diff --git a/lwr_notebook.ipynb b/MFG-Pure-PIDL-LWR.ipynb
similarity index 100%
rename from lwr_notebook.ipynb
rename to MFG-Pure-PIDL-LWR.ipynb
diff --git a/non-sep_notebook.ipynb b/MFG-Pure-PIDL-Non-Separable.ipynb
similarity index 100%
rename from non-sep_notebook.ipynb
rename to MFG-Pure-PIDL-Non-Separable.ipynb
diff --git a/sep_notebook.ipynb b/MFG-Pure-PIDL-Separable.ipynb
similarity index 100%
rename from sep_notebook.ipynb
rename to MFG-Pure-PIDL-Separable.ipynb
diff --git a/MFG_VI.py b/MFG-RL-PIDL.py
similarity index 83%
rename from MFG_VI.py
rename to MFG-RL-PIDL.py
index 5bc94e3..db92c25 100644
--- a/MFG_VI.py
+++ b/MFG-RL-PIDL.py
@@ -10,5 +10,4 @@
     option = options[2]
     d = np.loadtxt(f"data/rho-{option}.txt")[:, 0].flatten('F')
     train_ddpg(option, n_cell, T_terminal, d, fake_critic=True, pidl=True, surf_plot=True, smooth_plot=False,
-                      diff_plot=True)
-    # plot_diff("./diff/", smooth=False)
\ No newline at end of file
+                      diff_plot=True)
\ No newline at end of file
diff --git a/README.md b/README.md
new file mode 100644
index 0000000..18daaa1
--- /dev/null
+++ b/README.md
@@ -0,0 +1,12 @@
+# MFG-RL-PIDL
+
+This is the source code for paper - A Hybrid Framework of Reinforcement Learning and Physics-Informed Deep Learning for Spatiotemporal Mean Field Games.
+
+## File Structure
+
+- `data` folder includes the numerical results of MFGs.
+- `MFG-RL-PIDL.py` is the runner of Alg. 1 MFG RL-PIDL in our paper.
+- `value_iteration_DDPG.py` is the training function of Alg. 1 MFG RL-PIDL.
+- `MFG-Pure-PIDL-*.ipynb` are the source codes of the Alg. 2 MFG-Pure-PIDL.
+- `model.py` includes the PyTorch network models of $\rho$ -Net, V-Net and u-net.
+- `uitls.py` are the implementations of auxiliary function.
\ No newline at end of file
diff --git a/utils.py b/utils.py
index e3a5922..a8e15b2 100644
--- a/utils.py
+++ b/utils.py
@@ -237,8 +237,8 @@ def plot_diff(fig_path=None, smooth=False):
                 u_diff_plot = u_diff_hist
                 rho_diff_plot = rho_diff_hist
 
-            plt.plot(u_diff_plot, lw=3, label=r"$|u^{(k)} - u^{(k-1)}|$", c='steelblue', ls='--')
-            plt.plot(rho_diff_plot, lw=3, label=r"$|\rho^{(k)} - \rho^{(k-1)}|$", c='indianred', alpha=.8)
+            plt.plot(u_diff_plot, lw=3, label=r"$|u^{(i)} - u^{(i-1)}|$", c='steelblue', ls='--')
+            plt.plot(rho_diff_plot, lw=3, label=r"$|\rho^{(i)} - \rho^{(i-1)}|$", c='indianred', alpha=.8)
             plt.xlabel("iterations", fontsize=18, labelpad=6)
             plt.xticks(fontsize=18)
             plt.ylabel("convergence gap", fontsize=18, labelpad=6)
@@ -263,8 +263,8 @@ def plot_diff(fig_path=None, smooth=False):
                 u_diff_plot = u_diff_hist
                 rho_diff_plot = rho_diff_hist
 
-            plt.plot(u_diff_plot, lw=3, label=r"$|u^{(k)} - u^*|$", c='steelblue', ls='--')
-            plt.plot(rho_diff_plot, lw=3, label=r"$|\rho^{(k)} - \rho^*|$", c='indianred', alpha=.8)
+            plt.plot(u_diff_plot, lw=3, label=r"$|u^{(i)} - u^*|$", c='steelblue', ls='--')
+            plt.plot(rho_diff_plot, lw=3, label=r"$|\rho^{(i)} - \rho^*|$", c='indianred', alpha=.8)
             plt.xlabel("iterations", fontsize=18, labelpad=6)
             plt.xticks(fontsize=18)
             plt.ylabel("loss", fontsize=18, labelpad=6)