From c5dc81a1d9ec3e88ab9382b629f643c847329f83 Mon Sep 17 00:00:00 2001
From: Wei-Tse Hsu <wehs7661@colorado.edu>
Date: Thu, 7 Mar 2024 02:07:55 +0800
Subject: [PATCH] Updated Example_1.ipynb

---
 examples/Example_1.ipynb         | 360 +++++++++++++++++--------------
 sampling_simulator/simulators.py |  14 +-
 2 files changed, 209 insertions(+), 165 deletions(-)

diff --git a/examples/Example_1.ipynb b/examples/Example_1.ipynb
index 989f05b..66c51ce 100644
--- a/examples/Example_1.ipynb
+++ b/examples/Example_1.ipynb
@@ -17,7 +17,7 @@
     "- The sampling in the configurational space is completely ignored, which implies the following:\n",
     "  - $\\Delta U$ in the calculation of the acceptance ratio is always 0.\n",
     "  - There are no exchanges between coordinates, so an REXEE simulation can be reprented by an ensemble of decoupled EXE simulations sampling different alchemical ranges. \n",
-    "- We have not implemented the $1/t$-variant of the Wang-Landau algorithm in `wang_landau_algorithm.py`."
+    "- We have not implemented the $1/t$-variant of the Wang-Landau algorithm in `EE_Simulator`."
    ]
   },
   {
@@ -49,7 +49,7 @@
     "import matplotlib.pyplot as plt\n",
     "from matplotlib import rc\n",
     "from sampling_simulator.utils import utils\n",
-    "from sampling_simulator.wang_landau_algorithm import WL_Simulator\n",
+    "from sampling_simulator.simulators import EE_Simulator\n",
     "\n",
     "rc('font', **{\n",
     "        'family': 'sans-serif',\n",
@@ -100,7 +100,7 @@
    "id": "fc0b85d2",
    "metadata": {},
    "source": [
-    "Note that the reference free energy surface above was obtained from an MBAR calculation from a GROMACS EXE simulation of a real system (CB7-10 binding complex). The free energy parameters used in this GROMACS EXE simulation are the same as the ones we use here (e.g., `wl_scale=0.7`, `wl_ratio=0.8`, etc.). Below we use `WL_Simulator` to simulate such an EXE simulation in 3 replicates."
+    "Note that the reference free energy surface above was obtained from an MBAR calculation from a GROMACS EXE simulation of a real system (CB7-10 binding complex). The free energy parameters used in this GROMACS EXE simulation are the same as the ones we use here (e.g., `wl_scale=0.7`, `wl_ratio=0.8`, etc.). Below we use `EE_Simulator` to simulate such an EXE simulation in 3 replicates."
    ]
   },
   {
@@ -116,18 +116,18 @@
      "output_type": "stream",
      "text": [
       "Whole-range EXE simulation\n",
-      "  Equilibration time: 46493 +/- 991 steps\n",
-      "  RMSE: 0.020 +/- 0.006 kT\n"
+      "  Equilibration time: 46219 +/- 1614 steps\n",
+      "  RMSE: 0.016 +/- 0.004 kT\n"
      ]
     }
    ],
    "source": [
     "t_equil_list, rmse_list = [], []\n",
     "for i in range(3):\n",
-    "    simulator = WL_Simulator(params_dict, f_ref)\n",
+    "    simulator = EE_Simulator(params_dict, f_ref, fixed_weight=False)\n",
     "    simulator.run()\n",
     "    t_equil_list.append(simulator.equil_time)\n",
-    "    rmse_list.append(utils.calc_rmse(simulator.g, f_ref - f_ref[0]))\n",
+    "    rmse_list.append(utils.calc_rmse(simulator.g_current, f_ref - f_ref[0]))\n",
     "    \n",
     "\n",
     "t_equil = np.mean(t_equil_list)\n",
