approximate_steady_state_error.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# Approximate steady state error\n",
    "\n",
    "We approximate the maximum error due to the steady state assumptions by following a 9 step work flow.\n",
    "The theory behind this approach is laied out in Appendix C of the paper.\n",
    "\n",
    " 1. draw initial demand\n",
    " 2. solve state equations (steady state)\n",
    " 3. modify demand (i.e. modify mass flows at demand)\n",
    " 4. solve hydraulic system with new mass flows\n",
    " 5. solve thermal system with new mass flows\n",
    " 6. solve steady state with new demands\n",
    " 7. compare thermal solution (5) and steady-state solution (6); i.e., compare temperatures at demands\n",
    " 8. store results over multiple runs and calculate means and variances\n",
    "\n"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Imports:"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:From C:\\Users\\Andreas Bott\\MeFlexWaerme\\venv\\lib\\site-packages\\tensorflow\\python\\autograph\\pyct\\static_analysis\\liveness.py:83: Analyzer.lamba_check (from tensorflow.python.autograph.pyct.static_analysis.liveness) is deprecated and will be removed after 2023-09-23.\n",
      "Instructions for updating:\n",
      "Lambda fuctions will be no more assumed to be used in the statement where they are used, or at least in the same block. https://github.com/tensorflow/tensorflow/issues/56089\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import tensorflow as tf\n",
    "from libdnnmcmc.utility import load_scenario\n",
    "from libdnnmcmc.steady_state_solvers import SE_solver, my_fixpoint_iteratror\n",
    "\n",
    "SE, VM, d_prior_dist, _ = load_scenario('loop')\n",
    "cycles = VM.cycles\n",
    "FI = my_fixpoint_iteratror()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### settings:"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "outputs": [],
   "source": [
    "n_runs = 50\n",
    "q_modifier = [0.7, 1.3]"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### setup:"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "outputs": [],
   "source": [
    "n_modifier = len(q_modifier)\n",
    "# init arrays to store results:\n",
    "z_pattern = np.zeros((n_runs, n_modifier))\n",
    "Ta_ss, Tb_ss, Tc_ss, Td_ss = np.zeros_like(z_pattern), np.zeros_like(z_pattern), np.zeros_like(z_pattern), np.zeros_like(z_pattern)\n",
    "Ta_qss, Tb_qss, Tc_qss, Td_qss = np.zeros_like(z_pattern), np.zeros_like(z_pattern), np.zeros_like(z_pattern), np.zeros_like(z_pattern)\n",
    "\n",
    "# define wrapper around solver:\n",
    "solve_SE = SE_solver()\n",
    "def _solve_SE(demands, SE):\n",
    "    for dem in SE.demands.keys():\n",
    "        ind = SE.dem_ind[dem]\n",
    "        d = demands[ind]\n",
    "        SE.Q_heat[ind].assign(d)\n",
    "    solve_SE(SE, cycles)\n",
    "    return tf.reduce_sum(SE.evaluate_state_equations('forwardpass')**2)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Analysis:"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "T_diff Dem A: [0.16886726] \n",
      " T_diff Dem B: [1.74257629] \n",
      " T_diff Dem c: [0.05077148] \n",
