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‎.gitignore‎

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*.pptx
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.ipynb_checkpoints/
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.DS_Store
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__pycache__/

‎example/Cooling_Opt.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Optimization of a radiative cooling structure\n",
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"This notebook will optimize a multi-layer structure inspired by Raman 𝑒𝑡 𝑎𝑙. , Nature 515, 540-546 (2014), utilizing analytic gradients of the three terms that dominate\n",
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"the radiative flux: absorption of solar radiation, absorption of atmospheric thermal radiation (both warming), and thermal emission (cooling). \n",
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"\n",
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"**Note that the explit angle and polarization dependence will be included in these gradients, and so each gradient evaluation will be ~14 times slower than comparable gradient evaluations when angle- and polarization dependence are ignored as in other optimization demos [see, for example, here](http://localhost:8888/notebooks/CODE/wptherml/example/Incandescent_Opt.ipynb)**."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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" Temperature not specified!\n",
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" Proceeding with default T = 300 K\n",
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"xs is \n",
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"[230, 485, 688, 13, 73, 34, 54]\n",
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" This structure is net cooling with net power out being 63.525923254487594\n",
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" This structure is net cooling with net power out being 26.93358430958938\n",
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" This structure is net cooling with net power out being 26.987684491357246\n",
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" This structure is net cooling with net power out being 31.257424595611454\n",
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" This structure is net cooling with net power out being 59.933261081356505\n",
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" This structure is net cooling with net power out being 68.59349206988524\n",
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" This structure is net cooling with net power out being 69.19255314674987\n",
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" This structure is net cooling with net power out being 69.53944029636773\n",
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" This structure is net cooling with net power out being 69.07278380133678\n",
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" This structure is net cooling with net power out being 70.57523013190401\n",
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" This structure is net cooling with net power out being 70.49876027675884\n",
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" This structure is net cooling with net power out being 70.85380995302663\n",
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" This structure is net cooling with net power out being 70.79612870829939\n",
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" This structure is net cooling with net power out being 70.86055573829051\n",
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" This structure is net cooling with net power out being 70.56282333077554\n",
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" This structure is net cooling with net power out being 70.88045444055962\n",
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" This structure is net cooling with net power out being 70.89025678075966\n",
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" This structure is net cooling with net power out being 70.89100749911535\n",
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" This structure is net cooling with net power out being 70.89121169266468\n",
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" This structure is net cooling with net power out being 70.89166953716105\n",
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" This structure is net cooling with net power out being 70.89224257525305\n",
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" This structure is net cooling with net power out being 70.89260757037914\n",
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" This structure is net cooling with net power out being 70.89261054829753\n",
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" This structure is net cooling with net power out being 70.8926105873357\n",
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"[300. 296.22235003 300. 200.02210915 277.76544865\n",
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" 294.76122768 300. ]\n",
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"70.8926105873357\n"
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]
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}
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],
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"source": [
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"### Import WPTHERML class!\n",
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"from wptherml.wpml import multilayer\n",
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"from matplotlib import pyplot as plt\n",
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"from wptherml.datalib import datalib\n",
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"import numpy as np\n",
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"from scipy.optimize import minimize\n",
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"from scipy.optimize import basinhopping\n",
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"import time\n",
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"import numpy as np\n",
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"\n",
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"### Define structure!\n",
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"structure = {\n",
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"\n",
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" 'Material_List': ['Air', 'SiO2', 'HfO2', 'SiO2', 'HfO2', 'SiO2', 'HfO2', 'SiO2', 'Ag', 'Air'],\n",
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" 'Thickness_List': [0, 230e-9, 485e-9, 688e-9, 13e-9, 73e-9, 34e-9, 54e-9, 200e-9, 0],\n",
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" 'Lambda_List': [300e-9, 20000e-9, 1000],\n",
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" ### we will compute gradients wrt thickness of first 7 layers, Ag thickness will not change\n",
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" 'Gradient_List': [1,2,3,4,5,6,7],\n",
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" 'EXPLICIT_ANGLE': 1,\n",
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" 'COOLING': 1\n",
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" \n",