@@ -159,28 +159,28 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Final alchemical weights: [  0.          57.81506594 112.48595431 163.93769856 211.12970278\n",
-      " 254.59500002 295.58512862 334.67247063 371.45655369 406.6828836\n",
-      " 439.31786591 469.4258732  497.17607357 522.47357118 545.42680259\n",
-      " 566.14796951 584.61134917 600.52079803 614.33517239 625.69339986\n",
-      " 634.91490611 639.2228388  643.38143946 647.320049   650.91276085\n",
-      " 652.55335598 653.97305694 655.1961736  656.05154366 656.27754473\n",
-      " 656.18895926 655.7263484  654.80215044 653.43590957 651.91450631\n",
-      " 650.43820119 649.16578627 647.83885486 646.88374511 645.46044346]\n",
-      "Biased free energies: [2704.97017966 2704.96032909 2704.9774789  2704.93786155 2704.96334491\n",
-      " 2704.95577697 2704.95113226 2704.95085915 2704.96839293 2704.94323176\n",
-      " 2704.94150192 2704.97322194 2704.94990889 2704.94299866 2704.9591124\n",
-      " 2704.92101351 2704.93080397 2704.94701964 2704.94669352 2704.93907844\n",
-      " 2704.95528441 2704.96148022 2704.95830694 2704.94823696 2704.96146883\n",
-      " 2704.94482901 2704.97458776 2704.95290707 2704.93216741 2704.94599066\n",
-      " 2704.98424905 2704.98724121 2704.95173094 2704.95141511 2704.945462\n",
-      " 2704.95880768 2704.96012797 2704.95924777 2704.96206136 2704.98285427]\n",
-      "Equilibration time: 46723 steps\n"
+      "Final alchemical weights: [  0.          57.78410359 112.49059518 163.92815931 211.10368792\n",
+      " 254.5837178  295.5630185  334.66198806 371.45275967 406.65024929\n",
+      " 439.2896742  469.41334784 497.12533572 522.47627998 545.42359269\n",
+      " 566.10501851 584.55913495 600.49823178 614.29675976 625.69601841\n",
+      " 634.88970391 639.20856094 643.3524987  647.29005157 650.91562914\n",
+      " 652.51980681 653.97121437 655.17783443 656.0036289  656.27560947\n",
+      " 656.20965641 655.7642928  654.77874899 653.41572015 651.89105261\n",
+      " 650.41076886 649.12382948 647.8242118  646.88412155 645.48515796]\n",
+      "Biased free energies: [2709.86391745 2709.88502923 2709.86657582 2709.8411386  2709.88309756\n",
+      " 2709.86079698 2709.86698018 2709.85507952 2709.86592475 2709.86960386\n",
+      " 2709.86343142 2709.87948508 2709.89438452 2709.83402765 2709.85606009\n",
+      " 2709.8577023  2709.87675599 2709.86332368 2709.87884395 2709.83019767\n",
+      " 2709.8742244  2709.86949587 2709.88098549 2709.87197219 2709.85233833\n",
+      " 2709.87211597 2709.87016813 2709.86498403 2709.87381996 2709.84166371\n",
+      " 2709.85728969 2709.8430346  2709.86887018 2709.86534233 2709.86265349\n",
+      " 2709.8799778  2709.89582255 2709.86762863 2709.85542271 2709.85187756]\n",
+      "Equilibration time: 44708 steps\n"
      ]
     }
    ],
    "source": [
-    "print(f'Final alchemical weights: {simulator.g}')\n",
+    "print(f'Final alchemical weights: {simulator.g_current}')\n",
     "print(f'Biased free energies: {simulator.f_current}')\n",
     "print(f'Equilibration time: {simulator.equil_time} steps')"
    ]
@@ -190,7 +190,7 @@
    "id": "dd0558ff",
    "metadata": {},
    "source": [
-    "Or, one can plot the following figures using other functions defined in the class `WL_simulator`:"
