Update 00-IntroductionDay2.ipynb

e5fe159c · Jan Janssen · GitHub · 887d8538 · e5fe159c
Unverified Commit e5fe159c authored Mar 09, 2021 by Jan Janssen Committed by GitHub Mar 09, 2021
--- a/day_2/00-IntroductionDay2.ipynb
+++ b/day_2/00-IntroductionDay2.ipynb
@@ -158,7 +158,7 @@
   "metadata": {},
   "outputs": [],
   "source": [
-    "data_pr = Project(\"../datasets/import_database/\")"
+    "data_pr = Project(\"..\")"
   ]
  },
  {

 %% Cell type:markdown id: tags:

 # Day 2 - Parameterization of interatomic potentials

 %% Cell type:markdown id: tags:

 In this tutorial we will do simple fits for three different interatomic potentials.
 * Embedded Atom Method Potential
 * Neural Network Potential
 * Atomic Cluster Expansion

 Some details of these potentials will be summarized in the following.

 %% Cell type:markdown id: tags:

 ## Embedded Atom Method Potential

 %% Cell type:markdown id: tags:

 * Atomic descriptors: pair functions

 $\rho_i = \sum_j \phi(r_{ij})$ (density)

 $V_i = \sum_j V(r_{ij})$ (pair repulsion)

 * Atomic energy

 $E_i = F( \rho_i ) + V_i$

 with non-linear embedding function $F$

 %% Cell type:markdown id: tags:

 ## Neural Network Potential

 %% Cell type:markdown id: tags:

 * Atomic descriptors: pair and three-body symmetry functions

 $G_i = \sum_j \phi(r_{ij})$

 $G_i = \sum_{jk} \phi(r_{ij},r_{ik}, \cos_{jik})$

 * Atomic energy

 $E_i = NN(G_i)$

 with neural network $NN$. Various different $G_i$ are the inputs to the $NN$.

 %% Cell type:markdown id: tags:

 ## Atomic Cluster Expansion

 %% Cell type:markdown id: tags:

 * Atomic descriptors: pair, three-body, ... many-body basis functions

 $A_i = \sum_j \phi(\pmb{r}_{ij})$       (many different basis functions that depend on direction and length of $r_{ij}$)

 $\varphi_i = c_1 A_i + c_2 A_i A_i + c_3 A_i A_i A_i + ...$

 * Atomic energy

 $E_i = F(\varphi_i)$

 with general non-linear function $F$ and several $\varphi_i$. In the tutorial we will use $E_i =  \sqrt{\varphi^{(1)}_i} +  \varphi^{(2)}_i$ to make contact to the Embedded Atom Method.

 %% Cell type:markdown id: tags:

 # Reference data

 %% Cell type:markdown id: tags:

 The potentials are parameterized by fitting to reference data. Here we use DFT data for Cu that we generated with the FHI-aims code. In the following we summarize key properties of the dataset.

 %% Cell type:code id: tags:

 ``` python
 %pylab inline
 ```

 %% Output

    Populating the interactive namespace from numpy and matplotlib

 %% Cell type:code id: tags:

 ``` python
 import pandas as pd
 ```

 %% Cell type:code id: tags:

 ``` python
 from pyiron import Project
 ```

 %% Cell type:code id: tags:

 ``` python
 def proces_df(df):
    df["energy_per_atom"] = df["energy"]/df["number_of_atoms"]
    df["volume"]=df["atoms"].map(lambda at: at.get_volume())
    df["volume_per_atom"] = df["volume"]/df["number_of_atoms"]
 ```

 %% Cell type:code id: tags:

 ``` python
-data_pr = Project("../datasets/import_database/")
+data_pr = Project("..")
 ```

 %% Cell type:code id: tags:

 ``` python
 data_pr.job_table()
 ```

 %% Output

        id    status chemicalformula                         job  \
    0  303  finished            None  df1_A1_A2_A3_EV_elast_phon
    1  304  finished            None                     df3_10k
    2  305  finished            None                      df2_1k
    3  306  finished            None           df4_2_5eV_25A3_8K
    
                            subjob                              projectpath  \
    0  /df1_A1_A2_A3_EV_elast_phon  /home/yury/PycharmProjects/pyiron-2021/
    1                     /df3_10k  /home/yury/PycharmProjects/pyiron-2021/
    2                      /df2_1k  /home/yury/PycharmProjects/pyiron-2021/
    3           /df4_2_5eV_25A3_8K  /home/yury/PycharmProjects/pyiron-2021/
    
