EMPS-train-and-analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a5de4184",
   "metadata": {},
   "source": [
    "## EMPS Training and results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "910feef1",
   "metadata": {},
   "outputs": [],
   "source": [
    "import deepSI\n",
    "from deepSI import System_data, System_data_list\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "import torch\n",
    "from torch import optim, nn\n",
    "from tqdm.auto import tqdm\n",
    "import matplotlib\n",
    "matplotlib.rcParams['pdf.fonttype'] = 42\n",
    "matplotlib.rcParams['ps.fonttype'] = 42"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "0d18cd3e",
   "metadata": {},
   "outputs": [],
   "source": [
    "train, test = deepSI.datasets.EMPS(split_data=True)\n",
    "train.y *= 1000 #rescale to  mm\n",
    "test.y *= 1000\n",
    "train, val =  train.train_test_split(0.28)\n",
    "dt = 0.001 #1 ms\n",
    "t = np.arange(len(test_sim.y))*dt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "062c5d44",
   "metadata": {},
   "outputs": [],
   "source": [
    "load = True\n",
    "if not load:\n",
    "    kwargs = {'n_nodes_per_layer':30, 'n_hidden_layers': 1}\n",
    "    sys = deepSI.fit_systems.SS_encoder_deriv_general(nx=2, na=20, nb=20, tau=100, f_net_kwargs=kwargs, h_net_kwargs=kwargs)\n",
    "    sys.fit(train, val_sys_data=val, epochs=4000, batch_size=1024, loss_kwargs=dict(nf=200),validation_measure='sim-RMS')\n",
    "    sys.save_system('models-encoder-CT-EMPS/CT-encoder-model-EMPS')\n",
    "else:\n",
    "    sys = deepSI.load_system('models-encoder-CT-EMPS/CT-encoder-model-EMPS')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e78d8c69",
   "metadata": {},
   "outputs": [],
   "source": [
    "test_sim = sys.apply_experiment(test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "0b8be9d1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMS = 4.614317967710199\n"
     ]
    }
   ],
   "source": [
    "RMS = test_sim.RMS(test)\n",
    "print(f'RMS = {RMS}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "01adac91",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 405x315 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 405x315 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "z = 0.9\n",
    "plt.figure(figsize=(z*4.5,z*3.5))\n",
    "plt.plot(test.y,'k',label='System')\n",
    "plt.plot(test_sim.y,'r--',label='CT SUBNET model ($\\\\Delta t/\\\\tau = 0.01$)')\n",
    "plt.grid()\n",
    "plt.legend(loc=(0.1+0.015,1.0+0.015))\n",
    "plt.xlim(min(t), max(t))\n",
    "plt.ylabel('$y$ (mm)')\n",
    "plt.xlabel('Index time')\n",
    "plt.tight_layout(pad=0.9)\n",
    "plt.savefig('figures-for-paper/EMPS-CT-SUBNET-sim.jpg',dpi=400)\n",
    "plt.savefig('figures-for-paper/EMPS-CT-SUBNET-sim.pdf')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "2e5fba4b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.04308890581131"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sys.time[-1]/60/60"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cec35ca8",
   "metadata": {},
   "source": [
    "## NeuralODE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "47dc2782",
   "metadata": {},
   "outputs": [],
   "source": [
    "import enum\n",
    "import os\n",
    "import argparse\n",
    "import logging\n",
    "import time\n",
    "import numpy as np\n",
    "import numpy.random as npr\n",
    "import matplotlib\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.optim as optim\n",
    "import torch.nn.functional as F\n",