+    "Or, one can plot the following figures using other functions defined in the class `EE_simulator`:"
    ]
   },
   {
@@ -201,7 +201,53 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "simulator.plot_hist()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "32224b7d",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "simulator.plot_timeseries(simulator.dg, 'Δg')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "7c0e09c5",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
       "text/plain": [
        "<Figure size 432x288 with 1 Axes>"
       ]
@@ -213,8 +259,6 @@
     }
    ],
    "source": [
-    "simulator.plot_hist()\n",
-    "simulator.plot_timeseries(simulator.dg, 'Δg')\n",
     "simulator.plot_timeseries(simulator.traj, 'State index')"
    ]
   },
@@ -228,7 +272,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 9,
    "id": "dfc4bb04",
    "metadata": {},
    "outputs": [],
@@ -257,7 +301,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 10,
    "id": "62801371",
    "metadata": {},
    "outputs": [],
@@ -270,10 +314,10 @@
     "        t_equil_list, rmse_list = [], []\n",
     "        for j in range(n_replicates):\n",
     "            f_ref_sub = f_ref[i * s : i * s + n_sub]\n",
-    "            simulator = WL_Simulator(params_dict, f_ref_sub)\n",
+    "            simulator = EE_Simulator(params_dict, f_ref_sub, fixed_weight=False)\n",
     "            simulator.run()\n",
     "            t_equil_list.append(simulator.equil_time)\n",
-    "            rmse_list.append(utils.calc_rmse(simulator.g, f_ref_sub - f_ref_sub[0]))\n",
+    "            rmse_list.append(utils.calc_rmse(simulator.g_current, f_ref_sub - f_ref_sub[0]))\n",
     "\n",
     "        t_equil = np.mean(t_equil_list)\n",
     "        t_equil_err = np.std(t_equil_list, ddof=1)\n",
@@ -293,7 +337,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 11,
    "id": "87c5c5fb",
    "metadata": {
     "scrolled": false
@@ -306,182 +350,182 @@
       "Test 1: n_sim = 4, s = 1, n_sub = 37\n",
       "====================================\n",
       "State range: 0-36\n",
-      "  Equilibration time: 47360 +/- 4802 steps\n",
-      "  RMSE: 0.024 +/- 0.011 kT\n",
+      "  Equilibration time: 41951 +/- 4897 steps\n",
+      "  RMSE: 0.020 +/- 0.003 kT\n",
       "\n",
       "State range: 1-37\n",
-      "  Equilibration time: 39723 +/- 3317 steps\n",
-      "  RMSE: 0.015 +/- 0.001 kT\n",
+      "  Equilibration time: 39806 +/- 2568 steps\n",
+      "  RMSE: 0.019 +/- 0.001 kT\n",
       "\n",
       "State range: 2-38\n",
-      "  Equilibration time: 41269 +/- 2020 steps\n",
-      "  RMSE: 0.021 +/- 0.003 kT\n",
+      "  Equilibration time: 41109 +/- 2136 steps\n",
+      "  RMSE: 0.018 +/- 0.004 kT\n",
       "\n",
       "State range: 3-39\n",
-      "  Equilibration time: 42411 +/- 1202 steps\n",
-      "  RMSE: 0.024 +/- 0.008 kT\n",
+      "  Equilibration time: 39631 +/- 2136 steps\n",
+      "  RMSE: 0.017 +/- 0.003 kT\n",
       "\n",
-      "Computational cost: 189439 +/- 19207 A.U. \n",
+      "Computational cost: 167805 +/- 19589 A.U. \n",
       "\n",
       "Test 2: n_sim = 4, s = 2, n_sub = 34\n",
       "====================================\n",
       "State range: 0-33\n",