      " T_diff Dem D: [0.16594071] \n",
      " \n",
      "T_diff Dem A: [0.20352625] \n",
      " T_diff Dem B: [0.49475922] \n",
      " T_diff Dem c: [0.04029388] \n",
      " T_diff Dem D: [0.19316898] \n",
      " \n",
      "T_diff Dem A: [0.30564609] \n",
      " T_diff Dem B: [0.97170311] \n",
      " T_diff Dem c: [0.03681089] \n",
      " T_diff Dem D: [0.19846425] \n",
      " \n",
      "T_diff Dem A: [0.16090781] \n",
      " T_diff Dem B: [0.87829356] \n",
      " T_diff Dem c: [0.04576766] \n",
      " T_diff Dem D: [0.62237516] \n",
      " \n",
      "T_diff Dem A: [0.21125695] \n",
      " T_diff Dem B: [-3.57838673] \n",
      " T_diff Dem c: [0.05206049] \n",
      " T_diff Dem D: [1.60035737] \n",
      " \n",
      "T_diff Dem A: [0.24622681] \n",
      " T_diff Dem B: [0.71053122] \n",
      " T_diff Dem c: [0.0362094] \n",
      " T_diff Dem D: [0.13871323] \n",
      " \n",
      "T_diff Dem A: [0.28344678] \n",
      " T_diff Dem B: [0.98361553] \n",
      " T_diff Dem c: [0.03814324] \n",
      " T_diff Dem D: [0.15163684] \n",
      " \n",
      "T_diff Dem A: [0.28553158] \n",
      " T_diff Dem B: [0.75545733] \n",
      " T_diff Dem c: [0.04720897] \n",
      " T_diff Dem D: [0.16853765] \n",
      " \n",
      "T_diff Dem A: [0.1634733] \n",
      " T_diff Dem B: [1.15117604] \n",
      " T_diff Dem c: [0.04749986] \n",
      " T_diff Dem D: [0.33834093] \n",
      " \n",
      "T_diff Dem A: [0.17287745] \n",
      " T_diff Dem B: [1.5784323] \n",
      " T_diff Dem c: [0.0428713] \n",
      " T_diff Dem D: [0.32274927] \n",
      " \n",
      "T_diff Dem A: [0.29579767] \n",
      " T_diff Dem B: [0.8285769] \n",
      " T_diff Dem c: [0.029501] \n",
      " T_diff Dem D: [0.20063354] \n",
      " \n",
      "T_diff Dem A: [0.29771858] \n",
      " T_diff Dem B: [1.01626151] \n",
      " T_diff Dem c: [0.03975923] \n",
      " T_diff Dem D: [0.16193052] \n",
      " \n",
      "T_diff Dem A: [0.16225709] \n",
      " T_diff Dem B: [0.9766505] \n",
      " T_diff Dem c: [0.02675478] \n",
      " T_diff Dem D: [0.27588503] \n",
      " \n",
      "T_diff Dem A: [0.34420275] \n",
      " T_diff Dem B: [1.35715233] \n",
      " T_diff Dem c: [0.0330718] \n",
      " T_diff Dem D: [0.14701158] \n",
      " \n",
      "T_diff Dem A: [0.60819041] \n",
      " T_diff Dem B: [1.82889849] \n",
      " T_diff Dem c: [0.03194865] \n",
      " T_diff Dem D: [0.13505299] \n",
      " \n",
      "T_diff Dem A: [0.18925683] \n",
      " T_diff Dem B: [4.06568593] \n",
      " T_diff Dem c: [0.04748744] \n",
      " T_diff Dem D: [0.18589547] \n",
      " \n",
      "T_diff Dem A: [0.38723522] \n",
      " T_diff Dem B: [0.91700124] \n",
      " T_diff Dem c: [0.05526121] \n",
      " T_diff Dem D: [0.25420686] \n",
      " \n",
      "T_diff Dem A: [0.28748018] \n",
      " T_diff Dem B: [0.64352073] \n",
      " T_diff Dem c: [0.0508293] \n",
      " T_diff Dem D: [0.31341913] \n",
      " \n",
      "T_diff Dem A: [0.20401547] \n",
      " T_diff Dem B: [0.72531011] \n",
      " T_diff Dem c: [0.03337782] \n",
      " T_diff Dem D: [0.31241456] \n",
      " \n",
