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Example of Bayesian regression applied to the thermodynamics of miscibility gap systems. Updated to include use of pymc3.Potential() to constrain parameters to physical values.
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"cell_type": "markdown",
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"source": [
"# Minimial working example of Miscibility gap uncertainty propagation"
]
},
{
"cell_type": "code",
"execution_count": 1,
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"collapsed": false,
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"source": [
"# Jupyter Magics\n",
"%load_ext autoreload\n",
"%autoreload 2\n",
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true,
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"outputs": [],
"source": [
"import numpy as np\n",
"from matplotlib import pyplot as plt\n",
"#import pandas as pd\n",
"import seaborn as sns\n",
"\n",
"import pymc3 as pm\n",
"\n",
"from scipy.optimize import root\n",
"\n",
"from theano import as_op, shared\n",
"import theano.tensor as tt"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"## Thermodynamics of a regular solution model system with a miscibility gap.\n",
"The equations below define the thermodynamics of the system. $H$ will be used as part of the Bayesian modeling to determine estimates of $\\\\alpha$ given observed mixing enthalpy data."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true,
"deletable": true,
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"outputs": [],
"source": [
"BOLTZCONST = 8.617e-2 # meV/K\n",
"\n",
"def H(x, alpha):\n",
" \"\"\"\n",
" Regular solution-model mixing enthalpy: H = alpha*x*(1-x)\n",
" \n",
" Parameters\n",
" ----------\n",
" x : float\n",
" Composition in atomic fraction.\n",
" alpha : float\n",
" Regular-solution model parameter in meV/atom.\n",
" \n",
" Returns\n",
" -------\n",
" H : float\n",
" Mixing enthalpy in meV/atom.\n",
" \n",
" \"\"\"\n",
" return alpha*x*(1.-x)\n",
"\n",
"def S_ideal(x):\n",
" \"\"\"\n",
" Ideal mixing entropy: S = -(xlnx + (1-x)ln(1-x))\n",
" \n",
" Parameters\n",
" ----------\n",
" x : float\n",
" Composition in atomic fraction.\n",
" \n",
" Returns\n",
" -------\n",
" S : float\n",
" Ideal mixing entropy in Boltzmann constants/atom.\n",
" \n",
" \"\"\"\n",
" return -1.*(x*np.log(x) + (1.-x)*np.log(1.-x))\n",
"\n",
"def G(x, T, alpha):\n",
" \"\"\"\n",
" Gibbs energy of mixing: G = H - T*S\n",
" \n",
" Parameters\n",
" ----------\n",
" x : float\n",
" Composition in atomic fraction.\n",
" T : float\n",
" Temperature in Kelvin.\n",
" alpha : float\n",
" Regular-solution model parameter in meV/atom.\n",
" \n",
" Returns\n",
" -------\n",
" G : float\n",
" Gibbs energy in meV/atom.\n",
" \n",
" \"\"\"\n",
" G = H(x, alpha) - T*BOLTZCONST*S_ideal(x)\n",
" return G\n",
"\n",
"def T_c(alpha):\n",
" \"\"\"\n",
" Regular-solution-model Critical temperature: alpha/2/k_B\n",
" \n",
" Parameters\n",
" ----------\n",
" alpha : float\n",
" Regular solution model parameter\n",
" \n",
" Returns\n",
" -------\n",
" T_c : float\n",
" Critical temperature in Kelvin.\n",
" \n",
" \"\"\"\n",
" return alpha/2./BOLTZCONST"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false,
"deletable": true,
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"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x7fb1f88ce9d0>"
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},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
},