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" }\n",
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"\n",
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"### create instance of multilayer class called cool_ml\n",
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"cool_ml = multilayer(structure)\n",
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"### get length of gradient vector\n",
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"length = cool_ml.gradient_dimension\n",
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"\n",
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"def update_multilayer(x):\n",
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" for i in range(0,len(x)):\n",
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" cool_ml.d[i+1] = x[i]*1e-9\n",
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" ### now we have the new structure, update fresnel quantities\n",
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" cool_ml.fresnel_ea()\n",
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" cool_ml.thermal_emission_ea()\n",
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" ### now we have new emissivity, update thermal emission\n",
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" cool_ml.cooling_power()\n",
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"\n",
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" ### return negative of cooling power - minimize functions want \n",
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" ### to minimize, so trick them by passing negative of the objective you\n",
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" ### want to maximize\n",
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" return -cool_ml.cooling_power_val\n",
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"\n",
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"### given an array of thicknesses of the coating, update\n",
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"### the structure and compute the gradient vector of conversion efficiency wrt layer thicknesses\n",
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"def analytic_grad(x0):\n",
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" cur = update_multilayer(x0)\n",
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" cool_ml.fresnel_prime_ea()\n",
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" cool_ml.thermal_emission_prime_ea()\n",
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" cool_ml.cooling_power_prime()\n",
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" ### now there will be three contributions to the\n",
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" ### gradient vector... two warming contributions \n",
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" ### (solar_power_grad and atmospheric_power_grad)\n",
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" ### and one cooling contribution (radiative_power_grad)\n",
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" ### and the total gradient is the sum of all three\n",
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" g = cool_ml.cooling_power_grad\n",
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" ### scale gradient to be in nm^-1 rather than over m^-1\n",
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" return -g*1e-9\n",
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"\n",
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"### Function that gets the negative of the efficiency and the \n",
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"### negative of the gradient for use in the l-bfgs-b algorithm\n",
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"### also prints out the time for timing purposes!\n",
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"def SuperFunc(x0):\n",
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" en = update_multilayer(x0)\n",
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" c_time = time.time()\n",
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" if en<0:\n",
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" print(\" This structure is net cooling with net power out being\",-en)\n",
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" else:\n",
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" print(\" This structure is net warming with net poer in being\",-en)\n",
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" gr = analytic_grad(x0)\n",
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" return en, gr\n",
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"\n",
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"\n",
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"# the bounds for L-BFGS-B updates!\n",
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"bfgs_xmin = np.ones(length)\n",
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"bfgs_xmax = 300*np.ones(length)\n",
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"\n",
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"# rewrite the bounds in the way required by L-BFGS-B\n",
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"bfgs_bounds = [(low, high) for low, high in zip(bfgs_xmin, bfgs_xmax)]\n",
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"\n",
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"### initialize the solution vector xs to be the thicknesses from \n",
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"### Raman et al. paper\n",
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"xs = [230, 485, 688, 13, 73, 34, 54]\n",
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"\n",
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"### print out initial solution vector and initial efficiency\n",
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"print(\"xs is \")\n",
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"print(xs)\n",
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"pflux = -update_multilayer(xs)\n",
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"if pflux>0:\n",
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" print(\" This structure is net cooling with net power out being\",pflux) \n",
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"else:\n",
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" print(\" This structure is net warming with net poer in being\",pflux)\n",
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"\n",
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"\n",
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"### run l-bfgs-b algorithm!\n",
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"ret = minimize(SuperFunc, xs, method=\"L-BFGS-B\", jac=True, bounds=bfgs_bounds)\n",
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"\n",
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"### print optimal solution and its efficiency!\n",
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"print(ret.x)\n",
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"print(-update_multilayer(ret.x))\n",
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" \n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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},
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.7.3"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}