      "T_diff Dem A: [0.28884174] \n",
      " T_diff Dem B: [0.95565339] \n",
      " T_diff Dem c: [0.03280294] \n",
      " T_diff Dem D: [0.15662956] \n",
      " \n",
      "T_diff Dem A: [0.21976343] \n",
      " T_diff Dem B: [1.18606284] \n",
      " T_diff Dem c: [0.04061329] \n",
      " T_diff Dem D: [0.32002555] \n",
      " \n",
      "T_diff Dem A: [0.16597908] \n",
      " T_diff Dem B: [1.06056257] \n",
      " T_diff Dem c: [0.03165483] \n",
      " T_diff Dem D: [0.30081099] \n",
      " \n",
      "T_diff Dem A: [0.2441713] \n",
      " T_diff Dem B: [0.98192674] \n",
      " T_diff Dem c: [0.06333256] \n",
      " T_diff Dem D: [0.30159727] \n",
      " \n",
      "T_diff Dem A: [0.15462978] \n",
      " T_diff Dem B: [0.85747879] \n",
      " T_diff Dem c: [0.0502677] \n",
      " T_diff Dem D: [0.25959448] \n",
      " \n",
      "T_diff Dem A: [1.39473616] \n",
      " T_diff Dem B: [1.01186023] \n",
      " T_diff Dem c: [0.06206167] \n",
      " T_diff Dem D: [0.17780373] \n",
      " \n",
      "T_diff Dem A: [0.47911176] \n",
      " T_diff Dem B: [2.20379178] \n",
      " T_diff Dem c: [0.05094279] \n",
      " T_diff Dem D: [0.24295021] \n",
      " \n",
      "T_diff Dem A: [0.19572145] \n",
      " T_diff Dem B: [1.66683256] \n",
      " T_diff Dem c: [0.04928732] \n",
      " T_diff Dem D: [0.34811236] \n",
      " \n",
      "T_diff Dem A: [0.18469569] \n",
      " T_diff Dem B: [1.26782915] \n",
      " T_diff Dem c: [0.03860449] \n",
      " T_diff Dem D: [0.32466692] \n",
      " \n",
      "T_diff Dem A: [0.32625399] \n",
      " T_diff Dem B: [1.62006953] \n",
      " T_diff Dem c: [0.05219525] \n",
      " T_diff Dem D: [0.17667657] \n",
      " \n",
      "T_diff Dem A: [0.76513977] \n",
      " T_diff Dem B: [0.85641223] \n",
      " T_diff Dem c: [0.05479981] \n",
      " T_diff Dem D: [0.31527071] \n",
      " \n",
      "T_diff Dem A: [0.29919819] \n",
      " T_diff Dem B: [0.98688659] \n",
      " T_diff Dem c: [0.03910554] \n",
      " T_diff Dem D: [0.16864715] \n",
      " \n",
      "T_diff Dem A: [0.28391884] \n",
      " T_diff Dem B: [0.6299526] \n",
      " T_diff Dem c: [0.04292157] \n",
      " T_diff Dem D: [0.37374198] \n",
      " \n",
      "T_diff Dem A: [0.18626084] \n",
      " T_diff Dem B: [1.31886812] \n",
      " T_diff Dem c: [0.03054041] \n",
      " T_diff Dem D: [0.36500888] \n",
      " \n",
      "T_diff Dem A: [0.17447071] \n",
      " T_diff Dem B: [6.49540808] \n",
      " T_diff Dem c: [0.04819317] \n",
      " T_diff Dem D: [0.17147782] \n",
      " \n",
      "T_diff Dem A: [0.15670539] \n",
      " T_diff Dem B: [2.63117823] \n",
      " T_diff Dem c: [0.03435715] \n",
      " T_diff Dem D: [0.15402947] \n",
      " \n",
      "T_diff Dem A: [0.23698624] \n",
      " T_diff Dem B: [1.28496902] \n",
      " T_diff Dem c: [0.02186071] \n",
      " T_diff Dem D: [0.14569466] \n",
      " \n",
      "T_diff Dem A: [0.42147558] \n",
      " T_diff Dem B: [1.57563311] \n",
      " T_diff Dem c: [0.02826378] \n",
      " T_diff Dem D: [0.22180184] \n",
      " \n",
      "T_diff Dem A: [0.45202757] \n",
      " T_diff Dem B: [2.67008725] \n",
