Analyse de séries temporelles avec IA

Contenu

6. Analyse de séries temporelles avec IA#

Marc Buffat dpt mécanique, UCB Lyon1

time series

import tensorflow as tf

2025-03-19 18:04:52.914706: I external/local_xla/xla/tsl/cuda/cudart_stub.cc:32] Could not find cuda drivers on your machine, GPU will not be used.
2025-03-19 18:04:52.918206: I external/local_xla/xla/tsl/cuda/cudart_stub.cc:32] Could not find cuda drivers on your machine, GPU will not be used.
2025-03-19 18:04:52.928638: E external/local_xla/xla/stream_executor/cuda/cuda_fft.cc:477] Unable to register cuFFT factory: Attempting to register factory for plugin cuFFT when one has already been registered
WARNING: All log messages before absl::InitializeLog() is called are written to STDERR
E0000 00:00:1742403892.946106 3690842 cuda_dnn.cc:8310] Unable to register cuDNN factory: Attempting to register factory for plugin cuDNN when one has already been registered
E0000 00:00:1742403892.951244 3690842 cuda_blas.cc:1418] Unable to register cuBLAS factory: Attempting to register factory for plugin cuBLAS when one has already been registered
2025-03-19 18:04:52.969235: I tensorflow/core/platform/cpu_feature_guard.cc:210] This TensorFlow binary is optimized to use available CPU instructions in performance-critical operations.
To enable the following instructions: AVX2 FMA, in other operations, rebuild TensorFlow with the appropriate compiler flags.

%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
# police des titres
plt.rc('font', family='serif', size='18')
from IPython.display import display,Markdown
# IA
import sklearn as sk
import tensorflow as tf

_uid_ = 12345
def serie_temp(N,a0=1.0,a1=0.5,a2 = 0.4, a3=0.1):
    # data / jours 
    np.random.seed(_uid_)
    # time series
    Ts = np.array([x for x in np.arange(N)],dtype=int)
    ys = [ a0*np.sin(2*np.pi*x/180) + a1*np.cos(2*np.pi*x/15) \
         + a2*x/360  for x in range(N)] + \
           a3*np.random.normal(size=N,scale=0.2)
    return Ts,ys

6.1. Objectifs#

On étudie un système temporel $Y (t)$ et on souhaite prédire l’évolution du système: i.e. la prévision de ses futures réalisations en se basant sur ses valeurs passées

Une série temporelle Yt est communément décomposée en tendance, saisonnalité, bruit:

Y (t) = T (t) + S (t) + ϵ (t)

tendance $T (t)$ = évolution à long terme
saisonnalité $S (t)$ = phénoméne périodique
bruit $ϵ (t)$ = partie aléatoire

6.1.1. méthodes#

méthodes classiques: (modélisation de série chro. linéaires):

lissages exponentiels,
modèles de régression (régression linéaire, modèles non-paramétriques… ),
modèles SARIMA

utilisation de l’IA:

random forest,
réseaux de neuronnes récurrents LSTM

6.2. Génération des données#

Série temporelle $Y = Y (t)$
N mesures à intervalle régulier $Δ t$
- tableau de données ys
  
  $y s [i] = Y (i Δ t)$
- tableau ts (pour l’analyse)
  
  $t s [i] = i Δ t$

tests

série périodique simple
serie bi-périodique (modulation)
avec tendance à long terme
avec du bruit

# construction serie temporelle
# cas periodique le plus simple
Ts,ys = serie_temp(1000,a0=0,a1=0.5,a2=0.0,a3 = 0.)
# cas bi-periodique 
#Ts,ys = serie_temp(1000,a0=1.0,a1=0.5,a2=0.0,a3=0.0)
# + tendance 
#Ts,ys = serie_temp(1000,a0=1.0,a1=0.5,a2=0.2,a3=0.0)
# + bruit
Ts,ys = serie_temp(1000,a0=1.0,a1=0.5,a2=0.2,a3=0.3)

plt.figure(figsize=(12,8))
plt.subplot(1,2,1)
plt.plot(Ts[:],ys)
plt.xlabel("jour")
plt.title("serie temporelle");
plt.subplot(1,2,2)
plt.plot(Ts[:100],ys[:100])
plt.xlabel("jour")

Text(0.5, 0, 'jour')

../../_images/bf9b80bd688eda840d0243d4f61002379bb6d6331c1d67c910d6515d340fa59d.png