-      "  Equilibration time: 36453 +/- 1093 steps\n",
-      "  RMSE: 0.023 +/- 0.007 kT\n",
+      "  Equilibration time: 36786 +/- 3812 steps\n",
+      "  RMSE: 0.018 +/- 0.002 kT\n",
       "\n",
       "State range: 2-35\n",
-      "  Equilibration time: 37172 +/- 1996 steps\n",
-      "  RMSE: 0.019 +/- 0.003 kT\n",
+      "  Equilibration time: 38373 +/- 160 steps\n",
+      "  RMSE: 0.023 +/- 0.005 kT\n",
       "\n",
       "State range: 4-37\n",
-      "  Equilibration time: 34696 +/- 1855 steps\n",
-      "  RMSE: 0.016 +/- 0.003 kT\n",
+      "  Equilibration time: 35398 +/- 2224 steps\n",
+      "  RMSE: 0.019 +/- 0.005 kT\n",
       "\n",
       "State range: 6-39\n",
-      "  Equilibration time: 33870 +/- 1411 steps\n",
-      "  RMSE: 0.018 +/- 0.003 kT\n",
+      "  Equilibration time: 34273 +/- 507 steps\n",
+      "  RMSE: 0.017 +/- 0.002 kT\n",
       "\n",
-      "Computational cost: 148689 +/- 7983 A.U. \n",
+      "Computational cost: 153493 +/- 639 A.U. \n",
       "\n",
       "Test 3: n_sim = 4, s = 3, n_sub = 31\n",
       "====================================\n",
       "State range: 0-30\n",
-      "  Equilibration time: 36470 +/- 1037 steps\n",
-      "  RMSE: 0.022 +/- 0.007 kT\n",
+      "  Equilibration time: 33204 +/- 2589 steps\n",
+      "  RMSE: 0.017 +/- 0.001 kT\n",
       "\n",
       "State range: 3-33\n",
-      "  Equilibration time: 32024 +/- 2576 steps\n",
-      "  RMSE: 0.019 +/- 0.001 kT\n",
+      "  Equilibration time: 29608 +/- 1678 steps\n",
+      "  RMSE: 0.017 +/- 0.001 kT\n",
       "\n",
       "State range: 6-36\n",
-      "  Equilibration time: 33072 +/- 2476 steps\n",
-      "  RMSE: 0.023 +/- 0.003 kT\n",
+      "  Equilibration time: 28812 +/- 2505 steps\n",
+      "  RMSE: 0.016 +/- 0.003 kT\n",
       "\n",
       "State range: 9-39\n",
-      "  Equilibration time: 29698 +/- 1883 steps\n",
-      "  RMSE: 0.018 +/- 0.003 kT\n",
+      "  Equilibration time: 30850 +/- 1215 steps\n",
+      "  RMSE: 0.020 +/- 0.005 kT\n",
       "\n",
-      "Computational cost: 145879 +/- 4149 A.U. \n",
+      "Computational cost: 132817 +/- 10357 A.U. \n",
       "\n",
       "Test 4: n_sim = 4, s = 4, n_sub = 28\n",
       "====================================\n",
       "State range: 0-27\n",
-      "  Equilibration time: 30343 +/- 1711 steps\n",
-      "  RMSE: 0.015 +/- 0.002 kT\n",
+      "  Equilibration time: 27667 +/- 1156 steps\n",
+      "  RMSE: 0.029 +/- 0.011 kT\n",
       "\n",
       "State range: 4-31\n",
-      "  Equilibration time: 28208 +/- 2441 steps\n",
-      "  RMSE: 0.019 +/- 0.008 kT\n",
+      "  Equilibration time: 30139 +/- 1727 steps\n",
+      "  RMSE: 0.016 +/- 0.001 kT\n",
       "\n",
       "State range: 8-35\n",
-      "  Equilibration time: 27246 +/- 3309 steps\n",
-      "  RMSE: 0.020 +/- 0.006 kT\n",
+      "  Equilibration time: 25257 +/- 3743 steps\n",
+      "  RMSE: 0.016 +/- 0.002 kT\n",
       "\n",
       "State range: 12-39\n",
-      "  Equilibration time: 24609 +/- 817 steps\n",
-      "  RMSE: 0.023 +/- 0.004 kT\n",
+      "  Equilibration time: 26577 +/- 1979 steps\n",
+      "  RMSE: 0.025 +/- 0.009 kT\n",
       "\n",
-      "Computational cost: 121373 +/- 6845 A.U. \n",
+      "Computational cost: 120557 +/- 6907 A.U. \n",
