🛠️ updated PINNs with feed back and fergus and michael edits

PINN.yml

@@ -5,9 +5,9 @@ channels:
 dependencies:
   - python
   - notebook
-  - tensorflow
   - matplotlib
   - scipy
   - pandas  
   - pip
-    - pyDOE
+    - pyDOE
+    - tensorflow=>2.1

PINNs_1DHeatEquation_nonML.ipynb

@@ -33,6 +33,7 @@
     "git submodule update --init --recursive\n",
     "```\n",
     "    \n",
+    "**If this does not work please clone the [PINNs](https://github.com/maziarraissi/PINNs) repository into your Physics_Informed_Neural_Networks folder**\n",
     "</div>"
    ]
   },
@@ -102,7 +103,7 @@
     "\n",
     "where $\\mathcal{u(t,x)}$ denores the hidden solution, $\\mathcal{N}$ is a nonlinear differential operator acting on $u$, $\\mathcal{\\lambda}$ and $\\Omega$ is a \\subset of \\mathbb{R}^D$ (the prescribed data). This set up an encapsulation of a wide range of problems such as diffusion processes, conservation laws,  advection-diffusion-reaction  systems,  and  kinetic  equations and conservation laws.\n",
     "\n",
-    "Here we will go though this for the Burgers equation and Navier stokes equations\n",
+    "Here we will go though this for the 1 Heat equation and Navier stokes equations\n",
     "\n",
     "\n",
     "</div>    "
@@ -147,13 +148,13 @@
     "\n",
     "* Python 3\n",
     "* tensorflow > 2\n",
-    "* numpy as np\n",
+    "* numpy \n",
     "* matplotlib\n",
     "* scipy\n",
     "\n",
     "<h2> Data Requirements</h2>\n",
     "    \n",
-    "This notebook referes to some data included in the git hub repositroy\n",
+    "This notebook referes to some data included in the git hub repositroy imported via the git submodules command mentioned in the installation instructions\n",
     "    \n",
     "</div>\n"
    ]
@@ -166,9 +167,9 @@
     "**Contents:**\n",
     "\n",
     "1. **[1D Heat Equation Non ML Example](PINNs_1DHeatEquations_nonML.ipynb)**\n",
-    "2. [Burgers Equation PINN Example](PINNs_BurgersEquationExample.ipynb)\n",
-    "3. [Navier-Stokes PINNs discovery of PDE’s](PINNs_Navier_Stokes_example.ipynb)\n",
-    "\n"
+    "2. [1D Heat Equation PINN Example](PINNs_1DHeatEquationExample.ipynb)\n",
+    "3. [Navier-Stokes PINNs discovery of PDE’s](PINNs_NavierStokes_example.ipynb)\n",
+    "4. [Navier-Stokes PINNs Hidden Fluid Mechanics](PINNs_NavierStokes_HFM.ipynb)\n"
    ]
   },
   {
@@ -177,7 +178,7 @@
    "metadata": {},
    "source": [
     "<div style=\"background-color: #cce5ff; padding: 10px;\">\n",
-    "Load in all required modules (including some auxiliary code) and turn off warnings. Make sure Keras session is clear\n",
+    "Load in all required modules (including some auxiliary code) and turn off warnings.\n",
     "</div>"
    ]
   },
@@ -629,7 +630,7 @@
     "\n",
     "Now we've gone through a Naive manual approach to solving a simple 1D Heat equation we look at the benefits of using neural networks to solve more complex equations starting with the next notebook linked below: \n",
     "    \n",
-    "[Burgers Equation PINN Example](PINNs_BurgersEquationExample.ipynb)\n",
+    "[1D Heat Equation PINN Example](PINNs_1DHeatEquationExample.ipynb)\n",
     "    \n",
     "</div>"
    ]