AC299R Research Website

Neural Networks for Differential Equations

View the Project on GitHub

Contents

import pde_nn.channel_flow as chan
import utils
import numpy as np
import os
import matplotlib.pyplot as plt
import pandas as pd

Baseline

# def load_cv_kappas(top_dir):
top_dir='data/cv_kappa/'
preds=[]
hypers=[]
for d in os.listdir(top_dir):
    hyp=np.load(top_dir+d+'/hypers.npy').item()
    pred=np.load(top_dir+d+'/preds.npy')
    hypers.append(hyp)
    preds.append(pred)
    print('KAPPA = {}'.format(hyp['k']))
#     utils.expose_results('cv_kappa/{}'.format(d))


KAPPA = 0.5
KAPPA = 0.3
KAPPA = 0.1
KAPPA = 0.2
KAPPA = 0.41

import pandas as pd
y = np.linspace(-1,1,1000)
fig,  ax = plt.subplots(1,1, figsize=(15,10))
dns = pd.read_csv('data/LM_Channel_Retau180.txt', delimiter=' ')
utils.plot_dns(ax, dns, hypers[0], color='black')
for i,p in enumerate(preds):
    ax.plot(p, y, '--', label='$\kappa$={}'.format(hypers[i]['k']))
plt.title('Velocity profiles for different mixing lengths')
plt.ylabel('$y$')
plt.xlabel('$<u>$')
plt.legend();

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Baseline v2

# def load_cv_kappas(top_dir):
top_dir='data/cv_kappa_retau180/'
preds=[]
hypers=[]
for d in os.listdir(top_dir):
    hyp=np.load(top_dir+d+'/hypers.npy').item()
    pred=np.load(top_dir+d+'/preds.npy')
    hypers.append(hyp)
    preds.append(pred)
    print('KAPPA = {}'.format(hyp['k']))
#     utils.expose_results('cv_kappa_retau180/{}'.format(d))

KAPPA = 0.12
KAPPA = 0.19
KAPPA = 0.18
KAPPA = 0.15
KAPPA = 0.17

import pandas as pd
y = np.linspace(-1,1,1000)
fig,  ax = plt.subplots(1,1, figsize=(15,10))
dns = pd.read_csv('data/LM_Channel_Retau180.txt', delimiter=' ')
utils.plot_dns(ax, dns, hypers[0], color='black')
for i,p in enumerate(preds):
    ax.plot(p, y, '--', label='$\kappa$={}'.format(hypers[i]['k']))
plt.title('Velocity profiles for different mixing lengths (Retau = 180)')
plt.ylabel('$y$')
plt.xlabel('$<u>$')
plt.legend();

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$Re_{tau} = 1000$

# def load_cv_kappas(top_dir):
top_dir='data/cv_kappa_retau1k/'
preds1k=[]
hypers1k=[]
for d in os.listdir(top_dir):
    hyp=np.load(top_dir+d+'/hypers.npy').item()
    pred=np.load(top_dir+d+'/preds.npy')
    hypers1k.append(hyp)
    preds1k.append(pred)
    print('KAPPA = {}'.format(hyp['k']))
#     utils.expose_results('cv_kappa_retau1k/{}'.format(d), dns_file='data/LM_Channel_Retau1000.txt',
#                          numerical_file='data/mixlen_numerical_u1000.npy')


KAPPA = 0.19
KAPPA = 0.12
KAPPA = 0.15
KAPPA = 0.18
KAPPA = 0.17

import pandas as pd
y = np.linspace(-1,1,1000)
fig,  ax = plt.subplots(1,1, figsize=(15,10))
dns = pd.read_csv('data/LM_Channel_Retau1000.txt', delimiter=' ')
utils.plot_dns(ax, dns, hypers1k[0], color='black')
for i,p in enumerate(preds1k):
    ax.plot(p, y, '--', label='$\kappa$={}'.format(hypers1k[i]['k']))
plt.title('Velocity profiles for different mixing lengths (Retau = 1000)')
plt.ylabel('$y$')
plt.xlabel('$<u>$')
plt.legend();

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2x Units ($Re_{tau} = 180$)

# def load_cv_kappas(top_dir):
top_dir='data/cvkappa_2by80units/'
preds80unit=[]
hypers80unit=[]
for d in os.listdir(top_dir):
    hyp=np.load(top_dir+d+'/hypers.npy').item()
    pred=np.load(top_dir+d+'/preds.npy')
    hypers80unit.append(hyp)
    preds80unit.append(pred)
    print('KAPPA = {}'.format(hyp['k']))
    utils.expose_results('cvkappa_2by80units/{}'.format(d), dns_file='data/LM_Channel_Retau180.txt',
                         numerical_file='data/mixlen_numerical_u180.npy')