6.3. préparation des données#

fenêtrage des données:

choix d’une fenêtre de nav jours précédents pour prédire nap valeurs (i.e. sur nap jours)

nav taille de la fenêtre d’histoire (avant)
nap taille de la fenêtre prédiction (après)
N nbre de fenêtres
t0 date de début prédiction

def dataset(Ts,ys,nav,nap,N,t0):
    # choix d'une fenetre de nav jours précédents pour prédir nap valeurs (i.e. sur nap jours)
    # nav taille de la fenetre d'histoire (avant)
    # nap taille de la fenetre prediction (apres)
    # N nbre de fenetres
    # t0 date de debut prediction
    # 
    t1 = t0 - N - nav -nap
    print(f"apprentissage sur {N} fenetres de {nav}-{nap} jours entre le jour {t1} et {t0}")
    # 
    X  = np.zeros((N,nav))
    y  = np.zeros((N,nap))
    t  = np.zeros(N,dtype=int)
    # construction de la base de données
    for i in range(N):
        X[i,:] = ys[t1+i:t1+i+nav]
        y[i]   = ys[t1+i+nav:t1+i+nav+nap]
        t[i]   = Ts[t1+i+nav]
    return X,y,t

# N fenetres: de 14 jours -> 7 jours pour prediction à partir du jour t0
nav = 14
nap = 7
#N  = 200
#t0 = 300
N = 400
t0 = 600
X,y,t = dataset(Ts,ys,nav,nap,N,t0)

apprentissage sur 400 fenetres de 14-7 jours entre le jour 179 et 600

X.shape, y.shape, t.shape

((400, 14), (400, 7), (400,))

def plot_dataset():
    plt.figure(figsize=(14,6))
    plt.subplot(1,2,1)
    plt.plot(t-nav,X[:,0])
    plt.plot(t,y[:,0])
    plt.xlabel("jour")
    plt.ylabel("y")
    plt.title("data apprentissage")
    plt.subplot(1,2,2)
    plt.plot(np.arange(t[0]-nav,t[0]+nap),ys[t[0]-nav:t[0]+nap],'--')
    plt.plot(np.arange(t[0]-nav,t[0]),X[0,:],'or')
    plt.plot(np.arange(t[0],t[0]+nap),y[0,:],'xg')
    plt.plot(np.arange(t[-1]-nav,t[-1]+nap),ys[t[-1]-nav:t[-1]+nap],'--')
    plt.plot(np.arange(t[-1]-nav,t[-1]),X[-1,:],'or')
    plt.plot(np.arange(t[-1],t[-1]+nap),y[-1,:],'xg')
    plt.xlabel("jour")
    plt.title("first/last window");
    return

plot_dataset()

../../_images/d3ab5bfeb0f4bad6b29fbeee0fbae3990913353745ba27072e90fc94e31e28db.png

6.4. Scikit Learn RandomForest#

“forêt aléatoire” d’arbres de décision

prédiction 1 valeur à la fois

random forest

6.5. Réseau de neurones: LSTM/ RNN#

LSTM = Long Short-Term Memory

réseau RNN récurrent
fonction activation: évite l’explosion de la sortie (tanh )
méthode de gradient numérique ( $α$ taux d’apprentissage) $ $w_{k + 1} = w_{k} - α F_{w}$ $
EPOCH = nbre d’epoques pour l’apprentissage

Le nombre d’époques est un hyperparamètre qui définit le nombre de fois que l’algorithme d’apprentissage parcours l’ensemble des données d’entraînement

Modèle de neuronne informatique

la sortie $y$ est une fonction non linéaire des entrées (f = fonction d’activation)

y = f (\sum_{i} w_{i} x_{i} + b)

les coefficients $w_{i}, b$ sont obtenu par minimisation d’une erreur $E r r = | | y_{p r e d} - \hat{y} | |$ à partir d’une base de données d’apprentissage $\hat{y}$ en utilisant des algorithmes de minimisation (gradient)

Réseau de neuronnes par couche

Réseau de neuronnes récurrents (traitement de séquence temporelle)

y^{t} = f (\sum_{i} w_{i} x_{i}^{t} + b + \sum_{j} r_{j} y_{j}^{t})

6.5.1. Réseaux RNN#

images/Architecture-RNN.jpg

6.5.2. La problématique de l’apprentissage d’un réseau récurrent#

réseau récurrent simple classique constitué d’une couche récurrente suivie d’une couche dense :

Il comprend trois matrices de poids : W, R et V ; R étant la matrice des poids récurrents. L’apprentissage du réseau consiste donc à apprendre ces trois matrices sur une base d’exemples étiquetés.

