coords to xy\n",
    "    '''\n",
    "    try: \n",
    "        xy = np.zeros_like(ql)\n",
    "        sin = np.sin\n",
    "        cos = np.cos\n",
    "    except: \n",
    "        xy = torch.zeros_like(ql)\n",
    "        sin = torch.sin\n",
    "        cos = torch.cos\n",
    "\n",
    "    xy[:, 0] = ql[:, 0]*sin(ql[:, 1])\n",
    "    xy[:, 1] = -ql[:, 0]*cos(ql[:, 1])\n",
    "    return xy  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "31.3 ms ± 598 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
    }
   ],
   "source": [
    "t = np.arange(0, 5, 0.005)\n",
    "\n",
    "q0 = np.array([1.1, 0.5])\n",
    "q0p = np.array([1.1 + 1e-5, 0.5])\n",
    "qt0 = np.array([0.0, 0.0])\n",
    "\n",
    "%timeit path = anal_solve_ode(q0, qt0, t)\n",
    "ppath = anal_solve_ode(q0p, qt0, t)\n",
    "xy = q2xy(path)\n",
    "pxy = q2xy(ppath)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "[<matplotlib.lines.Line2D at 0x1209dcf40>]"
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     "metadata": {},
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    },
    {
     "output_type": "display_data",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.plot(xy[:, 0], xy[:, 1])\n",
    "plt.plot(pxy[:, 0], pxy[:, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also solve using pytorch to autodiff the lagrangian, an use the following version of the EL equations (after Cranmer et al.), with $q=(r, \\theta)$:\n",
    "\n",
    "$\\ddot q = (\\nabla_{\\dot q}\\nabla_{\\dot q}^{\\top}\\mathcal{L})^{-1}[\\nabla_q \\mathcal{L} - (\\nabla_{q}\\nabla_{\\dot q}^{\\top}\\mathcal{L})\\dot q]$\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_xt(lagrangian, t, x):\n",
    "    n = x.shape[0]//2\n",
    "    xv = torch.autograd.Variable(x, requires_grad=True)\n",
    "    tq, tqt = torch.split(xv, 2, dim=0)\n",
    "\n",
    "    A = torch.inverse(hessian(lagrangian, xv, create_graph=True)[n:, n:])\n",
    "    B = jacobian(lagrangian, xv, create_graph=True)[:n]\n",
    "    C = hessian(lagrangian, xv, create_graph=True)[n:, :n]\n",
    "\n",
    "    tqtt = A @ (B - C @ tqt)\n",
    "\n",
    "    xt = torch.cat([tqt, torch.squeeze(tqtt)])\n",
    "\n",
    "    return xt\n",
    "\n",
    "\n",
    "def torch_solve_ode(x0, t, lagrangian):\n",
    "    f = partial(get_xt, lagrangian)\n",
    "    return tor_odeint(f, x0, t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "6.7 s ± 87.2 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
    }
   ],
   "source": [
    "tx0 = torch.cat([torch.tensor(q0), torch.tensor(qt0)])\n",
    "tt = torch.tensor(t)\n",
    "%timeit tpath = torch_solve_ode(tx0, tt, lagrangian)\n",
    "txy = q2xy(tpath)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.plot(xy[:, 0], xy[:, 1])\n",
    "plt.plot(txy[:, 0], txy[:, 1])\n",
    "En = [E(x) for x in path]\n",
    "Ent = [E(x) for x in tpath]\n",
    "plt.show()\n",
    "plt.plot(t, En)\n",
    "plt.plot(t, Ent)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "[<matplotlib.lines.Line2D at 0x12cae9a90>]"
     },
     "metadata": {},
     "execution_count": 154
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.plot(t, np.sum((tpath - path)**2, axis=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rk4_step(f, x, t, h):\n",
    "  # one step of runge-kutta integration\n",
    "  k1 = h * f(x, t)\n",
    "  k2 = h * f(x + k1/2, t + h/2)\n",
    "  k3 = h * f(x + k2/2, t + h/2)\n",
    "  k4 = h * f(x + k3, t + h)\n",
    "  return x + 1/6 * (k1 + 2 * k2 + 2 * k3 + k4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "t_train = torch.tensor(np.linspace(0, 10, 1500)).float()\n",
    "t_test = torch.tensor(np.linspace(10, 20, 1500)).float()\n",
    "\n",
    "tstep = t_train[1].item() \n",
    "\n",
    "x_train = torch.tensor(anal_solve_ode(q0, qt0, t_train)).float()\n",
    "xt_train = torch.tensor(get_xt_anal(x_train, t_train)).float()\n",
    "y_train = torch.tensor(rk4_step(get_xt_anal, x_train, t_train, tstep)).float()\n",
    "\n",
    "x_test = torch.tensor(anal_solve_ode(q0, qt0, t_test)).float()\n",
    "xt_test = torch.tensor(get_xt_anal(x_test, t_test)).float()\n",
    "y_test = torch.tensor(rk4_step(get_xt_anal, x_test, t_test, tstep)).float()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [],
   "source": [
    "class LNN(nn.Module):\n",
    "    def __init__(self):\n",
    "        super(LNN, self).__init__()\n",
    "        self.fc1 = nn.Linear(4, 128)\n",