                                                         project  \
    0  pyiron_potentialfit/datasets/import_database/Cu_database/
    1  pyiron_potentialfit/datasets/import_database/Cu_database/
    2  pyiron_potentialfit/datasets/import_database/Cu_database/
    3  pyiron_potentialfit/datasets/import_database/Cu_database/
    
                       timestart timestop totalcputime        computer  \
    0 2021-02-18 19:49:53.061360     None         None  zora@cmti001#1
    1 2021-02-18 19:49:55.496691     None         None  zora@cmti001#1
    2 2021-02-18 19:49:56.101883     None         None  zora@cmti001#1
    3 2021-02-18 19:49:57.547918     None         None  zora@cmti001#1
    
                hamilton hamversion parentid masterid
    0  TrainingContainer        0.4     None     None
    1  TrainingContainer        0.4     None     None
    2  TrainingContainer        0.4     None     None
    3  TrainingContainer        0.4     None     None

 %% Cell type:code id: tags:

 ``` python
 df1_job = data_pr.load('df1_A1_A2_A3_EV_elast_phon')
 df2_job = data_pr.load('df2_1k')
 df3_job = data_pr.load('df3_10k')
 df4_job = data_pr.load('df4_2_5eV_25A3_8K')
 ```

 %% Cell type:code id: tags:

 ``` python
 df1 = df1_job.to_pandas()
 df2 = df2_job.to_pandas()
 df3 = df3_job.to_pandas()
 df4 = df4_job.to_pandas()

 dfs = [df1,df2,df3,df4]
 ```

 %% Cell type:code id: tags:

 ``` python
 for df in dfs:
    proces_df(df)
 ```

 %% Cell type:code id: tags:

 ``` python
 df_size=[len(df) for df in dfs]
 df_num_atoms=[int(df["number_of_atoms"].sum()) for df in dfs]
 labels=["df1","df2","df3","df4"]
 ```

 %% Cell type:code id: tags:

 ``` python
 df_stats = pd.DataFrame({"Name":labels, "Structures":df_size, "Atoms":df_num_atoms})
 df_stats
 ```

 %% Output

      Name  Structures  Atoms
    0  df1         105    368
    1  df2        1000  11309
    2  df3       10000  84133
    3  df4        8073  71979

 %% Cell type:markdown id: tags:

 * Dataset1 (df1): 105 structures: E-V, elastic matrix and phonopy deformations for fcc, bcc, hcp
 * Dataset2 (df2): 1k structures: Dataset1+ more prototypes (ideal and distroted), selected within 1eV window above  groundstate
 * Dataset3 (df3): 10k structures: Dataset2 + long-range E-V curves + 1000 fcc surface structures (stretched, shaked, etc.)
 * Dataset4 (df4): 8k structures: all structures within 2.5eV/atom window above ground state and up to 25 A^3/atom volume

 %% Cell type:code id: tags:

 ``` python
 xs = np.arange(len(df_size))
 width = 0.75
 colors=["red","green","blue","orange"]

 fig, (ax,ax2) = plt.subplots(1,2,figsize=(6,3), dpi=150)

 ax.bar(df_stats.index, df_stats["Structures"], width=width, color=colors)
 ax.set_yscale('log')
 ax.set_title('Number of structures')
 ax.set_xticks(df_stats.index)
 ax.set_xticklabels(df_stats["Name"])

 ax2.bar(df_stats.index, df_stats["Atoms"], width=width, color=colors)
 ax2.set_yscale('log')
 ax2.set_title('Number of atoms')
 ax2.set_xticks(df_stats.index)
 ax2.set_xticklabels(df_stats["Name"])

 fig.tight_layout()
 ```

 %% Output



 %% Cell type:code id: tags:

 ``` python
 alpha= 0.35
 s=25

 plt.figure(figsize=(10,5), dpi=150)
 plt.scatter(df3["volume_per_atom"], df3["energy_per_atom"], label="df3", s=s, color="blue",ec=None, alpha=alpha)
 plt.scatter(df4["volume_per_atom"], df4["energy_per_atom"], label="df4", s=s, color="orange",ec=None, alpha=alpha)
 plt.scatter(df2["volume_per_atom"], df2["energy_per_atom"], label="df2", s=s, color="green",ec=None, alpha=alpha)
 plt.scatter(df1["volume_per_atom"], df1["energy_per_atom"], label="df1", s=s, color="red",ec=None, alpha=alpha)
 plt.xscale('log')
 plt.xlabel('V, $\\AA^3$/atom')
 plt.ylabel('E, eV/atom')
 plt.legend()
 ```

 %% Output

    <matplotlib.legend.Legend at 0x7f7f3fef9220>



 %% Cell type:code id: tags:

 ``` python
 ```