‎example/Example1.ipynb‎

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‎example/Incandescent_Opt.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"This notebook demonstrates the local optimization of a filter coupled to a W thermal emitter,\n",
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"and should reproduce the efficiency reported in Table II \"W + F$_{opt}$\" in \n",
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"\"Accelerating the discovery of multi-layer nanostructures with analytic differentiation \n",
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"of the transfer matrix equations\" by J. F. Varner, D. Wert, A. Matari, R. Nofal, and J. J. Foley IV."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"from wptherml.wpml import multilayer\n",
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"from matplotlib import pyplot as plt\n",
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"from scipy.optimize import minimize\n",
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"from scipy.optimize import basinhopping\n",
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"import time\n",
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"import numpy as np\n",
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"\n",
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"### This will define a thick tungsten slab\n",
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"w_struct = {\n",
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"\n",
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" 'Material_List': ['Air', 'W', 'Air'],\n",
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" 'Thickness_List': [0, 900e-9, 0],\n",
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" 'Lambda_List': [300e-9, 4000e-9, 1000],\n",
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" 'Temperature': 2700,\n",
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" 'LIGHTBULB': 1\n",
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"\n",
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" }\n",
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"\n",
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"### create instance of the tungsten emitter structure\n",
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"w = multilayer(w_struct)\n",
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"\n",
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"\n",
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"### Create a global variable called emissivity that will NOT change from the original emissivity of W slab\n",
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"e_emissivity = w.emissivity_array\n",
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"\n",
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"### This will define the base filter that will be optimized\n",
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"structure = {\n",
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" 'Material_List' : ['Air', 'Ta2O5','SiO2','Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5','SiO2', 'Ta2O5', 'SiO2', 'Air'],\n",
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" ### Thicknesses just chosen arbitrarily, replace with \"optimal\" values\n",
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" 'Thickness_List': [0, 18e-9, 47e-9, 156e-9, 212e-9, 178e-9, 23e-9, 51e-9, 224e-9, 150e-9, 205e-9, 258e-9, 187e-9, 243e-9, 190e-9, 266e-9, 215e-9, 153e-9, 227e-9, 154e-9, 226e-9, 152e-9, 245e-9, 24e-9, 229e-9, 263e-9, 190e-9, 257e-9, 200e-9, 260e-9, 224e-9, 27e-9, 229e-9, 154e-9, 219e-9, 274e-9, 198e-9, 405e-9, 211e-9, 166e-9, 233e-9, 47e-9, 66e-9, 17e-9, 125e-9, 153e-9, 237e-9, 151e-9, 225e-9, 147e-9, 193e-9, 127e-9, 214e-9, 135e-9, 173e-9, 112e-9, 165e-9, 130e-9, 223e-9, 130e-9, 163e-9, 112e-9, 164e-9, 114e-9, 167e-9, 121e-9, 378e-9, 114e-9, 160e-9, 113e-9, 174e-9, 117e-9, 211e-9, 23e-9, 221e-9, 261e-9, 399e-9, 266e-9, 390e-9, 28e-9, 18e-9, 367e-9, 198e-9, 302e-9, 28e-9, 33e-9, 426e-9, 31e-9, 15e-9, 222e-9, 96e-9, 0 ],\n",
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" 'Lambda_List': [300e-9, 4000e-9, 1000],\n",
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" 'Temperature': 2700,\n",
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" 'LIGHTBULB': 1\n",
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"\n",
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" }\n",
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"### create instance called cc\n",
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"cc = multilayer(structure)\n",
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"\n",
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"### get initial luminous efficiency of W-emitter / filter pair\n",
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"cc.luminous_efficiency_filter(e_emissivity)\n",
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"print(\" Filtered Multilayer Luminous Efficiency\", cc.luminous_efficiency_val*100)\n",
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"\n",
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"### How many elements in the filter will be varied over?\n",
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"length = len(cc.luminous_efficiency_grad)\n",
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"print(\"length is \",length)\n",
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"\n",
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"### given an array of thicknesses for the filter, update the filter and\n",
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"### re-compute the luminous efficiency of the W-emitter / filter pair\n",
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"def update_multilayer(x0):\n",
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" ### use gradient_list to define which layers are updated!\n",
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" dim = len(x0)\n",
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" for i in range(1,dim+1):\n",
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" cc.d[i] = x0[i-1]*1e-9\n",
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" \n",
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" cc.fresnel()\n",
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" cc.thermal_emission()\n",
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" cc.luminous_efficiency_filter(e_emissivity)\n",
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" ### return the negative of the efficiency since the \n",
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" ### scipy minimize functions find the MINIMUM not the MAXIMUM...\n",
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" ### we of course want the MAXIMUM efficiency which is the same\n",
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" ### as the MINIMUM of the negative of the efficiency\n",
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" return -cc.luminous_efficiency_val*100\n",
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"\n",
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"### given an array of thicknesses for the filter, update the filter\n",
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"### and compute the gradient of its transmissivity...\n",
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"### use that to compute the gradient of the luminous efficiency\n",
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"### return the negative of the luminous efficiency gradient \n",
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"### scaled by 10^-7 \n",
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"def analytic_grad(x0):\n",
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" dim = len(x0)\n",
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" g = np.zeros(dim)\n",
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" cur = update_multilayer(x0)\n",
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" cc.fresnel_prime()\n",
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" cc.luminous_efficiency_filter_prime(e_emissivity)\n",
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" g = cc.luminous_efficiency_grad\n",
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" return -g*1e-7\n",
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"\n",
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"### Function that gets the negative of the efficiency and the \n",
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"### negative of the gradient for use in the l-bfgs-b algorithm\n",
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"### also prints out the time for timing purposes!\n",
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"def SuperFunc(x0):\n",
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" en = update_multilayer(x0)\n",
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" c_time = time.time()\n",
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" print(en,\",\",c_time)\n",
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" gr = analytic_grad(x0)\n",
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" return en, gr\n",
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"\n",
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"\n",
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"# the bounds for L-BFGS-B updates!\n",
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"bfgs_xmin = np.ones(length)\n",
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"bfgs_xmax = 405*np.ones(length)\n",
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"\n",
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"# rewrite the bounds in the way required by L-BFGS-B\n",
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"bfgs_bounds = [(low, high) for low, high in zip(bfgs_xmin, bfgs_xmax)]\n",
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"\n",
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"### initialize the solution vector xs to be the thicknesses from \n",
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"### the structure dictionary\n",
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"xs = np.zeros(length)\n",
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"for i in range(0,length):\n",
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" xs[i] = cc.d[i+1]*1e9\n",
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"\n",
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"### print out initial solution vector and initial efficiency\n",
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"print(\"xs is \")\n",
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"print(xs)\n",
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"print(\"efficiency is \",update_multilayer(xs))\n",
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"\n",
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"### run l-bfgs-b algorithm!\n",
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"ret = minimize(SuperFunc, xs, method=\"L-BFGS-B\", jac=True, bounds=bfgs_bounds)\n",
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"\n",
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"### print optimal solution and its efficiency!\n",
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"print(ret.x)\n",
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"print(update_multilayer(ret.x))\n",
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" "
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]
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},
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{
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"cell_type": "code",
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‎example/Incandescent_Plot.ipynb‎

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