Design informatics lab main

.gitignore

@@ -0,0 +1 @@
+Project/rocket_v2.ipynb

Homework/1

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+# Problem 1 : Least squares fitting for vapor-liquid equilibrium
+import torch
+import numpy as np
+import matplotlib.pyplot as plt
+
+SMOOTH = 1e-5
+
+
+def model(X, A, p_sat):
+    # Question : Temporary variables and the computational graph ...
+    k1 = A[0]*(A[1]*X[1]/(A[0]*X[0] + A[1]*X[1]))
+    k2 = A[1]*(A[0]*X[0]/(A[0]*X[0] + A[1]*X[1]))
+    t1 = X[0]*torch.exp((k1**2))*p_sat[0]
+    t2 = X[1]*torch.exp((k2**2))*p_sat[1]
+    return t1 + t2
+
+
+# Define the variables to be optimized over
+A = torch.tensor([2.5,2.8], requires_grad = True, dtype = torch.float64)
+# Data
+X = np.asarray([np.arange(0,1.1,0.1), 1-np.arange(0,1.1,0.1)])
+X = torch.from_numpy(X)
+p = torch.tensor([28.1, 34.4, 36.7, 36.9, 36.8, 36.7, 36.5, 35.4, 32.9, 27.8, 17.5], requires_grad =  False, dtype = torch.float64)
+
+# Constants
+# a = torch.tensor([[8.07131, 1730.63, 233.426],[7.43155, 1554.679, 240.337]], requires_grad= False)
+# T = 20
+# p_sat_water = torch.tensor(a[0][0] - (a[0][1]/(T + a[0][2])))
+# p_sat_dioxane = torch.tensor(a[1][0] - (a[1][1]/(T + a[1][2])))
+p_sat = torch.tensor([1.2424, 1.4598], requires_grad = False, dtype = torch.float64)
+
+
+def phi(alpha,X, A, p_sat):
+    return model(X, A, p_sat) - alpha*0.8*np.dot(A.grad.detach().numpy(), A.grad.detach().numpy())
+
+def line_search(X, A, p_sat):
+    alpha = 0.001  # initialize step size
+    while np.linalg.norm(np.nan_to_num(phi(alpha,X, A, p_sat).detach().numpy()))<np.linalg.norm(np.nan_to_num(model(X = X, A = A-alpha*A.grad, p_sat = p_sat).detach().numpy())):  # if f(x+a*d)>phi(a) then backtrack. d is the search direction
+        # print("Backtracking...")
+        alpha = 0.5*alpha
+    return alpha
+
+for i in range(5000):
+    # Define the loss function
+    loss = torch.sum((p - model(X, A, p_sat))**2)
+    loss.backward()
+    alpha = line_search(X = X, A = A, p_sat = p_sat)
+    print("Alpha:", alpha, "Loss:", loss.data.numpy(), "Gradient:", A.grad.numpy(), "Parameter:", A.data.numpy())
+
+    with torch.no_grad():
+        A -= alpha * A.grad
+        A.grad.zero_()
+
+p_final = model(X, A, p_sat)
+print("Model: ", p_final)
+print("Truth: ", p)