    "        self.fc2 = nn.Linear(128, 128)\n",
    "        self.fc3 = nn.Linear(128, 1)\n",
    "    \n",
    "    def lagrangian(self, x): \n",
    "        x = F.softmax(self.fc1(x))\n",
    "        x = F.softmax(self.fc2(x))\n",
    "        x = self.fc3(x)\n",
    "        return x \n",
    "\n",
    "    def forward(self, x):\n",
    "\n",
    "        n = x.shape[1]//2\n",
    "        xv = torch.autograd.Variable(x, requires_grad=True)\n",
    "        xv_tup = tuple([xi for xi in x]) \n",
    "\n",
    "        tqt = xv[:, n:]\n",
    "\n",
    "\n",
    "        jacpar = partial(jacobian,  self.lagrangian, create_graph=True)\n",
    "        hesspar = partial(hessian,  self.lagrangian, create_graph=True)\n",
    "\n",
    "        A = tuple(map(hesspar, xv_tup))\n",
    "        B = tuple(map(jacpar, xv_tup))\n",
    "\n",
    "        \n",
    "        multi = lambda Ai, Bi, tqti, n:  torch.inverse(Ai[n:, n:]) @ (Bi[:n, 0] - Ai[n:, :n] @ tqti) \n",
    "        multi_par = partial(multi, n=n)\n",
    "\n",
    "        tqtt_tup = tuple(map(multi_par, A, B, tqt))\n",
    "        tqtt = torch.cat([tqtti[None] for tqtti in tqtt_tup])\n",
    "\n",
    "        xt = torch.cat([tqt, tqtt], axis=1)\n",
    "        xt.retain_grad()\n",
    "        return xt\n",
    "\n",
    "    def t_forward(self, t, x):\n",
    "        return self.forward(x)\n",
    "\n",
    "\n",
    "\n",
    "    \n",
    "def loss(pred, targ):\n",
    "    return torch.mean((pred - targ)**2)\n",
    "\n",
    "def nn_solve_ode(model, x0, t):\n",
    "\n",
    "    x0 = x0.detach().numpy()\n",
    "    def f(x, t):\n",
    "        x_tor = torch.tensor(np.expand_dims(x, 0), requires_grad=True).float()\n",
    "        return np.squeeze(model(x_tor).detach().numpy(), axis=0)\n",
    "    return odeint(f, x0, t)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "[1,    15] loss: 455.2153637975\n[2,    15] loss: 9.7381901016\n[3,    15] loss: 29.1845553964\n[4,    15] loss: 63.8707298787\n[5,    15] loss: 37.2992564697\n[6,    15] loss: 39.5541002579\n[7,    15] loss: 14.5610445531\n[8,    15] loss: 3.1170572319\n[9,    15] loss: 2.5411200695\n[10,    15] loss: 2.5637215309\n[11,    15] loss: 2.5671767139\n[12,    15] loss: 2.5433052311\n[13,    15] loss: 2.5168358434\n[14,    15] loss: 2.4936192252\n[15,    15] loss: 2.4737230962\n[16,    15] loss: 2.4561784185\n[17,    15] loss: 2.4401843039\n[18,    15] loss: 2.4254116166\n[19,    15] loss: 2.4116630898\n[20,    15] loss: 2.3987121499\n[21,    15] loss: 2.3866905460\n[22,    15] loss: 2.3753447901\n[23,    15] loss: 2.3647259032\n[24,    15] loss: 2.3547427578\n[25,    15] loss: 2.3454292272\n[26,    15] loss: 2.3366362222\n[27,    15] loss: 2.3284198926\n"
    },
    {
     "output_type": "error",
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-134-0897fe8172bf>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     15\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     16\u001b[0m         \u001b[0mloss_val\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mloss\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mxt_pred\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxt_train\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 17\u001b[0;31m         \u001b[0mloss_val\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbackward\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     18\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     19\u001b[0m         \u001b[0moptimizer\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstep\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/miniconda3/envs/pytorch/lib/python3.8/site-packages/torch/tensor.py\u001b[0m in \u001b[0;36mbackward\u001b[0;34m(self, gradient, retain_graph, create_graph)\u001b[0m\n\u001b[1;32m    196\u001b[0m                 \u001b[0mproducts\u001b[0m\u001b[0;34m.