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pGuxO12B3tDr9ANPjSbnEnc8lNiGb2IRsTBQy2jR3olOgKx0CXcVsfcJ1apTo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\nhV4IIYQwY1LohRBCCDMmhV4IIYQwY/8LrrhaMa73eKUAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fb1fa95fc10>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.linspace(0., 1., 100)\n",
"alpha = 300. # meV/atom\n",
"T = 1500. # K\n",
"\n",
"fig, ax = plt.subplots(3, 1, sharex=True)\n",
"ax[0].plot(x, H(x, alpha))\n",
"ax[0].text(0.5, 50, '$H = \\\\alpha x(1-x)$', ha='center', va='bottom')\n",
"ax[0].text(0.5, 10, '$\\\\alpha$ = '+str(alpha)+' meV/atom', ha='center')\n",
"ax[0].set_ylabel('$H$ (meV/atom)')\n",
"\n",
"ax[1].plot(x, S_ideal(x))\n",
"ax[1].set_ylabel('$S$ ($k_B$/atom)')\n",
"ax[1].text(0.5, 0.45, '$S = -k_B[x$ln$x + (1-x)$ln$(1-x)]$', ha='center')\n",
"\n",
"ax[2].plot(x, G(x, 1200., alpha))\n",
"ax[2].text(0.5, -2, '$G = H - TS$', ha='center')\n",
"ax[2].text(0.5, -6., '$T$ = 1200 K', ha='center')\n",
"\n",
"ax[2].set_ylabel('$G$ (meV/atom)')\n",
"ax[2].set_xlabel('$x$ (atomic fraction)')\n",
"ax[2].set_xlim(0, 1)\n",
"\n",
"ax[0].set_title('Thermodynamics of a Regular Solution Model System')"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x7fb1f862c1d0>"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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ZJU7ZJhERuR/RE71Go8Gbb76JNWvW4O2338YPP/yAVatWYcmSJVizZg0SExOxfv16scPs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\nzSA55x5UAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fb1fa94fe90>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"Ts = [100, 1000, T_c(alpha), 2000]\n",
"\n",
"fig, ax = plt.subplots(1, len(Ts), sharey=True)\n",
"\n",
"for i, T in enumerate(Ts):\n",
" ax[i].plot(x, G(x, T, alpha))\n",
" ax[i].set_xlabel('$x$ (atomic fraction)')\n",
" ax[i].text(0.5, 0., '$T$ = '+str(np.round(T, -1))+' K', ha='center')\n",
"ax[0].set_ylabel('$G$ (meV/atom)')\n",
"\n",
"ax[2].text(0.5, 10, '$T_c$', ha='center')\n",
"ax[0].set_title('Below $T_c$ there are two minima, above $T_c$ there is one', ha='left')"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"## Derivatives of the Gibbs energy define the miscibility gap\n",
"\n",
"Below the critical temperature, two phases coexist in equilibrium. In the simple model system we are considering, the equations are symmetric about $x=0.5$, so we will only consider the range [0, 0.5] here. The composition of each phase in equilibrium below the critical temperature are defined by the composition where $\\frac{\\partial G}{\\partial x} = 0$. These compositions are found numerically, as there is no closed form solution to this equation. "
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": true,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"def dGdx(x, T, alpha):\n",
" return alpha*(1.-2.*x) + T*BOLTZCONST*(np.log(x) - np.log(1.-x))\n",
"\n",
"def tieline(T, alpha):\n",
" Tc = T_c(alpha)\n",
" if T <= Tc:\n",
" return root(dGdx, 1.e-5, args=(T, alpha))['x']\n",
" else:\n",
" return np.nan"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x7fb1f87583d0>"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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oqLYCqL+cblj/KPTrxt48Ed0YA5/IjQkhcOpCOb7JyEXGaROcQsDXR4lR8dEY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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fb1fa94f1d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"Ts = np.linspace(300., 2000., 100)\n",
"Tc = T_c(alpha)\n",
"\n",
"x_mgs = [tieline(T, alpha) for T in Ts]\n",
"\n",
"plt.plot(x_mgs, Ts)\n",
"plt.ylabel('$T$ (K)')\n",
"plt.xlabel('$x_A$ (atomic fraction)')\n",
"plt.title('Miscibility gap Temperature vs composition')"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"## Create toy data for this problem.\n",