       "\n",
       "Test 5: n_sim = 4, s = 5, n_sub = 25\n",
       "====================================\n",
       "State range: 0-24\n",
-      "  Equilibration time: 24849 +/- 1933 steps\n",
-      "  RMSE: 0.031 +/- 0.013 kT\n",
+      "  Equilibration time: 25729 +/- 2119 steps\n",
+      "  RMSE: 0.017 +/- 0.004 kT\n",
       "\n",
       "State range: 5-29\n",
-      "  Equilibration time: 22521 +/- 1035 steps\n",
-      "  RMSE: 0.019 +/- 0.000 kT\n",
+      "  Equilibration time: 22847 +/- 1529 steps\n",
+      "  RMSE: 0.016 +/- 0.003 kT\n",
       "\n",
       "State range: 10-34\n",
-      "  Equilibration time: 21761 +/- 820 steps\n",
-      "  RMSE: 0.021 +/- 0.002 kT\n",
+      "  Equilibration time: 23878 +/- 961 steps\n",
+      "  RMSE: 0.026 +/- 0.001 kT\n",
       "\n",
       "State range: 15-39\n",
-      "  Equilibration time: 22172 +/- 1455 steps\n",
-      "  RMSE: 0.017 +/- 0.003 kT\n",
+      "  Equilibration time: 21901 +/- 1289 steps\n",
+      "  RMSE: 0.018 +/- 0.006 kT\n",
       "\n",
-      "Computational cost: 99395 +/- 7731 A.U. \n",
+      "Computational cost: 102917 +/- 8475 A.U. \n",
       "\n",
       "Test 6: n_sim = 4, s = 6, n_sub = 22\n",
       "====================================\n",
       "State range: 0-21\n",
-      "  Equilibration time: 22170 +/- 592 steps\n",
-      "  RMSE: 0.023 +/- 0.005 kT\n",
+      "  Equilibration time: 20968 +/- 2680 steps\n",
+      "  RMSE: 0.022 +/- 0.010 kT\n",
       "\n",
       "State range: 6-27\n",
-      "  Equilibration time: 18257 +/- 325 steps\n",
-      "  RMSE: 0.021 +/- 0.013 kT\n",
+      "  Equilibration time: 19022 +/- 935 steps\n",
+      "  RMSE: 0.021 +/- 0.008 kT\n",
       "\n",
       "State range: 12-33\n",
-      "  Equilibration time: 18248 +/- 1497 steps\n",
-      "  RMSE: 0.020 +/- 0.001 kT\n",
+      "  Equilibration time: 19469 +/- 2623 steps\n",
+      "  RMSE: 0.017 +/- 0.003 kT\n",
       "\n",
       "State range: 18-39\n",
-      "  Equilibration time: 17214 +/- 652 steps\n",
-      "  RMSE: 0.019 +/- 0.003 kT\n",
+      "  Equilibration time: 18017 +/- 736 steps\n",
+      "  RMSE: 0.016 +/- 0.001 kT\n",
       "\n",
-      "Computational cost: 88681 +/- 2369 A.U. \n",
+      "Computational cost: 83871 +/- 10721 A.U. \n",
       "\n",
       "Test 7: n_sim = 4, s = 7, n_sub = 19\n",
       "====================================\n",
       "State range: 0-18\n",
-      "  Equilibration time: 16911 +/- 1110 steps\n",
-      "  RMSE: 0.018 +/- 0.004 kT\n",
+      "  Equilibration time: 15873 +/- 542 steps\n",
+      "  RMSE: 0.024 +/- 0.012 kT\n",
       "\n",
       "State range: 7-25\n",
-      "  Equilibration time: 15335 +/- 330 steps\n",
-      "  RMSE: 0.014 +/- 0.003 kT\n",
+      "  Equilibration time: 14710 +/- 1572 steps\n",
+      "  RMSE: 0.016 +/- 0.004 kT\n",
       "\n",
       "State range: 14-32\n",
-      "  Equilibration time: 13071 +/- 286 steps\n",
-      "  RMSE: 0.023 +/- 0.008 kT\n",
+      "  Equilibration time: 15528 +/- 1012 steps\n",
+      "  RMSE: 0.024 +/- 0.007 kT\n",
       "\n",
       "State range: 21-39\n",
-      "  Equilibration time: 15930 +/- 1963 steps\n",
-      "  RMSE: 0.018 +/- 0.004 kT\n",
+      "  Equilibration time: 14208 +/- 1051 steps\n",