    "from tqdm.auto import tqdm\n",
    "\n",
    "from torchdiffeq import odeint #includes exogenous inputs\n",
    "\n",
    "class LatentODEfunc(nn.Module):\n",
    "\n",
    "    def __init__(self, latent_dim=4, nhidden=20, udim=None):\n",
    "        super(LatentODEfunc, self).__init__()\n",
    "        self.elu = nn.ELU(inplace=True)\n",
    "        udim_val = 0 if udim is None else udim\n",
    "        self.fc1 = nn.Linear(latent_dim + udim_val, nhidden)\n",
    "        self.fc2 = nn.Linear(nhidden, nhidden)\n",
    "        self.fc3 = nn.Linear(nhidden, latent_dim)\n",
    "        self.nfe = 0\n",
    "\n",
    "    def forward(self, t, x, u=None):\n",
    "        self.nfe += 1\n",
    "        if u is not None: #append the input to the state\n",
    "            x = torch.cat([x,u[:,None] if u.ndim==1 else u],dim=1)\n",
    "        out = self.fc1(x)\n",
    "        out = self.elu(out)\n",
    "        out = self.fc2(out)\n",
    "        out = self.elu(out)\n",
    "        out = self.fc3(out)\n",
    "        return out\n",
    "\n",
    "\n",
    "class RecognitionRNN(nn.Module):\n",
    "\n",
    "    def __init__(self, latent_dim=4, obs_dim=2, nhidden=25, nbatch=1):\n",
    "        super(RecognitionRNN, self).__init__()\n",
    "        self.nhidden = nhidden\n",
    "        self.nbatch = nbatch\n",
    "        self.i2h = nn.Linear(obs_dim + nhidden, nhidden)\n",
    "        self.h2o = nn.Linear(nhidden, latent_dim * 2)\n",
    "\n",
    "    def forward(self, x, h):\n",
    "        combined = torch.cat((x, h), dim=1)\n",
    "        h = torch.tanh(self.i2h(combined))\n",
    "        out = self.h2o(h)\n",
    "        return out, h\n",
    "\n",
    "    def initHidden(self):\n",
    "        return torch.zeros(self.nbatch, self.nhidden)\n",
    "\n",
    "\n",
    "class Decoder(nn.Module):\n",
    "\n",
    "    def __init__(self, latent_dim=4, obs_dim=2, nhidden=20):\n",
    "        super(Decoder, self).__init__()\n",
    "        self.relu = nn.ReLU(inplace=True)\n",
    "        self.fc1 = nn.Linear(latent_dim, nhidden)\n",
    "        self.fc2 = nn.Linear(nhidden, obs_dim)\n",
    "\n",
    "    def forward(self, z):\n",
    "        out = self.fc1(z)\n",
    "        out = self.relu(out)\n",
    "        out = self.fc2(out)\n",
    "        return out\n",
    "\n",
    "\n",
    "class RunningAverageMeter(object):\n",
    "    \"\"\"Computes and stores the average and current value\"\"\"\n",
    "\n",
    "    def __init__(self, momentum=0.99):\n",
    "        self.momentum = momentum\n",
    "        self.reset()\n",
    "\n",
    "    def reset(self):\n",
    "        self.val = None\n",
    "        self.avg = 0\n",
    "\n",
    "    def update(self, val):\n",
    "        if self.val is None:\n",
    "            self.avg = val\n",
    "        else:\n",
    "            self.avg = self.avg * self.momentum + val * (1 - self.momentum)\n",
    "        self.val = val\n",
    "\n",
    "\n",
    "def log_normal_pdf(x, mean, logvar):\n",
    "    const = torch.from_numpy(np.array([2. * np.pi])).float().to(x.device)\n",
    "    const = torch.log(const)\n",
    "    return -.5 * (const + logvar + (x - mean) ** 2. / torch.exp(logvar))\n",
    "\n",
    "\n",
    "def normal_kl(mu1, lv1, mu2, lv2):\n",
    "    v1 = torch.exp(lv1)\n",
    "    v2 = torch.exp(lv2)\n",
    "    lstd1 = lv1 / 2.\n",
    "    lstd2 = lv2 / 2.\n",
    "\n",
    "    kl = lstd2 - lstd1 + ((v1 + (mu1 - mu2) ** 2.) / (2. * v2)) - .5\n",