"\n",
"Below we will construct toy data upon which to perform Bayesian inference. We will proceed with the following three steps to generate two sets of data - mixing enthalpy data and miscibility gap composition data.\n",
"\n",
"1. Set 'true' alpha parameter.\n",
"\n",
"2. Add random noise to mixing enthalpies evaluated at evenly spaced compositions using 'true' alpha.\n",
"\n",
"3. Add random noise to miscibility gap compositions evaluated at evenly spaced temperatures using 'true' alpha."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"true_alpha = 300.\n",
"\n",
"x_H = np.linspace(0.1, 1, 9, endpoint=False)\n",
"H_obs = H(x_H, true_alpha) + np.random.normal(0., 6., len(x_H))\n",
"\n",
"Tc_true = T_c(true_alpha)\n",
"\n",
"T_mg = np.linspace(300., Tc_true, 20)\n",
"x_mg_obs = np.array([tieline(T, true_alpha) for T in T_mg])[:, 0] + np.random.normal(0., 0.05, len(T_mg))\n",
"x_mg_obs = np.abs(x_mg_obs)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x7fb1f82de5d0>"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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Wi+See+45XnvtNRYvXsysWbNqttGrV6/b/i6Zm5szc+bMmrsm1Go1CxcupE2bNo3USsIY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\nUqj/BzmotBDiVlsLAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fb1fa94e910>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(x, H(x, true_alpha))\n",
"plt.plot(x_H, H_obs, '.', color='black')\n",
"plt.xlabel('$x$ (atomic fraction)')\n",
"plt.ylabel('$H$ (meV/atom)')\n",
"plt.title('Observed Mixing Enthalpies and \\'True\\' Values')"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x7fb1f8222e10>"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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ZGa2ouJSE46n8cCiZvSfSKCkt665v19zCrV1D6BMaTLMAH8f6qam5NVL75fR3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\npAAsfCIiIgX4H1coUz37xsbLAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fb1f82a6d50>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"Ts = np.linspace(300, Tc_true, 100)\n",
"plt.plot([tieline(T, true_alpha) for T in Ts], Ts)\n",
"plt.plot(x_mg_obs, T_mg, '.', color='black')\n",
"plt.xlabel('$x_A$ (atomic fraction)')\n",
"plt.ylabel('$T$ (K)')\n",
"plt.title('Observed Miscibility Gap compositions and \\'True\\' Values')"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"## Set up pymc3 model 1.\n",
"\n",
"First we need to implement a theano-compatible version of the miscibility gap composition finding function.\n",
"\n",
"Then we will fit the toy data to the following probabilistic model:\n",
"\n",
"\\begin{equation}\n",
"H_{obs} \\sim N\\left( H(x, \\alpha), \\sigma \\right) \\\\\n",
"\\alpha \\sim U(-1000 \\textrm{ meV/atom}, 1000 \\textrm{ meV/atom}) \\\\\n",
"\\sigma \\sim Exp(1)\n",
"\\end{equation}"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"@as_op(itypes=[tt.dvector, tt.dscalar], otypes=[tt.dvector])\n",
"def tt_tielines(Ts, alpha):\n",
" Tc = T_c(alpha)\n",
" output = []\n",
" for T in Ts:\n",
" if T <= Tc:\n",
" output.append(root(dGdx, 1.e-5, args=(T, alpha))['x'][0])\n",
" else:\n",
" #output.append(0.5)\n",
" \n",
" output.append(np.nan)\n",
" #output.append('None')\n",
" #output.append(-np.inf)\n",
" #output.append(np.inf)\n",
" return np.array(output)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|██████████| 20000/20000 [00:59<00:00, 335.98it/s]\n"
]
}
],
"source": [
"x_H_shared = shared(x_H)\n",
"\n",
"T_grid = np.linspace(300., 2000., 20)\n",
"T_mg_shared = shared(T_grid)\n",
"\n",
"with pm.Model() as example:\n",
" \n",
" alpha = pm.Uniform('alpha', lower=-1000., upper=1000., testval=350.)\n",