      " T_diff Dem c: [0.0724984] \n",
      " T_diff Dem D: [0.2375101] \n",
      " \n",
      "T_diff Dem A: [1.6960403] \n",
      " T_diff Dem B: [-3.4562892] \n",
      " T_diff Dem c: [0.04039164] \n",
      " T_diff Dem D: [0.18168899] \n",
      " \n",
      "T_diff Dem A: [0.1931712] \n",
      " T_diff Dem B: [1.97610198] \n",
      " T_diff Dem c: [0.05073075] \n",
      " T_diff Dem D: [0.79470118] \n",
      " \n",
      "T_diff Dem A: [0.24472088] \n",
      " T_diff Dem B: [0.54508716] \n",
      " T_diff Dem c: [0.02703342] \n",
      " T_diff Dem D: [0.35766321] \n",
      " \n",
      "T_diff Dem A: [0.16914491] \n",
      " T_diff Dem B: [1.06815756] \n",
      " T_diff Dem c: [0.03829294] \n",
      " T_diff Dem D: [0.34362601] \n",
      " \n",
      "T_diff Dem A: [0.17690344] \n",
      " T_diff Dem B: [1.98086563] \n",
      " T_diff Dem c: [0.06442385] \n",
      " T_diff Dem D: [0.31734778] \n",
      " \n",
      "T_diff Dem A: [0.29700152] \n",
      " T_diff Dem B: [0.85799616] \n",
      " T_diff Dem c: [0.03478873] \n",
      " T_diff Dem D: [0.16744668] \n",
      " \n",
      "T_diff Dem A: [0.43414354] \n",
      " T_diff Dem B: [2.15989786] \n",
      " T_diff Dem c: [0.0372552] \n",
      " T_diff Dem D: [0.21928221] \n",
      " \n",
      "T_diff Dem A: [0.15440547] \n",
      " T_diff Dem B: [0.83562752] \n",
      " T_diff Dem c: [0.03387235] \n",
      " T_diff Dem D: [0.2801716] \n",
      " \n",
      "T_diff Dem A: [0.30172482] \n",
      " T_diff Dem B: [1.10718086] \n",
      " T_diff Dem c: [0.03990457] \n",
      " T_diff Dem D: [0.15938903] \n",
      " \n",
      "T_diff Dem A: [0.2747129] \n",
      " T_diff Dem B: [0.7544542] \n",
      " T_diff Dem c: [0.02695849] \n",
      " T_diff Dem D: [0.15432405] \n",
      " \n",
      "T_diff Dem A: [0.16793151] \n",
      " T_diff Dem B: [4.4670764] \n",
      " T_diff Dem c: [0.03164588] \n",
      " T_diff Dem D: [0.16467541] \n",
      " \n",
      "T_diff Dem A: [0.30262841] \n",
      " T_diff Dem B: [3.14541455] \n",
      " T_diff Dem c: [0.05442951] \n",
      " T_diff Dem D: [0.15260902] \n",
      " \n",
      "T_diff Dem A: [-0.05672639] \n",
      " T_diff Dem B: [0.1540146] \n",
      " T_diff Dem c: [-0.01638579] \n",
      " T_diff Dem D: [-0.05544114] \n",
      " \n",
      "T_diff Dem A: [-0.07531165] \n",
      " T_diff Dem B: [2.12996726] \n",
      " T_diff Dem c: [-0.01433217] \n",
      " T_diff Dem D: [-0.07359895] \n",
      " \n",
      "T_diff Dem A: [-0.10206974] \n",
      " T_diff Dem B: [-0.33921043] \n",
      " T_diff Dem c: [-0.01140075] \n",
      " T_diff Dem D: [-0.06350314] \n",
      " \n",
      "T_diff Dem A: [-0.05354875] \n",
      " T_diff Dem B: [-0.33110685] \n",
      " T_diff Dem c: [-0.01473236] \n",
      " T_diff Dem D: [-0.1390009] \n",
      " \n",
      "T_diff Dem A: [-0.05240596] \n",
      " T_diff Dem B: [-0.67262777] \n",
      " T_diff Dem c: [-0.01301637] \n",
      " T_diff Dem D: [-0.35120079] \n",
      " \n",
      "T_diff Dem A: [-0.08207207] \n",
      " T_diff Dem B: [-0.24225001] \n",
      " T_diff Dem c: [-0.0111825] \n",
      " T_diff Dem D: [-0.04388309] \n",