+      "  RMSE: 0.021 +/- 0.006 kT\n",
       "\n",
-      "Computational cost: 67644 +/- 4440 A.U. \n",
+      "Computational cost: 63491 +/- 2167 A.U. \n",
       "\n",
       "Test 8: n_sim = 4, s = 8, n_sub = 17\n",
       "====================================\n",
       "State range: 0-16\n",
-      "  Equilibration time: 14599 +/- 742 steps\n",
-      "  RMSE: 0.019 +/- 0.009 kT\n",
+      "  Equilibration time: 14941 +/- 386 steps\n",
+      "  RMSE: 0.016 +/- 0.001 kT\n",
       "\n",
       "State range: 8-24\n",
-      "  Equilibration time: 13790 +/- 902 steps\n",
-      "  RMSE: 0.030 +/- 0.003 kT\n",
+      "  Equilibration time: 13924 +/- 1119 steps\n",
+      "  RMSE: 0.023 +/- 0.009 kT\n",
       "\n",
       "State range: 16-32\n",
-      "  Equilibration time: 12317 +/- 1433 steps\n",
-      "  RMSE: 0.018 +/- 0.004 kT\n",
+      "  Equilibration time: 12731 +/- 968 steps\n",
+      "  RMSE: 0.023 +/- 0.012 kT\n",
       "\n",
       "State range: 24-40\n",
-      "  Equilibration time: 10198 +/- 200 steps\n",
-      "  RMSE: 0.017 +/- 0.007 kT\n",
+      "  Equilibration time: 12300 +/- 1739 steps\n",
+      "  RMSE: 0.020 +/- 0.008 kT\n",
       "\n",
-      "Computational cost: 58395 +/- 2969 A.U. \n",
+      "Computational cost: 59763 +/- 1543 A.U. \n",
       "\n",
       "Test 9: n_sim = 4, s = 9, n_sub = 13\n",
       "====================================\n",
       "State range: 0-12\n",
-      "  Equilibration time: 10212 +/- 662 steps\n",
-      "  RMSE: 0.019 +/- 0.003 kT\n",
+      "  Equilibration time: 8625 +/- 713 steps\n",
+      "  RMSE: 0.021 +/- 0.009 kT\n",
       "\n",
       "State range: 9-21\n",
-      "  Equilibration time: 9360 +/- 1367 steps\n",
-      "  RMSE: 0.018 +/- 0.000 kT\n",
+      "  Equilibration time: 9351 +/- 811 steps\n",
+      "  RMSE: 0.018 +/- 0.011 kT\n",
       "\n",
       "State range: 18-30\n",
-      "  Equilibration time: 7520 +/- 414 steps\n",
-      "  RMSE: 0.025 +/- 0.003 kT\n",
+      "  Equilibration time: 9126 +/- 993 steps\n",
+      "  RMSE: 0.017 +/- 0.002 kT\n",
       "\n",
       "State range: 27-39\n",
-      "  Equilibration time: 8298 +/- 708 steps\n",
-      "  RMSE: 0.020 +/- 0.006 kT\n",
+      "  Equilibration time: 7956 +/- 608 steps\n",
+      "  RMSE: 0.018 +/- 0.002 kT\n",
       "\n",
-      "Computational cost: 40848 +/- 2650 A.U. \n",
+      "Computational cost: 37405 +/- 3243 A.U. \n",
       "\n"
      ]
     }
@@ -511,13 +555,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 12,
    "id": "12871969",
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "<Figure size 432x288 with 1 Axes>"
       ]
@@ -546,7 +590,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 13,
    "id": "bc704d80",
    "metadata": {},
    "outputs": [],
@@ -574,7 +618,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 14,
    "id": "0aa72350",
    "metadata": {},
    "outputs": [
@@ -585,82 +629,82 @@
       "Test: n_sim = 2, s = 1, n_sub = 37\n",
       "==================================\n",
       "State range: 0-20\n",
-      "  Equilibration time: 18959 +/- 2127 steps\n",
-      "  RMSE: 0.021 +/- 0.005 kT\n",
+      "  Equilibration time: 18034 +/- 2612 steps\n",
+      "  RMSE: 0.022 +/- 0.006 kT\n",
       "\n",