" sigma = pm.Exponential('sigma', lam=1.)\n",
" \n",
" H_model = x_H_shared*(1.-x_H_shared)*alpha\n",
" H_exp = pm.Normal('H_exp', mu=H_model, sd=sigma, observed=H_obs)\n",
" \n",
" Tc = pm.Deterministic('Tc', var=alpha/2./BOLTZCONST)\n",
" x_lines = tt_tielines(T_mg_shared, alpha)\n",
" x_a = pm.Deterministic('x_a', var=x_lines)\n",
" #invalid_alpha = pm.Potential('invalid_alpha', tt.switch(tt.any(tt.isnan(x_lines)), -np.inf, 0.))\n",
" \n",
" step = pm.Metropolis()\n",
" trace = pm.sample(20000, step=step)\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"alpha:\n",
"\n",
" Mean SD MC Error 95% HPD interval\n",
" -------------------------------------------------------------------\n",
" \n",
" 305.025 8.090 0.152 [289.341, 321.374]\n",
"\n",
" Posterior quantiles:\n",
" 2.5 25 50 75 97.5\n",
" |--------------|==============|==============|--------------|\n",
" \n",
" 288.723 300.048 304.918 310.084 321.047\n",
"\n",
"\n",
"sigma:\n",
"\n",
" Mean SD MC Error 95% HPD interval\n",
" -------------------------------------------------------------------\n",
" \n",
" 4.523 0.913 0.017 [2.960, 6.357]\n",
"\n",
" Posterior quantiles:\n",
" 2.5 25 50 75 97.5\n",
" |--------------|==============|==============|--------------|\n",
" \n",
" 3.117 3.882 4.378 5.038 6.623\n",
"\n",
"\n",
"Tc:\n",
"\n",
" Mean SD MC Error 95% HPD interval\n",
" -------------------------------------------------------------------\n",
" \n",
" 1769.901 46.940 0.884 [1678.897, 1864.768]\n",
"\n",
" Posterior quantiles:\n",
" 2.5 25 50 75 97.5\n",
" |--------------|==============|==============|--------------|\n",
" \n",
" 1675.312 1741.021 1769.283 1799.257 1862.872\n",
"\n",
"\n",
"x_a:\n",
"\n",
" Mean SD MC Error 95% HPD interval\n",
" -------------------------------------------------------------------\n",
" \n",
" 0.000 0.000 0.000 [0.000, 0.000]\n",
" 0.000 0.000 0.000 [0.000, 0.000]\n",
" 0.001 0.000 0.000 [0.000, 0.001]\n",
" 0.002 0.000 0.000 [0.001, 0.003]\n",
" 0.005 0.001 0.000 [0.003, 0.006]\n",
" 0.010 0.001 0.000 [0.007, 0.012]\n",
" 0.017 0.002 0.000 [0.012, 0.021]\n",
" 0.026 0.003 0.000 [0.020, 0.032]\n",
" 0.039 0.004 0.000 [0.030, 0.047]\n",
" 0.055 0.006 0.000 [0.043, 0.066]\n",
" 0.075 0.008 0.000 [0.059, 0.090]\n",
" 0.099 0.010 0.000 [0.078, 0.119]\n",
" 0.129 0.014 0.000 [0.102, 0.155]\n",
" 0.167 0.018 0.000 [0.131, 0.202]\n",
" 0.214 0.025 0.000 [0.166, 0.263]\n",
" nan nan nan [0.223, nan]\n",
" nan nan nan [0.188, nan]\n",
" nan nan nan [0.233, nan]\n",
" nan nan nan [0.294, nan]\n",
" nan nan nan [0.394, nan]\n",
"\n",
" Posterior quantiles:\n",
" 2.5 25 50 75 97.5\n",
" |--------------|==============|==============|--------------|\n",
" \n",
" 0.000 0.000 0.000 0.000 0.000\n",
" 0.000 0.000 0.000 0.000 0.000\n",
" 0.000 0.001 0.001 0.001 0.001\n",
" 0.001 0.002 0.002 0.002 0.003\n",
" 0.004 0.004 0.005 0.005 0.007\n",
" 0.007 0.009 0.010 0.010 0.012\n",
" 0.013 0.015 0.016 0.018 0.021\n",
" 0.021 0.024 0.026 0.028 0.033\n",
" 0.031 0.036 0.039 0.041 0.048\n",
" 0.044 0.051 0.055 0.058 0.068\n",
" 0.061 0.070 0.074 0.079 0.092\n",
" 0.081 0.092 0.099 0.105 0.122\n",
" 0.105 0.120 0.129 0.137 0.160\n",
" 0.135 0.155 0.165 0.177 0.208\n",
" 0.171 0.197 0.212 0.228 0.273\n",
" 0.216 0.253 0.275 0.298 0.379\n",
" 0.277 0.335 0.375 0.436 nan\n",
" 0.371 nan nan nan nan\n",
" nan nan nan nan nan\n",
" nan nan nan nan nan\n",
"\n"
]
}
],
"source": [
"pm.summary(trace)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x7fb1ec795ed0>"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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gD/Z323f6krpLnXJs6Vx7bNLdiWv3s9PN/V31NqwGhd3vvslbb77Cw+u24Pd5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\nrkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fb1f882fd90>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot([tieline(T, true_alpha) for T in Ts], Ts, '--', color='black')\n",