      " \n",
      "T_diff Dem A: [-0.09582944] \n",
      " T_diff Dem B: [-0.34785715] \n",
      " T_diff Dem c: [-0.01185506] \n",
      " T_diff Dem D: [-0.04840789] \n",
      " \n",
      "T_diff Dem A: [-0.0957064] \n",
      " T_diff Dem B: [-0.25870063] \n",
      " T_diff Dem c: [-0.01466238] \n",
      " T_diff Dem D: [-0.05370956] \n",
      " \n",
      "T_diff Dem A: [-0.0524009] \n",
      " T_diff Dem B: [-0.41557956] \n",
      " T_diff Dem c: [-0.01482574] \n",
      " T_diff Dem D: [-0.11001495] \n",
      " \n",
      "T_diff Dem A: [-0.05516856] \n",
      " T_diff Dem B: [-0.58325642] \n",
      " T_diff Dem c: [-0.01331448] \n",
      " T_diff Dem D: [-0.11015644] \n",
      " \n",
      "T_diff Dem A: [-0.09846386] \n",
      " T_diff Dem B: [-0.28504646] \n",
      " T_diff Dem c: [-0.00909919] \n",
      " T_diff Dem D: [-0.06417613] \n",
      " \n",
      "T_diff Dem A: [-0.10115539] \n",
      " T_diff Dem B: [-0.35778644] \n",
      " T_diff Dem c: [-0.01233774] \n",
      " T_diff Dem D: [-0.05162008] \n",
      " \n",
      "T_diff Dem A: [-0.0514686] \n",
      " T_diff Dem B: [-0.34153112] \n",
      " T_diff Dem c: [-0.0082275] \n",
      " T_diff Dem D: [-0.09204259] \n",
      " \n",
      "T_diff Dem A: [-0.10588558] \n",
      " T_diff Dem B: [-0.50804274] \n",
      " T_diff Dem c: [-0.01037556] \n",
      " T_diff Dem D: [-0.04753662] \n",
      " \n",
      "T_diff Dem A: [-0.13157451] \n",
      " T_diff Dem B: [-0.7653091] \n",
      " T_diff Dem c: [-0.0103564] \n",
      " T_diff Dem D: [-0.04539089] \n",
      " \n",
      "T_diff Dem A: [-0.06053833] \n",
      " T_diff Dem B: [-1.79204369] \n",
      " T_diff Dem c: [-0.01475047] \n",
      " T_diff Dem D: [-0.05944738] \n",
      " \n",
      "T_diff Dem A: [-0.13178009] \n",
      " T_diff Dem B: [-0.31898835] \n",
      " T_diff Dem c: [-0.01731077] \n",
      " T_diff Dem D: [-0.08243573] \n",
      " \n",
      "T_diff Dem A: [-0.09478026] \n",
      " T_diff Dem B: [-0.21684889] \n",
      " T_diff Dem c: [-0.01581207] \n",
      " T_diff Dem D: [-0.10182568] \n",
      " \n",
      "T_diff Dem A: [-0.06529767] \n",
      " T_diff Dem B: [-0.247329] \n",
      " T_diff Dem c: [-0.01031845] \n",
      " T_diff Dem D: [-0.1043391] \n",
      " \n",
      "T_diff Dem A: [-0.0978362] \n",
      " T_diff Dem B: [-0.33441954] \n",
      " T_diff Dem c: [-0.0101466] \n",
      " T_diff Dem D: [-0.04984509] \n",
      " \n",
      "T_diff Dem A: [-0.0704854] \n",
      " T_diff Dem B: [-0.42289505] \n",
      " T_diff Dem c: [-0.01259367] \n",
      " T_diff Dem D: [-0.10713158] \n",
      " \n",
      "T_diff Dem A: [-0.0528122] \n",
      " T_diff Dem B: [-0.37454444] \n",
      " T_diff Dem c: [-0.00977706] \n",
      " T_diff Dem D: [-0.10138784] \n",
      " \n",
      "T_diff Dem A: [-0.07851755] \n",
      " T_diff Dem B: [-0.34320556] \n",
      " T_diff Dem c: [-0.01972878] \n",
      " T_diff Dem D: [-0.09999845] \n",
      " \n",
      "T_diff Dem A: [-0.04897399] \n",
      " T_diff Dem B: [-0.29626386] \n",
      " T_diff Dem c: [-0.01555519] \n",
      " T_diff Dem D: [-0.0861148] \n",
      " \n",