       "State range: 19-39\n",
-      "  Equilibration time: 17987 +/- 2061 steps\n",
-      "  RMSE: 0.016 +/- 0.003 kT\n",
+      "  Equilibration time: 15484 +/- 896 steps\n",
+      "  RMSE: 0.027 +/- 0.009 kT\n",
       "\n",
-      "Computational cost: 37917 +/- 4254 A.U. \n",
+      "Computational cost: 36067 +/- 5225 A.U. \n",
       "\n",
       "Test: n_sim = 3, s = 2, n_sub = 34\n",
       "==================================\n",
       "State range: 0-13\n",
-      "  Equilibration time: 10607 +/- 690 steps\n",
-      "  RMSE: 0.020 +/- 0.008 kT\n",
+      "  Equilibration time: 11211 +/- 309 steps\n",
+      "  RMSE: 0.019 +/- 0.006 kT\n",
       "\n",
       "State range: 13-26\n",
-      "  Equilibration time: 9061 +/- 571 steps\n",
-      "  RMSE: 0.023 +/- 0.006 kT\n",
+      "  Equilibration time: 8331 +/- 237 steps\n",
+      "  RMSE: 0.017 +/- 0.002 kT\n",
       "\n",
       "State range: 26-39\n",
-      "  Equilibration time: 8615 +/- 759 steps\n",
-      "  RMSE: 0.025 +/- 0.003 kT\n",
+      "  Equilibration time: 9642 +/- 1168 steps\n",
+      "  RMSE: 0.020 +/- 0.005 kT\n",
       "\n",
-      "Computational cost: 31822 +/- 2070 A.U. \n",
+      "Computational cost: 33632 +/- 926 A.U. \n",
       "\n",
       "Test: n_sim = 5, s = 3, n_sub = 31\n",
       "==================================\n",
       "State range: 0-11\n",
-      "  Equilibration time: 8867 +/- 904 steps\n",
-      "  RMSE: 0.016 +/- 0.002 kT\n",
+      "  Equilibration time: 7564 +/- 417 steps\n",
+      "  RMSE: 0.013 +/- 0.002 kT\n",
       "\n",
       "State range: 7-18\n",
-      "  Equilibration time: 7520 +/- 490 steps\n",
-      "  RMSE: 0.023 +/- 0.013 kT\n",
+      "  Equilibration time: 7615 +/- 1286 steps\n",
+      "  RMSE: 0.015 +/- 0.003 kT\n",
       "\n",
       "State range: 14-25\n",
-      "  Equilibration time: 8724 +/- 1245 steps\n",
-      "  RMSE: 0.019 +/- 0.003 kT\n",
+      "  Equilibration time: 7684 +/- 504 steps\n",
+      "  RMSE: 0.017 +/- 0.005 kT\n",
       "\n",
       "State range: 21-32\n",
-      "  Equilibration time: 6709 +/- 1102 steps\n",
-      "  RMSE: 0.018 +/- 0.011 kT\n",
+      "  Equilibration time: 7019 +/- 1029 steps\n",
+      "  RMSE: 0.018 +/- 0.010 kT\n",
       "\n",
       "State range: 28-39\n",
-      "  Equilibration time: 7781 +/- 760 steps\n",
-      "  RMSE: 0.018 +/- 0.002 kT\n",
+      "  Equilibration time: 7703 +/- 819 steps\n",
+      "  RMSE: 0.020 +/- 0.009 kT\n",
       "\n",
-      "Computational cost: 44333 +/- 4520 A.U. \n",
+      "Computational cost: 38513 +/- 4097 A.U. \n",
       "\n",
       "Test: n_sim = 6, s = 4, n_sub = 28\n",
       "==================================\n",
       "State range: 0-9\n",
-      "  Equilibration time: 7019 +/- 669 steps\n",
-      "  RMSE: 0.020 +/- 0.002 kT\n",
+      "  Equilibration time: 6041 +/- 1021 steps\n",
+      "  RMSE: 0.020 +/- 0.010 kT\n",
       "\n",
       "State range: 6-15\n",
-      "  Equilibration time: 5494 +/- 684 steps\n",
-      "  RMSE: 0.022 +/- 0.007 kT\n",
+      "  Equilibration time: 6875 +/- 1588 steps\n",
+      "  RMSE: 0.021 +/- 0.006 kT\n",
       "\n",
       "State range: 12-21\n",
-      "  Equilibration time: 6192 +/- 408 steps\n",
-      "  RMSE: 0.023 +/- 0.007 kT\n",