Homework/Homework 1.ipynb

@@ -2,12 +2,6 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "metadata": {
-    "collapsed": true,
-    "pycharm": {
-     "name": "#%% md\n"
-    }
-   },
    "source": [
     "Solve the following problem using [Python SciPy.optimize][]. Please attach your code and\n",
     "results. Specify your initial guesses of the solution. If you change\n",
@@ -65,6 +59,41 @@
     "[Jupyter Notebook]: https://jupyter.org/try\n",
     "[Markdown]: https://guides.github.com/features/mastering-markdown/\n",
     "[Markdown Math]: http://luvxuan.top/posts/Markdown-math/"
+<<<<<<< HEAD
+   ],
+   "metadata": {
+    "collapsed": true,
+    "pycharm": {
+     "name": "#%% md\n"
+    }
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "source": [
+    "import scipy.optimize as opt\n",
+    "fun = lambda x: (x[0] - x[1])**2 + (x[1] + x[2] - 2)**2 + (x[3] - 1)**2 + (x[4] - 1)**2\n",
+    "cons = (\n",
+    "    {'type': 'eq', 'fun': lambda x: x[0] + 3*x[1]},\n",
+    "    {'type': 'eq', 'fun': lambda x: x[2] + x[3] - 2*x[4]},\n",
+    "    {'type': 'eq', 'fun': lambda x: x[1] - x[4]}\n",
+    ")\n",
+    "bnds = ((-10,10), (-10,10), (-10,10), (-10,10), (-10,10))\n",
+    "\n",
+    "res = opt.minimize(fun, (1,1,1,1,1), method = 'SLSQP', bounds = bnds, constraints = cons)\n",
+    "res\n"
+   ],
+   "outputs": [
+    {
+     "output_type": "execute_result",
+     "data": {
+      "text/plain": [
+       "     fun: 4.09302326452976\n",
+       "     jac: array([-2.04664832, -0.18578869, -2.23243701, -2.23257673, -1.48833793])\n",
+       " message: 'Optimization terminated successfully'\n",
+       "    nfev: 38\n",
+=======
    ]
   },
   {
@@ -101,10 +130,67 @@
        "     jac: array([-1.05454643, -1.34545355, -0.29090709, -0.29091084,  0.58181781])\n",
        " message: 'Optimization terminated successfully'\n",
        "    nfev: 37\n",
+>>>>>>> 8f90ced4bec79abb8b5d9fde08e3e33db602bff0
        "     nit: 6\n",
        "    njev: 6\n",
        "  status: 0\n",
        " success: True\n",
+<<<<<<< HEAD
+       "       x: array([-0.76749312,  0.25583104,  0.62795044, -0.11628835,  0.25583104])"
+      ]
+     },
+     "metadata": {},
+     "execution_count": 1
+    }
+   ],
+   "metadata": {}
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "source": [
+    "# Changing the initial guess\n",
+    "x_init = (2,3,1,4,5)\n",
+    "fun = lambda x: (x[0] - x[1])**2 + (x[1] + x[2] - 2)**2 + (x[3] - 1)**2 + (x[4] - 1)**2\n",
+    "cons = (\n",
+    "    {'type': 'eq', 'fun': lambda x: x[0] + 3*x[1]},\n",
+    "    {'type': 'eq', 'fun': lambda x: x[2] + x[3] - 2*x[4]},\n",
+    "    {'type': 'eq', 'fun': lambda x: x[1] - x[4]}\n",
+    ")\n",
+    "bnds = ((-10,10), (-10,10), (-10,10), (-10,10), (-10,10))\n",
+    "\n",
+    "res = opt.minimize(fun,x0 = x_init, method = 'SLSQP', bounds = bnds, constraints = cons)\n",
+    "res"
+   ],
+   "outputs": [
+    {
+     "output_type": "execute_result",
+     "data": {
+      "text/plain": [
+       "     fun: 4.093023288479049\n",
+       "     jac: array([-2.04646897, -0.18635827, -2.23282731, -2.2323209 , -1.4883827 ])\n",
+       " message: 'Optimization terminated successfully'\n",
+       "    nfev: 43\n",
+       "     nit: 7\n",
+       "    njev: 7\n",
+       "  status: 0\n",
+       " success: True\n",
+       "       x: array([-0.76742588,  0.25580863,  0.62777771, -0.11616046,  0.25580863])"
+      ]
+     },
+     "metadata": {},
+     "execution_count": 2
+    }
+   ],
+   "metadata": {}
+  },
+  {
+   "cell_type": "markdown",
+   "source": [
+    "Changing the initial guess does not change the minimum"
+   ],
+   "metadata": {}
+=======
        "       x: array([ 1.2       , -0.4       ,  1.72727322,  0.85454457,  1.2909089 ])"
       ]
      },
@@ -116,20 +202,23 @@
    "source": [
     "res"
    ]
+<<<<<<< HEAD
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": []
+>>>>>>> 8f90ced4bec79abb8b5d9fde08e3e33db602bff0
+=======
+>>>>>>> 5690077459f148361cc6fc1d86ad868d764ff9b2
   }
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3",
-   "language": "python",
-   "name": "python3"
+   "name": "python3",
+   "display_name": "Python 3.7.3 64-bit ('base': conda)"
   },
   "language_info": {
    "codemirror_mode": {
@@ -151,6 +240,9 @@
     },
     "source": []
    }
+  },
+  "interpreter": {
+   "hash": "283a19fe1c80cc8d674e9be3676f3725f85ae6255e6112c9eba9160b54893d27"
   }
  },
  "nbformat": 4,