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Example of Bayesian regression applied to the thermodynamics of miscibility gap systems. Updated to include use of TheanoOp with symbolic gradient calculated via implicit differentiation to enable NUTS MC sampling.
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"source": [
"# Minimial working example of Miscibility gap uncertainty propagation"
]
},
{
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"source": [
"# Jupyter Magics\n",
"%load_ext autoreload\n",
"%autoreload 2\n",
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
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"source": [
"import numpy as np\n",
"from matplotlib import pyplot as plt\n",
"#import pandas as pd\n",
"import seaborn as sns\n",
"from numba import jit\n",
"\n",
"import pymc3 as pm\n",
"\n",
"import corner\n",
"\n",
"from scipy.optimize import root\n",
"\n",
"import theano\n",
"from theano import as_op, shared\n",
"import theano.tensor as tt\n",
"from theano.tests import unittest_tools\n",
"\n",
"theano.config.compute_test_value = 'ignore'"
]
},
{
"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,
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"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": {
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"outputs": [
{
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"execution_count": 4,
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pGuxO12B3tDr9ANPjSbnEnc8lNiGb2IRsTBQy2jR3olOgKx0CXcVsfcJ1apTo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\nhV4IIYQwY1LohRBCCDMmhV4IIYQwY/8LrrhaMa73eKUAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fe8aa9115d0>"
]
},
"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 0x7fe8a85d5b50>"
]
},
"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 0x7fe8aa911410>"
]
},
"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": [
"@jit\n",
"def dGdx(x, T, alpha):\n",
" return alpha*(1.-2.*x) + T*BOLTZCONST*(np.log(x) - np.log(1.-x))\n",
"\n",
"@jit\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 0x7fe8a7baa450>"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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aa6/h+eefxz/+8Q8oFAo8/vjj8PX1bdZ27rzzTvzzn/9ERkYG/P39XXX84Q9/wIsvvujq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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fe8aa90df50>"
]
},
"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 0x7fe8a7ad3f90>"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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3XQPc+OXsFT6IPk5llRRy0fSkiItWZ/3e86zedQ6PNna8+Pu+tNc2bq1tIQDs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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fe8aa90d390>"
]
},
"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 0x7fe8a7c55c10>"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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5R/H6O3Sc2tBxzmxDlwZ+SEgIN9xQPunCkCFDWLRoEcOHDyc9Pd2+TmpqKlFR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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fe8a7a94e90>"
]
},
"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 [00:23<00:00, 839.86it/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",
" 295.755 9.594 0.159 [276.029, 314.319]\n",
"\n",
" Posterior quantiles:\n",
" 2.5 25 50 75 97.5\n",
" |--------------|==============|==============|--------------|\n",
" \n",
" 276.364 289.549 295.789 301.684 315.136\n",
"\n",
"\n",
"sigma:\n",
"\n",
" Mean SD MC Error 95% HPD interval\n",
" -------------------------------------------------------------------\n",
" \n",
" 5.450 1.050 0.019 [3.588, 7.492]\n",
"\n",
" Posterior quantiles:\n",
" 2.5 25 50 75 97.5\n",
" |--------------|==============|==============|--------------|\n",
" \n",
" 3.811 4.711 5.307 6.076 7.818\n",
"\n"
]
}
],
"source": [
"pm.summary(trace, varnames=['alpha', 'sigma'])"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x7fe8a224be90>"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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GIkQiqfvNFiu/euEdAH7505X8c8vfTyqLPcvJn/+6HZtZzzPPPMX69X896fWcnJx04H/4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\nHhL4ol/xBaPsO9re7XH6D3d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Y9v6Odh76wdfYv3cH5ZNn0tLmY/MeN0cOfYS/rRaAprpq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\ngg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fe8a7c04b10>"
]
},
"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,
"deletable": true,
"editable": true
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|██████████| 2000/2000 [00:13<00:00, 147.39it/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,
"deletable": true,
"editable": true
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x7fe898f9c7d0>"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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GrZoMuwGn1YBapSQiSexqddPU0T+oSnRKhSKhFetiTa1SMqMiC0eqns+2QeXJ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\nERGRn2ISJyIi8lNM4kRERH7q/wFJOM3Kdnp0wQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fe898fab110>"