Or l’algorithme de minimisation par gradient pour les réseaux de neuronnes utilise un algorithme appelé rétropropagation du gradient. Cet algorithme rétropropage le gradient de l’erreur à travers les différentes couches de poids du réseau, en remontant de la dernière à la première couche.

Malheureusement, dans le cas des réseaux récurrents, la présence du cycle de récurrence (matrice R) interdit l’utilisation de cet algorithme

6.5.3. solution : rétropropagation à travers le temps#

La solution à ce problème consiste à exploiter la version dépliée du réseau, qui élimine les cycles.

Nous allons donc utiliser une approximation du réseau récurrent par un réseau déplié K fois (K = profondeur = nbre de couches internes cachés de 10 a 100) , comme présenté sur la figure suivante avec K=2 :

Attention

Le réseau déplié étant plus profond, la disparition du gradient (ou gradient évanescent) est plus importante durant l’apprentissage, et il est plus difficile à entraîner à cause d’une erreur qui tend à s’annuler en se rapprochant des couches basses.

Il est donc important d’utiliser toutes les stratégies possibles permettant de lutter contre ce phénomène : Batch Normalization, dropout, régularisation L1 et L2, etc.

Comme les poids de la couche récurrente sont dupliqués, les réseaux récurrents sont également sujets à un autre phénomène appelé explosion du gradient. Il s’agit d’un gradient d’erreur dont la norme est supérieure à 1.

Une méthode simple et efficace pour éviter cela consiste à tester cette norme, et à la limiter si elle est trop importante (aussi appelée gradient clipping, en anglais).

6.5.4. neuronne LSTM : Long Short Term Memory#

Afin de modéliser des dépendances à très long terme, il est nécessaire de donner aux réseaux de neurones récurrents la capacité de maintenir un état sur une longue période de temps.

C’est le but des cellules LSTM (Long Short Term Memory), qui possèdent une mémoire interne appelée cellule (ou cell). La cellule permet de maintenir un état aussi longtemps que nécessaire. Cette cellule consiste en une valeur numérique que le réseau peut piloter en fonction des situations.

la cellule mémoire peut être pilotée par trois portes de contrôle qu’on peut voir comme des vannes :

la porte d’entrée décide si l’entrée doit modifier le contenu de la cellule
la porte d’oubli décide s’il faut remettre à 0 le contenu de la cellule
la porte de sortie décide si le contenu de la cellule doit influer sur la sortie du neurone

Le mécanisme des trois portes est strictement similaire. L’ouverture/la fermeture de la vanne est modélisée par une fonction d’activation f qui est généralement une sigmoïde. Cette sigmoïde est appliquée à la somme pondérée des entrées, des sorties et de la cellule, avec des poids spécifiques.

Pour calculer la sortie $y^{t}$ , on utilise donc l’entrée $x^{t}$ , les états cachés $h^{t - 1}$ ( $x^{t - 1}, x^{t - 2}$ ) (dépliement de la récurrence) qui représentent la mémoire à court terme (short-term mémory) et les états des cellules mémoires $c^{t - 1}$ qui représentent la mémoire à long terme (long-term memory)

Comme n’importe quel neurone, les neurones LSTM sont généralement utilisés en couches. Dans ce cas, les sorties de tous les neurones sont réinjectées en entrée de tous les neurones.

Compte tenu de toutes les connexions nécessaires au pilotage de la cellule mémoire, les couches de neurones de type LSTM sont deux fois plus « lourdes » que les couches récurrentes simples, qui elles-mêmes sont deux fois plus lourdes que les couches denses classiques.

Les couches LSTM sont donc à utiliser avec parcimonie !