"plt.plot(np.nanmean(trace['x_a'], axis=0), T_grid)\n",
"plt.fill_betweenx(\n",
" T_grid,\n",
" np.nanpercentile(trace['x_a'], 2.5, axis=0),\n",
" np.nanpercentile(trace['x_a'], 97.5, axis=0),\n",
" alpha=0.4\n",
")\n",
"plt.plot(x_mg_obs, T_mg, '.', color='black')\n",
"plt.xlabel('$x_a$ (atomic fraction)')\n",
"plt.ylabel('$T$ (K)')"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|██████████| 2000/2000 [00:13<00:00, 146.52it/s]\n"
]
}
],
"source": [
"x_new = np.linspace(0., 1., 100)\n",
"x_H_shared.set_value(x_new)\n",
"\n",
"ppd = pm.sample_ppc(trace, samples=2000, model=example)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x7fb1ea9ce790>"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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IprTAgEySqNm2gc8/Wc761StxO+08+uw/qRw9kfo9O2hrqWfKjDlkGU1HOMrAXfj9icRi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\nYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fb1eaaf8a10>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.fill_between(\n",
" x_new, \n",
" np.percentile(ppd['H_exp'], 2.5, axis=0), \n",
" np.percentile(ppd['H_exp'], 97.5, axis=0),\n",
" alpha=0.4,\n",
")\n",
"plt.plot(x_new, np.mean(ppd['H_exp'], axis=0))\n",
"plt.errorbar(x_H, y=H_obs, yerr=trace['sigma'].mean(axis=0), \n",
" fmt='o', \n",
" color='black',\n",
" )\n",
"plt.plot(x_new, H(x_new, true_alpha), '--', color='black')\n",
"plt.xlabel('$x$ (atomic fraction)')\n",
"plt.ylabel('$H$ (meV/atom)')"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"## Set up and run pymc3 model 2.\n",
"\n",
"The second probabilistic model will include the miscibility gap compositions:\n",
"\n",
"\\begin{equation}\n",
"x_{obs}^{mg} \\sim N\\left(x_{mg}(T, \\alpha), \\sigma_x \\right) \\\\\n",
"H_{obs} \\sim N\\left( H(x, \\alpha), \\sigma_H \\right) \\\\\n",
"\\alpha \\sim U(-1000 \\textrm{ meV/atom}, 1000 \\textrm{ meV/atom}) \\\\\n",
"\\sigma_H \\sim Exp(1) \\\\\n",
"\\sigma_x \\sim Exp(1)\n",
"\\end{equation}"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|██████████| 8000/8000 [01:19<00:00, 101.24it/s]\n"
]
}
],
"source": [
"x_H_shared = shared(x_H)\n",
"T_mg_shared = shared(T_mg)\n",
"\n",
"with pm.Model() as example2:\n",
" \n",
" alpha = pm.Uniform('alpha', lower=-1000., upper=1000., testval=350.)\n",
" sigma_H = pm.Exponential('sigma_H', lam=1.)\n",
" sigma_x = pm.Exponential('sigma_x', lam=1.)\n",
" \n",
" H_model = x_H_shared*(1.-x_H_shared)*alpha\n",
" H_exp = pm.Normal('H_exp', mu=H_model, sd=sigma_H, observed=H_obs)\n",
" \n",
" Tc = pm.Deterministic('Tc', var=alpha/2./BOLTZCONST)\n",
" x_lines = tt_tielines(T_mg_shared, alpha)\n",
" x_a = pm.Normal('x_a', mu=x_lines, sd=sigma_x, observed=x_mg_obs)\n",
" \n",
" invalid_alpha = pm.Potential('invalid_alpha', tt.switch(tt.any(tt.isnan(x_lines)), -np.inf, 0.))\n",
" \n",
" step = pm.Metropolis()\n",
" trace = pm.sample(8000, step=step)\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"alpha:\n",
"\n",
" Mean SD MC Error 95% HPD interval\n",
" -------------------------------------------------------------------\n",
" \n",
" 301.420 2.409 0.099 [300.001, 304.558]\n",
"\n",
" Posterior quantiles:\n",
" 2.5 25 50 75 97.5\n",
" |--------------|==============|==============|--------------|\n",
" \n",
" 300.016 300.319 300.846 301.898 305.687\n",
"\n",
"\n",
"sigma_H:\n",
"\n",
" Mean SD MC Error 95% HPD interval\n",
" -------------------------------------------------------------------\n",