\u001b[0m \u001b[0mDefaults\u001b[0m \u001b[0mto\u001b[0m\u001b[0;31m \u001b[0m\u001b[0;31m`\u001b[0m\u001b[0;31m`\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;31m`\u001b[0m\u001b[0;31m`\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    197\u001b[0m         \"\"\"\n\u001b[0;32m--> 198\u001b[0;31m         \u001b[0mtorch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mautograd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbackward\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgradient\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mretain_graph\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcreate_graph\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    199\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    200\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mregister_hook\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhook\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/miniconda3/envs/pytorch/lib/python3.8/site-packages/torch/autograd/__init__.py\u001b[0m in \u001b[0;36mbackward\u001b[0;34m(tensors, grad_tensors, retain_graph, create_graph, grad_variables)\u001b[0m\n\u001b[1;32m     96\u001b[0m         \u001b[0mretain_graph\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcreate_graph\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     97\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 98\u001b[0;31m     Variable._execution_engine.run_backward(\n\u001b[0m\u001b[1;32m     99\u001b[0m         \u001b[0mtensors\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgrad_tensors\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mretain_graph\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcreate_graph\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    100\u001b[0m         allow_unreachable=True)  # allow_unreachable flag\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "eps = 100\n",
    "N = 1500 \n",
    "batch_size = 100 \n",
    "\n",
    "model = LNN()\n",
    "\n",
    "optimizer = optim.Adam(model.parameters(), lr=1e-3)\n",
    "loss_list = []\n",
    "for e in range(eps):\n",
    "    running_loss = 0.\n",
    "    for i in range(1, N // batch_size):\n",
    "        optimizer.zero_grad()\n",
    "        xi = xt_train[(i-1)*batch_size:i*batch_size]\n",
    "        xt_pred = model(xi)\n",
    "\n",
    "        loss_val = loss(xt_pred, xt_train[i])\n",
    "        loss_val.backward()\n",
    "\n",
    "        optimizer.step()\n",
    "\n",
    "\n",
    "\n",
    "        running_loss += loss_val.item()\n",
    "\n",
    "\n",
    "    print('[%d, %5d] loss: %.10f' %\n",
    "          (e + 1, i + 1, running_loss/N))\n",
    "    \n",
    "    loss_list.append(running_loss/N)\n",
    "    running_loss = 0.0\n",
    "        \n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "\n",
    "nn_test = nn_solve_ode(model, x_train[0], t_train)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
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     "output_type": "display_data",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.plot(t_train, x_train[:, 0])\n",
    "plt.plot(t_train, nn_test[:, 0])\n",
    "plt.show()\n",
    "plt.plot(np.arange(len(loss_list)), loss_list)\n",
    "plt.yscale('log')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "(array([1.10000002, 0.5       , 0.        , 0.        ]), tensor([1.1000, 0.5000, 0.0000, 0.0000]))\n(array([1.10001986, 0.50017215, 0.00639064, 0.0529767 ]), tensor([ 1.0999,  0.4999, -0.0215, -0.0291]))\n(array([1.10009267, 0.50072905, 0.01613579, 0.11604361]), tensor([ 1.0997,  0.4996, -0.0430, -0.0582]))\n(array([1.10024763, 0.50175655, 0.03160623, 0.19565146]), tensor([ 1.0994,  0.4991, -0.0644, -0.0873]))\n(array([1.10054152, 0.50341503, 0.05997762, 0.31107476]), tensor([ 1.0989,  0.4984, -0.0856, -0.1164]))\n(array([1.10092408, 0.50520762, 0.13313947, 0.53411951]), tensor([ 1.0982,  0.4976, -0.1068, -0.1456]))\n(array([-4.02853669e-196, -2.54555040e-107,  6.73326509e-250,\n       -1.56545976e-267]), tensor([ 1.0974,  0.4965, -0.1277, -0.1748]))\n(array([-5.64080106e-294, -1.30961378e-266,  3.11432868e+279,\n        4.49510357e+260]), tensor([ 1.0965,  0.4952, -0.1484, -0.2040]))\n(array([-8.42783858e+162, -3.77048338e-132, -2.02912998e+077,\n       -7.59058940e-095]), tensor([ 1.0955,  0.4938, -0.1689, -0.2333]))\n(array([-1.28596910e-075, -1.23232218e-088,  1.17416594e+020,\n       -2.53081277e-269]), tensor([ 1.0943,  0.4921, -0.1890, -0.2627]))\n"
    }
   ],
   "source": [
    "for i in range(10):\n",
    "    print((nn_test[i], x_train[i]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "tensor([[ 0.0000,  0.0000, -3.2242, -4.3584],\n        [-0.0215, -0.0291, -3.2213, -4.3591],\n        [-0.0430, -0.0582, -3.2129, -4.3610],\n        ...,\n        [-0.4281, -1.6524,  3.5576, -3.0637],\n        [-0.4040, -1.6722,  3.6836, -2.8887],\n        [-0.3790, -1.6909,  3.8023, -2.7047]])"
     },
     "metadata": {},
     "execution_count": 164
    }
   ],
   "source": [
    "xt_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
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