+      "  Equilibration time: 5841 +/- 1096 steps\n",
+      "  RMSE: 0.020 +/- 0.002 kT\n",
       "\n",
       "State range: 18-27\n",
-      "  Equilibration time: 5124 +/- 74 steps\n",
-      "  RMSE: 0.019 +/- 0.007 kT\n",
+      "  Equilibration time: 5217 +/- 129 steps\n",
+      "  RMSE: 0.026 +/- 0.016 kT\n",
       "\n",
       "State range: 24-33\n",
-      "  Equilibration time: 5902 +/- 708 steps\n",
-      "  RMSE: 0.016 +/- 0.007 kT\n",
+      "  Equilibration time: 6085 +/- 1016 steps\n",
+      "  RMSE: 0.016 +/- 0.005 kT\n",
       "\n",
       "State range: 30-39\n",
-      "  Equilibration time: 5708 +/- 294 steps\n",
-      "  RMSE: 0.021 +/- 0.007 kT\n",
+      "  Equilibration time: 5286 +/- 259 steps\n",
+      "  RMSE: 0.022 +/- 0.009 kT\n",
       "\n",
-      "Computational cost: 42112 +/- 4013 A.U. \n",
+      "Computational cost: 41250 +/- 9526 A.U. \n",
       "\n"
      ]
     }
@@ -681,7 +725,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 15,
    "id": "41a259f3",
    "metadata": {},
    "outputs": [
@@ -691,13 +735,13 @@
        "Text(0, 0.5, 'Computational cost (A.U.)')"
       ]
      },
-     "execution_count": 13,
+     "execution_count": 15,
      "metadata": {},
      "output_type": "execute_result"
     },
     {
      "data": {
-      "image/png": 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\n",
+      "image/png": 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\n",
       "text/plain": [
        "<Figure size 432x288 with 1 Axes>"
       ]
diff --git a/sampling_simulator/simulators.py b/sampling_simulator/simulators.py
index eecfba3..fff9c44 100644
--- a/sampling_simulator/simulators.py
+++ b/sampling_simulator/simulators.py
@@ -123,11 +123,7 @@ def update(self):
             ]
             state_new = random.choices(range(self.n_states), weights=p_propose, k=1)[0]
         else:
-            p_current = utils.free2prob(self.g_current - self.f_true)
-            p_propose = [
-                p_current / (1 - p_current[i]) if i != self.state else 0
-                for i in range(self.n_states)
-            ]
+            p_current = utils.free2prob(self.f_current)
             state_new = random.choices(range(self.n_states), weights=p_current, k=1)[0]
 
         if self.verbose:
@@ -140,7 +136,11 @@ def update(self):
         if self.fixed_weight is True:
             p_acc = min(1, (1 - self.p_equil[self.state]) / (1 - self.p_equil[state_new]))
         else:
-            p_acc = min(1, (1 - p_current[self.state]) / (1 - p_current[state_new]))
+            delta = self.f_current[state_new] - self.f_current[self.state]
+            if delta <= 0:
+                p_acc = 1
+            else:
+                p_acc = np.exp(-delta)
         
         rand = random.random()
         if rand < p_acc:
@@ -176,7 +176,7 @@ def run(self):
                 if self.wl_delta < self.wl_delta_cutoff and self.equil is False:
                     self.equil = True
                     self.equil_time = i
-                    self.g_equil = copy.deepcopy(self.g)
+                    self.g_equil = copy.deepcopy(self.g_current)
                     if self.verbose is True:
                         print("  The alchemical weights have been equilibrated!")