" \n",
" 4.399 0.902 0.024 [2.967, 6.209]\n",
"\n",
" Posterior quantiles:\n",
" 2.5 25 50 75 97.5\n",
" |--------------|==============|==============|--------------|\n",
" \n",
" 3.038 3.756 4.267 4.941 6.403\n",
"\n",
"\n",
"sigma_x:\n",
"\n",
" Mean SD MC Error 95% HPD interval\n",
" -------------------------------------------------------------------\n",
" \n",
" 0.060 0.013 0.000 [0.040, 0.081]\n",
"\n",
" Posterior quantiles:\n",
" 2.5 25 50 75 97.5\n",
" |--------------|==============|==============|--------------|\n",
" \n",
" 0.043 0.052 0.058 0.066 0.088\n",
"\n",
"\n",
"Tc:\n",
"\n",
" Mean SD MC Error 95% HPD interval\n",
" -------------------------------------------------------------------\n",
" \n",
" 1748.985 13.977 0.577 [1740.750, 1767.192]\n",
"\n",
" Posterior quantiles:\n",
" 2.5 25 50 75 97.5\n",
" |--------------|==============|==============|--------------|\n",
" \n",
" 1740.837 1742.595 1745.654 1751.760 1773.743\n",
"\n"
]
}
],
"source": [
"pm.summary(trace)"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|██████████| 4000/4000 [01:49<00:00, 36.69it/s]\n"
]
}
],
"source": [
"x_new = np.linspace(0., 1., 100)\n",
"x_H_shared.set_value(x_new)\n",
"\n",
"T_mg_new = np.linspace(300., 2000., 100)\n",
"T_mg_shared.set_value(T_mg_new)\n",
"\n",
"ppd = pm.sample_ppc(trace, samples=4000, model=example2)"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x7fb1ed732b50>"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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KMiktSO4Xa+cKCl5/gA6ru9/NFoiBS4K4OGB12txsrOrs8xF4MKiwrd7Chh2ddLQ1s/az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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fb1ee509110>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.fill_between(\n",
" x_new, \n",
" np.percentile(ppd['H_exp'], 2.5, axis=0), \n",
" np.percentile(ppd['H_exp'], 97.5, axis=0),\n",
" alpha=0.4,\n",
")\n",
"plt.plot(x_new, np.mean(ppd['H_exp'], axis=0))\n",
"plt.errorbar(x_H, y=H_obs, yerr=trace['sigma_H'].mean(axis=0), \n",
" fmt='o', \n",
" color='black',\n",
" )\n",
"\n",
"plt.plot(x_new, H(x_new, true_alpha), '--', color='black')\n",
"\n",
"plt.xlabel('$x$ (atomic fraction)')\n",
"plt.ylabel('$H$ (meV/atom)')"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/jdoak/Envs/pymc3/lib/python2.7/site-packages/numpy/lib/function_base.py:4116: RuntimeWarning: Invalid value encountered in percentile\n",
" interpolation=interpolation)\n"
]
},
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x7fb1ef617910>"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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GlOVh0MswvhCRErUevl6vR68/9nQHDhxgz5493H333fz2t78FwGq1kpub2/mY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\niBSADZ+IiEgB/g+NYe5WlGV2tgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fb1f859e710>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.fill_betweenx(\n",
" T_mg_new, \n",
" np.percentile(ppd['x_a'], 2.5, axis=0), \n",
" np.percentile(ppd['x_a'], 97.5, axis=0),\n",
" alpha=0.4,\n",
")\n",
"plt.plot(np.mean(ppd['x_a'], axis=0), T_mg_new)\n",
"plt.errorbar(x=x_mg_obs, y=T_mg, xerr=trace['sigma_x'].mean(axis=0), \n",
" fmt='o', \n",
" color='black',\n",
" )\n",
"\n",
"plt.plot([tieline(T, true_alpha) for T in Ts], Ts, '--', color='black')\n",
"\n",
"plt.xlabel('$x_a$ (atomic fraction)')\n",
"plt.ylabel('$T$ (K)')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "pymc3(2.7.13)",
"language": "python",
"name": "pymc3_2.7.13"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.13"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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