    "    return kl\n",
    "\n",
    "def get_train_val_test(dataset):\n",
    "    import deepSI\n",
    "    from deepSI import System_data_list\n",
    "    if dataset=='CED':\n",
    "        data_full = deepSI.datasets.CED()\n",
    "        train = System_data_list([data_i[:300] for data_i in data_full])\n",
    "        test = System_data_list([data_i[300:] for data_i in data_full])\n",
    "        val = System_data_list([t[:100] for t in test])\n",
    "    elif dataset=='CCT':\n",
    "        train, test = deepSI.datasets.Cascaded_Tanks()\n",
    "        val, test = test[:len(test)//2], test\n",
    "    elif dataset=='EMPS':\n",
    "        train, test = deepSI.datasets.EMPS(split_data=True)\n",
    "        train.y *= 1000 #rescale to  mm\n",
    "        test.y *= 1000\n",
    "        train, val =  train.train_test_split(0.28)\n",
    "    return train, val, test\n",
    "\n",
    "def get_torch_data(dataset, device=torch.device('cpu')):\n",
    "    train, val, test = get_train_val_test(dataset)\n",
    "    from deepSI.system_data import System_data_norm\n",
    "    norm = System_data_norm() #normalization\n",
    "    norm.fit(train)\n",
    "    train, val, test = [norm.transform(t) for t in [train, val, test]]\n",
    "\n",
    "    if dataset=='CCT' or dataset=='EMPS':\n",
    "        samp_trajs = train.y[None,:,None]\n",
    "        u_samp_trajs = train.u[None,:,None]\n",
    "        orig_trajs = test.y[None,:,None]\n",
    "        u_orig_trajs = test.u[None,:,None]\n",
    "        val_trajs = val.y[None,:,None]\n",
    "        u_val_trajs = val.u[None,:,None]\n",
    "\n",
    "        sample_time = 4. if dataset=='CCT' else 1.\n",
    "        samp_ts = np.arange(len(train.y))*sample_time\n",
    "\n",
    "    elif dataset=='CED':\n",
    "        samp_trajs = np.array([ti.y[:,None] for ti in train])\n",
    "        u_samp_trajs =  np.array([ti.u for ti in train])\n",
    "        orig_trajs = np.array([ti.y[:,None] for ti in test])\n",
    "        u_orig_trajs = np.array([ti.u for ti in test])\n",
    "        val_trajs = np.array([ti.y[:,None] for ti in val])\n",
    "        u_val_trajs = np.array([ti.u[:,None] for ti in val])\n",
    "\n",
    "        sample_time = 1/50\n",
    "        samp_ts = np.arange(len(train[0]))*sample_time\n",
    "\n",
    "    orig_trajs = torch.from_numpy(orig_trajs).float().to(device) #samples, time\n",
    "    u_orig_trajs = torch.from_numpy(u_orig_trajs).float().to(device)\n",
    "    samp_trajs = torch.from_numpy(samp_trajs).float().to(device)\n",
    "    u_samp_trajs = torch.from_numpy(u_samp_trajs).float().to(device)\n",
    "    samp_ts = torch.from_numpy(samp_ts).float().to(device)\n",
    "    u_val_trajs = torch.from_numpy(u_val_trajs).float().to(device)\n",
    "    val_trajs = torch.from_numpy(val_trajs).float().to(device)\n",
    "    \n",
    "    return orig_trajs, u_orig_trajs, samp_trajs, u_samp_trajs, samp_ts, \\\n",
    "            u_val_trajs, val_trajs, sample_time, norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "f168b316",
   "metadata": {},
   "outputs": [],
   "source": [
    "dataset='EMPS'\n",
    "method = 'rk4' #exogenous inputs only implemented for Euler, RK4 and midpoint.\n",
    "device = torch.device('cpu')\n",
    "train_dir = './models-neural-ode/'\n",
    "niters = 20000\n",
    "\n",
    "#given by latent_ODE:\n",
    "nhidden = 20\n",
    "rnn_nhidden = 25\n",
    "obs_dim = 1\n",
    "noise_std = 0.1\n",
    "\n",