      "T_diff Dem A: [-0.19264809] \n",
      " T_diff Dem B: [-0.46892047] \n",
      " T_diff Dem c: [-0.02186882] \n",
      " T_diff Dem D: [-0.0671131] \n",
      " \n",
      "T_diff Dem A: [-0.16767498] \n",
      " T_diff Dem B: [-0.86565326] \n",
      " T_diff Dem c: [-0.01609172] \n",
      " T_diff Dem D: [-0.07970926] \n",
      " \n",
      "T_diff Dem A: [-0.06273468] \n",
      " T_diff Dem B: [-0.61986116] \n",
      " T_diff Dem c: [-0.01535439] \n",
      " T_diff Dem D: [-0.11892343] \n",
      " \n",
      "T_diff Dem A: [-0.05900027] \n",
      " T_diff Dem B: [-0.45589195] \n",
      " T_diff Dem c: [-0.01196938] \n",
      " T_diff Dem D: [-0.10997281] \n",
      " \n",
      "T_diff Dem A: [-0.11128226] \n",
      " T_diff Dem B: [-0.59951836] \n",
      " T_diff Dem c: [-0.0162599] \n",
      " T_diff Dem D: [-0.05649201] \n",
      " \n",
      "T_diff Dem A: [-0.26265982] \n",
      " T_diff Dem B: [-0.29541765] \n",
      " T_diff Dem c: [-0.0170794] \n",
      " T_diff Dem D: [-0.10449699] \n",
      " \n",
      "T_diff Dem A: [-0.10087415] \n",
      " T_diff Dem B: [-0.34559059] \n",
      " T_diff Dem c: [-0.01212289] \n",
      " T_diff Dem D: [-0.05374862] \n",
      " \n",
      "T_diff Dem A: [-0.09352832] \n",
      " T_diff Dem B: [-0.21194127] \n",
      " T_diff Dem c: [-0.01332012] \n",
      " T_diff Dem D: [-0.12240266] \n",
      " \n",
      "T_diff Dem A: [-0.0598024] \n",
      " T_diff Dem B: [-0.47944945] \n",
      " T_diff Dem c: [-0.00946908] \n",
      " T_diff Dem D: [-0.12408393] \n",
      " \n",
      "T_diff Dem A: [-0.0554235] \n",
      " T_diff Dem B: [-3.22190044] \n",
      " T_diff Dem c: [-0.01492104] \n",
      " T_diff Dem D: [-0.0545509] \n",
      " \n",
      "T_diff Dem A: [-0.04977136] \n",
      " T_diff Dem B: [-1.05890094] \n",
      " T_diff Dem c: [-0.0106025] \n",
      " T_diff Dem D: [-0.04891543] \n",
      " \n",
      "T_diff Dem A: [-0.07795987] \n",
      " T_diff Dem B: [-0.46269094] \n",
      " T_diff Dem c: [-0.00669339] \n",
      " T_diff Dem D: [-0.04601013] \n",
      " \n",
      "T_diff Dem A: [-0.14845551] \n",
      " T_diff Dem B: [-0.58349031] \n",
      " T_diff Dem c: [-0.00876837] \n",
      " T_diff Dem D: [-0.0719166] \n",
      " \n",
      "T_diff Dem A: [-0.16253273] \n",
      " T_diff Dem B: [-1.07569266] \n",
      " T_diff Dem c: [-0.02295025] \n",
      " T_diff Dem D: [-0.0776511] \n",
      " \n",
      "T_diff Dem A: [-0.23939924] \n",
      " T_diff Dem B: [-0.47400666] \n",
      " T_diff Dem c: [-0.01096248] \n",
      " T_diff Dem D: [-0.04987701] \n",
      " \n",
      "T_diff Dem A: [-0.06482404] \n",
      " T_diff Dem B: [-0.82218161] \n",
      " T_diff Dem c: [-0.01640818] \n",
      " T_diff Dem D: [-0.18692843] \n",
      " \n",
      "T_diff Dem A: [-0.07994109] \n",
      " T_diff Dem B: [-0.18145214] \n",
      " T_diff Dem c: [-0.00830946] \n",
      " T_diff Dem D: [-0.11671156] \n",
      " \n",
      "T_diff Dem A: [-0.05424473] \n",
      " T_diff Dem B: [-0.3821832] \n",
      " T_diff Dem c: [-0.01192912] \n",
      " T_diff Dem D: [-0.11214372] \n",
      " \n",