]
},
"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 [00:32<00:00, 247.74it/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.bound(pm.Normal('x_a', mu=x_lines, sd=sigma_x, observed=x_mg_obs), lower=0., upper=1.)\n",
" \n",
" invalid_alpha = pm.Potential('invalid_alpha', tt.switch(tt.any(tt.isnan(x_lines)), -np.inf, 0.))\n",
" #invalid_xlines = pm.Potential('invalid_xlines', tt.switch(tt.any(tt.lt(x_lines, 0)), -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",
" 301.540 3.286 0.238 [300.001, 304.536]\n",
"\n",
" Posterior quantiles:\n",
" 2.5 25 50 75 97.5\n",
" |--------------|==============|==============|--------------|\n",
" \n",
" 300.043 300.394 300.846 301.759 306.735\n",
"\n",
"\n",
"sigma_H:\n",
"\n",
" Mean SD MC Error 95% HPD interval\n",
" -------------------------------------------------------------------\n",
" \n",
" 5.364 1.051 0.033 [3.586, 7.545]\n",
"\n",
" Posterior quantiles:\n",
" 2.5 25 50 75 97.5\n",
" |--------------|==============|==============|--------------|\n",
" \n",
" 3.761 4.623 5.197 5.930 7.903\n",
"\n",
"\n",
"sigma_x:\n",
"\n",
" Mean SD MC Error 95% HPD interval\n",
" -------------------------------------------------------------------\n",
" \n",
" 0.054 0.023 0.001 [0.037, 0.073]\n",
"\n",
" Posterior quantiles:\n",
" 2.5 25 50 75 97.5\n",
" |--------------|==============|==============|--------------|\n",
" \n",
" 0.039 0.047 0.052 0.058 0.077\n",
"\n"
]
}
],
"source": [
"pm.summary(trace, varnames=['alpha', 'sigma_H', 'sigma_x'])"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|██████████| 4000/4000 [01:13<00:00, 54.30it/s]\n"
]
}
],
"source": [
"x_new = np.linspace(0.0001, 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 0x7fe892e06190>"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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9GfgMeg2ZydEUD4tj0ogUJg1PITPJiDqCF/9l5xXzl2ffIjltGGUb/sWrz/2J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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fe892db1250>"
]
},
"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": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x7fe892d18590>"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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zOH10L8rfXoOAz4M7734Ipf0HdatcSRBw77Lv4NEfx+7pE/UmDPhE1KsYHexr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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fe892e75b10>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.fill_betweenx(\n",
" T_mg_new, \n",
" np.nanpercentile(ppd['x_a'], 2.5, axis=0), \n",
" np.nanpercentile(ppd['x_a'], 97.5, axis=0),\n",
" alpha=0.4,\n",
")\n",
"plt.plot(np.nanmean(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 T_mg_new], T_mg_new, '--', color='black')\n",
"\n",
"plt.xlabel('$x_a$ (atomic fraction)')\n",
"plt.ylabel('$T$ (K)')"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true,
"deletable": true,
"editable": true
},
"source": [
"## Theano Op using implicit differentiation to obtain gradient"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": true,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"class TielineOp(tt.Op):\n",
" \"\"\"\n",
" \"\"\"\n",
" itypes = [tt.dvector, tt.dscalar]\n",
" otypes = [tt.dvector]\n",
" \n",
" def perform(self, node, inputs, outputs):\n",
" Ts, alpha = inputs\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(np.nan)\n",
" outputs[0][0] = np.array(output)\n",
" \n",
" def grad(self, inputs, output_gradients):\n",
" Ts, alpha = inputs\n",
" xs = self(Ts, alpha)\n",
"\n",
" gs, = output_gradients\n",
"\n",
" dxdTs = (xs*BOLTZCONST*(xs*tt.log(xs) - xs*tt.log(1-xs) - tt.log(xs) + tt.log(1-xs))\n",
" /(2*alpha*tt.sqr(xs)-2*alpha*xs+BOLTZCONST*Ts))\n",
" dxdas = xs*(-2*xs**2 + 3*xs - 1)/(BOLTZCONST*Ts + 2*alpha*xs**2 - 2*alpha*xs)\n",
"\n",
" dCdTs = dxdTs*gs\n",
" dCda = tt.dot(gs, dxdas)\n",
" \n",
" return [dCdTs, dCda]\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true,
"scrolled": false
},
"outputs": [],
"source": [
"unittest_tools.verify_grad(TielineOp(), [np.linspace(300., 1000., 50), np.array(300.)])"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true,
"scrolled": true
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Auto-assigning NUTS sampler...\n",
"Initializing NUTS using advi...\n",
"Average ELBO = -11.75: 100%|██████████| 200000/200000 [04:23<00:00, 758.25it/s] \n",
"Finished [100%]: Average ELBO = -11.741\n",
"100%|██████████| 1000/1000 [00:45<00:00, 21.89it/s]\n"
]
}
],
"source": [
"x_H_shared = shared(x_H)\n",
"T_mg_shared = shared(T_mg)\n",
"\n",
"with pm.Model() as example3:\n",
" \n",
" alpha = pm.Uniform('alpha', lower=max(2*BOLTZCONST*T_mg), upper=1000.)\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 = TielineOp()(T_mg_shared, alpha)\n",
" x_a = pm.Bound(pm.Normal('x_a', mu=x_lines, sd=sigma_x, observed=x_mg_obs), lower=0., upper=1.)\n",
" \n",
" trace = pm.sample(1000)\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|██████████| 1000/1000 [00:17<00:00, 56.90it/s]\n"
]
}
],
"source": [