6.6. Mise en oeuvre#

6.6.1. Apprentissage RandomForest#

scikit learn

from sklearn.linear_model import LinearRegression
from sklearn.ensemble import RandomForestRegressor
from sklearn.neighbors import KNeighborsRegressor
from sklearn.metrics   import r2_score
# choix de l'algorithme
clf = RandomForestRegressor()
#clf = KNeighborsRegressor()
#clf = LinearRegression()
Xlearn = X.copy()
ylearn = y[:,0]
clf.fit(Xlearn,ylearn)

RandomForestRegressor()

In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.

print("score = {:2d}%".format(int(100*clf.score(Xlearn, ylearn))))
yp = clf.predict(Xlearn)
print("R2 = {:3.2f}%".format(r2_score(ylearn,yp)))

score = 99%
R2 = 1.00%

def plot_pred():
    plt.figure(figsize=(10,6))
    plt.plot(Ts[t2:t2+nap],ypred,'x')
    plt.plot(Ts[t2-nav:t2],Xpred[0],'--o')
    plt.plot(Ts[t2-nav:t2+nap],ys[t2-nav:t2+nap],'--')
    plt.xlabel("jour")
    plt.title(f"prediction sur {nap} jours à partir du jour {t2}");
    return

# prediction à partir de t2
t2 = t0 
Xpred  = np.array([ys[t2-nav:t2]])
ypred  = np.zeros(nap)
Xp     = Xpred.copy()
ypred[0] = clf.predict(Xp)[0]
for i in range(1,nap):
    Xp[0,:-i] = Xpred[0,i:]
    Xp[0,-i:] = ypred[:i]
    ypred[i] = clf.predict(Xp)[0]
Xpred.shape, ypred.shape

((1, 14), (7,))

plot_pred()

../../_images/79f480d398aa718a733d769ad75cd2cabf127fd10181be7eaea7c6f649cc6515.png

6.6.2. Mise en oeuvre LSTM RNN#

bibliothèque tensor flow Keras RNN

#Machine learning
from sklearn import preprocessing
import tensorflow as tf
import statsmodels as st
from statsmodels.tsa.seasonal import STL
from sklearn.model_selection  import train_test_split

Xlearn = X.copy()
ylearn = y.copy()
Xlearn = Xlearn.reshape(X.shape[0], nav, 1)
ylearn = ylearn.reshape(y.shape[0], nap, 1)
Xlearn.shape, ylearn.shape

((400, 14, 1), (400, 7, 1))

#Nombre d'époque d'entrainement (fenetre de taille nav)
#EPOQUE = 300
EPOQUE = 200
#EPOQUE = 50
# modèle du réseaux de neurones(4 rangées (100,100,50,50) dont la première LSTM)
# si pas activation: activation='linear' lineaire a(x)=x, sinon test avec 'relu'
modele_lstm = tf.keras.models.Sequential([
    tf.keras.layers.LSTM(nav),
    tf.keras.layers.Dense(nav,activation='tanh'),
    tf.keras.layers.Dense(nap,activation='tanh'),
    tf.keras.layers.Dense(nap)
])
#Configuration du modèle(on minimise avec la méthode des moindres carrés)
modele_lstm.compile(optimizer='adam', metrics=['mae'], loss='mse')
print(EPOQUE)

W0000 00:00:1742403896.757141 3690842 gpu_device.cc:2344] Cannot dlopen some GPU libraries. Please make sure the missing libraries mentioned above are installed properly if you would like to use GPU. Follow the guide at https://www.tensorflow.org/install/gpu for how to download and setup the required libraries for your platform.
Skipping registering GPU devices...

#Lance l'entrainement du modèle
import time
time_start = time.time()
modele_lstm.fit(Xlearn, ylearn, epochs=EPOQUE, verbose = True)
print('phase apprentissage: {:.2f} seconds'.format(time.time()-time_start))

Epoch 1/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 18s 2s/step - loss: 0.6802 - mae: 0.7018


13/13 ━━━━━━━━━━━━━━━━━━━━ 2s 4ms/step - loss: 0.7459 - mae: 0.7292

Epoch 2/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.5280 - mae: 0.6003


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.6000 - mae: 0.6464

Epoch 3/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.5777 - mae: 0.6389


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.5172 - mae: 0.5948

Epoch 4/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.3407 - mae: 0.4792


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.3876 - mae: 0.5078

Epoch 5/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.3395 - mae: 0.4724


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.3204 - mae: 0.4629

Epoch 6/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 1s 97ms/step - loss: 0.2947 - mae: 0.4571


 7/13 ━━━━━━━━━━━━━━━━━━━━ 0s 9ms/step - loss: 0.2669 - mae: 0.4230


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 9ms/step - loss: 0.2684 - mae: 0.4250

Epoch 7/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 0.2939 - mae: 0.4495


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.2495 - mae: 0.4112

Epoch 8/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 1s 102ms/step - loss: 0.2348 - mae: 0.3924