      "T_diff Dem A: [-0.05648222] \n",
      " T_diff Dem B: [-0.75518743] \n",
      " T_diff Dem c: [-0.02007239] \n",
      " T_diff Dem D: [-0.10792249] \n",
      " \n",
      "T_diff Dem A: [-0.10032621] \n",
      " T_diff Dem B: [-0.29730327] \n",
      " T_diff Dem c: [-0.01077453] \n",
      " T_diff Dem D: [-0.05340093] \n",
      " \n",
      "T_diff Dem A: [-0.15403034] \n",
      " T_diff Dem B: [-0.84228823] \n",
      " T_diff Dem c: [-0.01166453] \n",
      " T_diff Dem D: [-0.0714345] \n",
      " \n",
      "T_diff Dem A: [-0.04902965] \n",
      " T_diff Dem B: [-0.28927397] \n",
      " T_diff Dem c: [-0.01046872] \n",
      " T_diff Dem D: [-0.09336286] \n",
      " \n",
      "T_diff Dem A: [-0.10228922] \n",
      " T_diff Dem B: [-0.39694569] \n",
      " T_diff Dem c: [-0.01243248] \n",
      " T_diff Dem D: [-0.05105736] \n",
      " \n",
      "T_diff Dem A: [-0.09229973] \n",
      " T_diff Dem B: [-0.2588337] \n",
      " T_diff Dem c: [-0.00831129] \n",
      " T_diff Dem D: [-0.04906203] \n",
      " \n",
      "T_diff Dem A: [-0.0533526] \n",
      " T_diff Dem B: [-2.04978424] \n",
      " T_diff Dem c: [-0.00973259] \n",
      " T_diff Dem D: [-0.05227606] \n",
      " \n",
      "T_diff Dem A: [-0.10933751] \n",
      " T_diff Dem B: [-1.29763533] \n",
      " T_diff Dem c: [-0.01697535] \n",
      " T_diff Dem D: [-0.04882753] \n",
      " \n",
      "########################## probabilistic comaprison: ############################## \n",
      "\n",
      "q_modifier: 0.7 \n",
      "T_diff Dem A: mean: 0.320411, std: 0.278607 \n",
      "T_diff Dem B: mean: 1.576392, std: 1.464184 \n",
      "T_diff Dem C: mean: 0.042193, std: 0.010959 \n",
      "T_diff Dem D: mean: 0.278834, std: 0.223719\n",
      "q_modifier: 1.3 \n",
      "T_diff Dem A: mean: 0.093414, std: 0.047194 \n",
      "T_diff Dem B: mean: 0.617416, std: 0.657955 \n",
      "T_diff Dem C: mean: 0.013152, std: 0.003579 \n",
      "T_diff Dem D: mean: 0.085424, std: 0.048943\n"
     ]
    }
   ],
   "source": [
    "# 1 draw inital demand:\n",
    "q_init = d_prior_dist.sample(n_runs)\n",
    "\n",
    "for mod_ind, modifier in enumerate(q_modifier):\n",
    "    q_new = q_init * modifier\n",
    "\n",
    "    for run_ind in range(n_runs):\n",
    "\n",
    "        # 2. solve state equations:\n",
    "        psi = _solve_SE(q_init[run_ind, :], SE)\n",
    "\n",
    "        # if the calculations did not converge reset the internal state of the SE object and try again\n",
    "        if psi > 1.e-5:\n",
    "            SE.set_init_state()\n",
    "            psi = _solve_SE(q_init[run_ind, :], SE)\n",
    "            if psi > 1.e-5:\n",
    "                raise Exception(f'System did not converge with psi = {psi:4f}')\n",
    "\n",
    "        # 3. modify mass flows according to demand:\n",
    "        mf_init = tf.concat([SE.mf[SE.find_edge[k]] for k in SE.demands.keys()], axis=0)\n",
    "        mf_new = mf_init * modifier\n",
    "\n",
    "        #  4. solve hydraulic system with new mass flows\n",
    "        FI.solve_mf(SE, mf_new, cycles)\n",
    "\n",
    "        #  5. solve thermal system with new mass flows\n",