"x_new = np.linspace(0.0001, 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=1000, model=example3)"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"samples = trace\n",
"sampled_ppd = ppd"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"alpha:\n",
"\n",
" Mean SD MC Error 95% HPD interval\n",
" -------------------------------------------------------------------\n",
" \n",
" 301.248 1.244 0.043 [300.005, 303.795]\n",
"\n",
" Posterior quantiles:\n",
" 2.5 25 50 75 97.5\n",
" |--------------|==============|==============|--------------|\n",
" \n",
" 300.030 300.356 300.831 301.803 304.547\n",
"\n",
"\n",
"sigma_H:\n",
"\n",
" Mean SD MC Error 95% HPD interval\n",
" -------------------------------------------------------------------\n",
" \n",
" 5.292 0.972 0.035 [3.649, 7.301]\n",
"\n",
" Posterior quantiles:\n",
" 2.5 25 50 75 97.5\n",
" |--------------|==============|==============|--------------|\n",
" \n",
" 3.782 4.593 5.136 5.848 7.536\n",
"\n",
"\n",
"sigma_x:\n",
"\n",
" Mean SD MC Error 95% HPD interval\n",
" -------------------------------------------------------------------\n",
" \n",
" 0.052 0.009 0.000 [0.037, 0.069]\n",
"\n",
" Posterior quantiles:\n",
" 2.5 25 50 75 97.5\n",
" |--------------|==============|==============|--------------|\n",
" \n",
" 0.038 0.047 0.051 0.058 0.073\n",
"\n",
"\n",
"Tc:\n",
"\n",
" Mean SD MC Error 95% HPD interval\n",
" -------------------------------------------------------------------\n",
" \n",
" 1747.985 7.220 0.250 [1740.773, 1762.764]\n",
"\n",
" Posterior quantiles:\n",
" 2.5 25 50 75 97.5\n",
" |--------------|==============|==============|--------------|\n",
" \n",
" 1740.920 1742.811 1745.567 1751.204 1767.126\n",
"\n"
]
}
],
"source": [
"pm.summary(trace)"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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17b8c2lGDgDrXOT434/gv+IY1oNZ1D1GYl83JrR+RuHspta4dTHbyb3z+xgRsdjv2Ujqs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\ngg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fe8930c2850>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pm.plot_posterior(samples, varnames=['alpha', 'sigma_H', 'sigma_x']);"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[<matplotlib.axes._subplots.AxesSubplot object at 0x7fe87e826510>],\n",
" [<matplotlib.axes._subplots.AxesSubplot object at 0x7fe879a73d10>],\n",
" [<matplotlib.axes._subplots.AxesSubplot object at 0x7fe8799f5b50>]], dtype=object)"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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0XwAAAO2dreF67ty5GjdunLKyslRRUdFqbOfOncrMzNS4ceO0ePFiO8toVwjD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\ndEgAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fe87c97f750>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pm.autocorrplot(samples, varnames=['alpha', 'sigma_H', 'sigma_x'])"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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crIG7u+G9Z9yV0NpnYVw6mBP79u3BlCkToNPpMHXqBPzvf6Fo3bpNjmMmIiLb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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fe8a471ba50>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"corner.corner(pm.trace_to_dataframe(samples, varnames=['alpha', 'sigma_H', 'sigma_x']));"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x7fe87f21ad10>"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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/h16fjx0HjJhtwVlkepDP6+XJh25l++bvOfGSR5hx4TT6pMQAEBuj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\nSfTv398TIXq9hvpwx44dyMvLw/jx4zFr1iykpaVh/vz5ngrVqzXUjxa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"text/plain": [
"<matplotlib.figure.Figure at 0x7fe892513f10>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.fill_between(\n",
" x_new, \n",
" np.percentile(sampled_ppd['H_exp'], 2.5, axis=0), \n",
" np.percentile(sampled_ppd['H_exp'], 97.5, axis=0),\n",
" alpha=0.4,\n",
")\n",
"plt.plot(x_new, np.mean(sampled_ppd['H_exp'], axis=0))\n",
"plt.errorbar(x_H, y=H_obs, yerr=samples['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": 32,
"metadata": {
"collapsed": false
},
"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 0x7fe87ea4f550>"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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gnzeIL+VnPpa8n/UhG8eckYV3mpub2b9/P7feeisALS0tLF68mB/84Ae4XJ83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\nAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fe87cf78790>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.fill_betweenx(\n",
" T_mg_new, \n",
" np.percentile(sampled_ppd['x_a'], 2.5, axis=0), \n",
" np.percentile(sampled_ppd['x_a'], 97.5, axis=0),\n",
" alpha=0.4,\n",
")\n",
"plt.plot(np.mean(sampled_ppd['x_a'], axis=0), T_mg_new)\n",
"plt.errorbar(x=x_mg_obs, y=T_mg, xerr=samples['sigma_x'].mean(axis=0), \n",
" fmt='o', \n",
" color='black',\n",
" )\n",
"\n",
"plt.plot([tieline(t, true_alpha) for t in T_mg_new], T_mg_new, '--', 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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