    "orig_trajs, u_orig_trajs, samp_trajs, u_samp_trajs, samp_ts, u_val_trajs, val_trajs, sample_time, norm = \\\n",
    "        get_torch_data(dataset, device=device)\n",
    "\n",
    "tau_1 = True\n",
    "\n",
    "if dataset=='CCT':\n",
    "    dttau = 0.032\n",
    "    latent_dim = 2\n",
    "    \n",
    "elif dataset=='CED':\n",
    "    dttau = 0.12\n",
    "    latent_dim = 3\n",
    "elif dataset=='EMPS':\n",
    "    dttau = 0.01\n",
    "    latent_dim = 2\n",
    "    \n",
    "tau = 1 if tau_1 else sample_time/dttau\n",
    "    \n",
    "samp_ts /= tau #dt /dt * dttau = dttau\n",
    "\n",
    "has_val = True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "14734eca",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "I=1\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "7bec770e88db490ea6a7ab2f4141e8e3",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/20000 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iter: 1, running avg elbo: nan rms val nan\n",
      "Iter: 2, running avg elbo: nan rms val nan\n",
      "Iter: 3, running avg elbo: nan rms val nan\n",
      "stopped by keyboard I=1\n"
     ]
    }
   ],
   "source": [
    "for I in range(1,100):\n",
    "    \n",
    "    # create model\n",
    "    print(f'I={I}')\n",
    "    udim = 1 if u_orig_trajs.ndim==2 else u_orig_trajs.shape[-1]\n",
    "    func = LatentODEfunc(latent_dim, nhidden, udim=udim).to(device)\n",
    "    rec = RecognitionRNN(latent_dim, obs_dim, rnn_nhidden, samp_trajs.shape[0]).to(device)\n",
    "    dec = Decoder(latent_dim, obs_dim, nhidden).to(device)\n",
    "    params = (list(func.parameters()) + list(dec.parameters()) + list(rec.parameters()))\n",
    "    optimizer = optim.Adam(params, lr=0.01)\n",
    "    loss_meter = RunningAverageMeter()\n",
    "\n",
    "    try: #for KeyboardInterrupt stopping of iterations\n",
    "        best_val = float('inf')\n",
    "        for itr in tqdm(range(1, niters + 1)):\n",
    "            optimizer.zero_grad()\n",
    "            # backward in time to infer q(z_0)\n",
    "            h = rec.initHidden().to(device)\n",
    "            for t in reversed(range(samp_trajs.size(1))):\n",
    "                obs = samp_trajs[:, t, :]\n",
    "                out, h = rec.forward(obs, h)\n",
    "            qz0_mean, qz0_logvar = out[:, :latent_dim], out[:, latent_dim:]\n",
    "            epsilon = torch.randn(qz0_mean.size()).to(device)\n",
    "            z0 = epsilon * torch.exp(.5 * qz0_logvar) + qz0_mean\n",
    "\n",
    "            # forward in time and solve ode for reconstructions\n",
    "            pred_z = odeint(func, z0, samp_ts, u=u_samp_trajs, method=method).permute(1, 0, 2)\n",
    "            pred_x = dec(pred_z)\n",
    "\n",
    "            # compute loss\n",
    "            noise_std_ = torch.zeros(pred_x.size()).to(device) + noise_std\n",
    "            noise_logvar = 2. * torch.log(noise_std_).to(device)\n",
    "            logpx = log_normal_pdf(\n",
    "                samp_trajs, pred_x, noise_logvar).sum(-1).sum(-1)\n",
    "            pz0_mean = pz0_logvar = torch.zeros(z0.size()).to(device)\n",
    "            analytic_kl = normal_kl(qz0_mean, qz0_logvar,\n",
    "                                    pz0_mean, pz0_logvar).sum(-1)\n",
    "            loss = torch.mean(-logpx + analytic_kl, dim=0)\n",
    "            loss.backward()\n",
    "            optimizer.step()\n",
    "            loss_meter.update(loss.item())\n",
    "\n",
    "\n",
    "            if has_val and itr%1==0:\n",