KAPPA = 0.13

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KAPPA = 0.12

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KAPPA = 0.18

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KAPPA = 0.15

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KAPPA = 0.14

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KAPPA = 0.16

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KAPPA = 0.17

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KAPPA = 0.19

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import pandas as pd
y = np.linspace(-1,1,1000)
fig,  ax = plt.subplots(1,1, figsize=(15,10))
dns = pd.read_csv('data/LM_Channel_Retau180.txt', delimiter=' ')
utils.plot_dns(ax, dns, hypers80unit[0], color='black')
for i,p in enumerate(preds80unit):
    ax.plot(p, y, '--', label='$\kappa$={}'.format(hypers80unit[i]['k']))
plt.title('Velocity profiles for different mixing lengths (Retau = 180) | Network with Double Num. Units')
plt.ylabel('$y$')
plt.xlabel('$<u>$')
plt.legend();

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fig,  ax = plt.subplots(1,1, figsize=(15,10))
dns = pd.read_csv('data/LM_Channel_Retau180.txt', delimiter=' ')
utils.plot_dns(ax, dns, hypers80unit[0], color='black')
ax.plot(preds[2], y, '--', label='k=0.18, 80 units')
ax.plot(preds[-1], y, '--', label='k=0.17, 80 units')
ax.plot(preds80unit[2], y, '-', label='k=0.18, 160 units')
ax.plot(preds80unit[-2], y, '-', label='k=0.17, 160 units')
ax.set_title('Comparison of velocity profiles with different kappa and number of units')
ax.set_xlabel('< u >')
ax.set_ylabel('y')
ax.legend();

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2x Points ($Re_{tau} = 180$)

# def load_cv_kappas(top_dir):
top_dir='data/cvkappa_2kpts/'
preds2kpts=[]
hypers2kpts=[]
for d in os.listdir(top_dir):
    hyp=np.load(top_dir+d+'/hypers.npy').item()
    pred=np.load(top_dir+d+'/preds.npy')
    hypers2kpts.append(hyp)
    preds2kpts.append(pred)
    print('KAPPA = {}'.format(hyp['k']))
    utils.expose_results('cvkappa_2kpts/{}'.format(d), dns_file='data/LM_Channel_Retau180.txt',
                         numerical_file='data/mixlen_numerical_u180.npy')


KAPPA = 0.17

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KAPPA = 0.18

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KAPPA = 0.15

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KAPPA = 0.12

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KAPPA = 0.13

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KAPPA = 0.16

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KAPPA = 0.19

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KAPPA = 0.14

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import pandas as pd
y = np.linspace(-1,1,1000)
fig,  ax = plt.subplots(1,1, figsize=(15,10))
dns = pd.read_csv('data/LM_Channel_Retau180.txt', delimiter=' ')
utils.plot_dns(ax, dns, hypers2kpts[0], color='black')
for i,p in enumerate(preds2kpts):
    ax.plot(p, y, '--', label='$\kappa$={}'.format(hypers2kpts[i]['k']))
plt.title('Velocity profiles for different mixing lengths (Retau = 180) | Network with 2K Points')
plt.ylabel('$y$')
plt.xlabel('$<u>$')
plt.legend();

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fig,  ax = plt.subplots(1,1, figsize=(15,10))
dns = pd.read_csv('data/LM_Channel_Retau180.txt', delimiter=' ')
utils.plot_dns(ax, dns, hypers2kpts[0], color='black')
ax.plot(preds[2], y, '--', label='k=0.18, 1k pts')
ax.plot(preds[-1], y, '--', label='k=0.17, 1k pts')
ax.plot(preds2kpts[1], y, '-', label='k=0.18, 2k pts')
ax.plot(preds2kpts[0], y, '-', label='k=0.17, 2k pts')
ax.set_title('Comparison of velocity profiles with different kappa and grid size')
ax.set_xlabel('< u >')
ax.set_ylabel('y')
ax.legend();

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## Kappa = 0.41, but use (y + 1) / 2 transform
utils.expose_results('1552060874.828267')

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## Kappa = 0.41, use y=y
utils.expose_results('1552284676.446561')

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utils.expose_results('1552285488.3520331')

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utils.expose_results('1552285971.611496')

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utils.expose_results('1552286320.534849')

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# def load_cv_kappas(top_dir):
top_dir='data/cvkappa_halfk/'
preds=[]
hypers=[]
for d in os.listdir(top_dir):
    hyp=np.load(top_dir+d+'/hypers.npy').item()
    pred=np.load(top_dir+d+'/preds.npy')
    hypers.append(hyp)
    preds.append(pred)
    print('KAPPA = {}'.format(hyp['k']))
#     utils.expose_results('cv_kappa/{}'.format(d))

KAPPA = 0.42
KAPPA = 0.41
KAPPA = 0.38
KAPPA = 0.39
KAPPA = 0.4

Half $\kappa$

y = np.linspace(-1,1,1000)
fig, ax = plt.subplots(1,1,figsize=(15,10))
dns = pd.read_csv('data/LM_Channel_Retau180.txt', delimiter=' ')
utils.plot_dns(ax, dns, hypers[0], color='black')
for i,p in enumerate(preds):
    plt.plot(p, y, label='k={}'.format(hypers[i]['k']))
plt.legend();

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