    "        FI.solve_temp(SE)\n",
    "        TA_qss = SE.T[SE.find_node['BS']]\n",
    "        TB_qss = SE.T[SE.find_node['FS']]\n",
    "        TC_qss = SE.T[SE.find_node['ES']]\n",
    "        TD_qss = SE.T[SE.find_node['IS']]\n",
    "        Ta_qss [run_ind, mod_ind], Tb_qss[run_ind, mod_ind], Tc_qss[run_ind, mod_ind], Td_qss[run_ind, mod_ind] = TA_qss, TB_qss, TC_qss, TD_qss\n",
    "\n",
    "        #  6. solve steady state with new demands\n",
    "        _solve_SE(q_new[run_ind,:], SE)\n",
    "\n",
    "        #  7. compare thermal solution and steady-state solution\n",
    "        TA_ss = SE.T[SE.find_node['BS']]\n",
    "        TB_ss = SE.T[SE.find_node['FS']]\n",
    "        TC_ss = SE.T[SE.find_node['ES']]\n",
    "        TD_ss = SE.T[SE.find_node['IS']]\n",
    "\n",
    "        # broadcast differences:\n",
    "        print(f'T_diff Dem A: {TA_ss - TA_qss} \\n'\n",
    "              f'T_diff Dem B: {TB_ss - TB_qss} \\n'\n",
    "              f'T_diff Dem c: {TC_ss - TC_qss} \\n'\n",
    "              f'T_diff Dem D: {TD_ss - TD_qss} \\n')\n",
    "\n",
    "        #  8. save results for further analysis\n",
    "        Ta_ss [run_ind, mod_ind], Tb_ss[run_ind, mod_ind], Tc_ss[run_ind, mod_ind], Td_ss[run_ind, mod_ind] = TA_ss, TB_ss, TC_ss, TD_ss"
   ],
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    "pycharm": {
     "name": "#%%\n"
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  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "########################## probabilistic comaprison: ############################## \n",
      "\n",
      "q_modifier: 0.7 \n",
      "T_diff Dem A: mean: 0.320411, std: 0.278607 \n",
      "T_diff Dem B: mean: 1.576392, std: 1.464184 \n",
      "T_diff Dem C: mean: 0.042193, std: 0.010959 \n",
      "T_diff Dem D: mean: 0.278834, std: 0.223719\n",
      "q_modifier: 1.3 \n",
      "T_diff Dem A: mean: 0.093414, std: 0.047194 \n",
      "T_diff Dem B: mean: 0.617416, std: 0.657955 \n",
      "T_diff Dem C: mean: 0.013152, std: 0.003579 \n",
      "T_diff Dem D: mean: 0.085424, std: 0.048943\n"
     ]
    }
   ],
   "source": [
    "# 8. calculate mean deviations and deviation variances\n",
    "print(f'########################## probabilistic comaprison: ############################## \\n')\n",
    "for mod_ind, mod in enumerate(q_modifier):\n",
    "    # 10 compare results over multiple runs:\n",
    "    diff_a = Ta_ss[:, mod_ind] - Ta_qss[:, mod_ind]\n",
    "    diff_b = Tb_ss[:, mod_ind] - Tb_qss[:, mod_ind]\n",
    "    diff_c = Tc_ss[:, mod_ind] - Tc_qss[:, mod_ind]\n",
    "    diff_d = Td_ss[:, mod_ind] - Td_qss[:, mod_ind]\n",
    "    print(f'q_modifier: {mod} \\n'\n",
    "          f'T_diff Dem A: mean: {np.mean(np.abs(diff_a)):2f}, std: {np.std(diff_a):2f} \\n'\n",
    "          f'T_diff Dem B: mean: {np.mean(np.abs(diff_b)):2f}, std: {np.std(diff_b):2f} \\n'\n",
    "          f'T_diff Dem C: mean: {np.mean(np.abs(diff_c)):2f}, std: {np.std(diff_c):2f} \\n'\n",
    "          f'T_diff Dem D: mean: {np.mean(np.abs(diff_d)):2f}, std: {np.std(diff_d):2f}')\n"
   ],
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