    "\n",
    "                h = rec.initHidden().to(device)\n",
    "                for t in reversed(range(val_trajs.size(1))):\n",
    "                    obs = val_trajs[:, t, :]\n",
    "                    out, h = rec.forward(obs, h)\n",
    "                qz0_mean, qz0_logvar = out[:, :latent_dim], out[:, latent_dim:]\n",
    "                epsilon = torch.randn(qz0_mean.size()).to(device)\n",
    "                z0 = epsilon * torch.exp(.5 * qz0_logvar) + qz0_mean\n",
    "\n",
    "                # forward in time and solve ode for reconstructions\n",
    "                pred_z = odeint(func, z0, samp_ts[:u_val_trajs.shape[1]], u=u_val_trajs, method=method).permute(1, 0, 2)\n",
    "                pred_x = dec(pred_z)\n",
    "                val_trajs_p = pred_x.detach()\n",
    "                RMS = torch.mean((val_trajs_p - val_trajs)**2).item()**0.5\n",
    "                print('Iter: {}, running avg elbo: {:.4f} rms val {:.4f}'.format(itr, -loss_meter.avg, RMS))\n",
    "                if RMS<best_val:\n",
    "                    best_val = RMS\n",
    "                    if train_dir is not None:\n",
    "                        if tau_1:\n",
    "                            ckpt_path = os.path.join(train_dir, f'ckpt-best-{dataset}-{I}-tau_1.pth')\n",
    "                        else:\n",
    "                            ckpt_path = os.path.join(train_dir, f'ckpt-best-{dataset}-{I}.pth')\n",
    "                        torch.save({\n",
    "                            'func':func,\n",
    "                            'rec':rec,\n",
    "                            'dec':dec,\n",
    "                            'func_state_dict': func.state_dict(),\n",
    "                            'rec_state_dict': rec.state_dict(),\n",
    "                            'dec_state_dict': dec.state_dict(),\n",
    "                            'optimizer_state_dict': optimizer.state_dict(),\n",
    "                            'orig_trajs': orig_trajs,\n",
    "                            'samp_trajs': samp_trajs,\n",
    "                            'samp_ts': samp_ts,\n",
    "                        }, ckpt_path)\n",
    "                        print('Stored ckpt at {} {}'.format(ckpt_path, RMS))\n",
    "\n",
    "    except KeyboardInterrupt:\n",
    "        print(f'stopped by keyboard I={I}')\n",
    "        break\n",
    "    if train_dir is not None:\n",
    "        if tau_1:\n",
    "            ckpt_path = os.path.join(train_dir, f'ckpt-last-{dataset}-{I}-tau_1.pth')\n",
    "        else:\n",
    "            ckpt_path = os.path.join(train_dir, f'ckpt-last-{dataset}-{I}.pth')\n",
    "        torch.save({\n",
    "            'func':func,\n",
    "            'rec':rec,\n",
    "            'dec':dec,\n",
    "            'func_state_dict': func.state_dict(),\n",
    "            'rec_state_dict': rec.state_dict(),\n",
    "            'dec_state_dict': dec.state_dict(),\n",
    "            'optimizer_state_dict': optimizer.state_dict(),\n",
    "            'orig_trajs': orig_trajs,\n",
    "            'samp_trajs': samp_trajs,\n",
    "            'samp_ts': samp_ts,\n",
    "        }, ckpt_path)\n",
    "        print('Stored ckpt at {}'.format(ckpt_path))\n",
    "    print('Training complete after {} iters.'.format(itr))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a93df682",
   "metadata": {},
   "source": [
    "## Did not converge"
   ]
  }
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