 6/13 ━━━━━━━━━━━━━━━━━━━━ 0s 11ms/step - loss: 0.2302 - mae: 0.3889


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 8ms/step - loss: 0.2299 - mae: 0.3910

Epoch 9/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.2648 - mae: 0.4380


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.2147 - mae: 0.3802

Epoch 10/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.2151 - mae: 0.3850


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.2203 - mae: 0.3883

Epoch 11/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.2063 - mae: 0.3779


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.2074 - mae: 0.3758

Epoch 12/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.2501 - mae: 0.4231


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.2262 - mae: 0.3947

Epoch 13/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 17ms/step - loss: 0.2226 - mae: 0.3952


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.2063 - mae: 0.3738

Epoch 14/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.1954 - mae: 0.3638


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.2036 - mae: 0.3730

Epoch 15/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.1790 - mae: 0.3399


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.2038 - mae: 0.3714

Epoch 16/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 1s 91ms/step - loss: 0.1980 - mae: 0.3691


 6/13 ━━━━━━━━━━━━━━━━━━━━ 0s 11ms/step - loss: 0.1979 - mae: 0.3669


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 10ms/step - loss: 0.1979 - mae: 0.3662

Epoch 17/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.1736 - mae: 0.3514


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.1932 - mae: 0.3620

Epoch 18/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.2336 - mae: 0.3998


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.1931 - mae: 0.3614

Epoch 19/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.1617 - mae: 0.3269


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.1892 - mae: 0.3565

Epoch 20/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.1935 - mae: 0.3567


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.1942 - mae: 0.3605

Epoch 21/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.1920 - mae: 0.3614


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.1863 - mae: 0.3557

Epoch 22/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 1s 100ms/step - loss: 0.2227 - mae: 0.4028


 7/13 ━━━━━━━━━━━━━━━━━━━━ 0s 9ms/step - loss: 0.1966 - mae: 0.3730


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 8ms/step - loss: 0.1934 - mae: 0.3659

Epoch 23/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.1862 - mae: 0.3534


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.1862 - mae: 0.3546

Epoch 24/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 1s 86ms/step - loss: 0.2125 - mae: 0.3836


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.1805 - mae: 0.3487

Epoch 25/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 77ms/step - loss: 0.1219 - mae: 0.2865


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.1727 - mae: 0.3394

Epoch 26/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.1548 - mae: 0.3218


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.1759 - mae: 0.3414


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.1761 - mae: 0.3417

Epoch 27/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 74ms/step - loss: 0.1678 - mae: 0.3361


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.1798 - mae: 0.3471

Epoch 28/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 1s 84ms/step - loss: 0.1310 - mae: 0.2943


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.1646 - mae: 0.3315

Epoch 29/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.1569 - mae: 0.3148


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.1681 - mae: 0.3325

Epoch 30/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 20ms/step - loss: 0.1699 - mae: 0.3320


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.1632 - mae: 0.3287

Epoch 31/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 20ms/step - loss: 0.1533 - mae: 0.3168


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.1535 - mae: 0.3187

Epoch 32/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.1418 - mae: 0.2987


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.1580 - mae: 0.3218

Epoch 33/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 26ms/step - loss: 0.1663 - mae: 0.3386


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.1530 - mae: 0.3179

Epoch 34/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 80ms/step - loss: 0.1709 - mae: 0.3418


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.1546 - mae: 0.3205

Epoch 35/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 81ms/step - loss: 0.1419 - mae: 0.2984


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.1488 - mae: 0.3098

Epoch 36/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 20ms/step - loss: 0.1370 - mae: 0.2918


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.1540 - mae: 0.3196

Epoch 37/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 1s 88ms/step - loss: 0.1258 - mae: 0.2747


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.1357 - mae: 0.2946

Epoch 38/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.1511 - mae: 0.3106


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.1381 - mae: 0.2962

Epoch 39/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.1051 - mae: 0.2543


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.1302 - mae: 0.2852

Epoch 40/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.1389 - mae: 0.3039


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.1341 - mae: 0.2935

Epoch 41/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.1284 - mae: 0.2719


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.1299 - mae: 0.2853

Epoch 42/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 17ms/step - loss: 0.1164 - mae: 0.2764


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.1237 - mae: 0.2802

Epoch 43/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.1261 - mae: 0.2743


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.1192 - mae: 0.2719

Epoch 44/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.1299 - mae: 0.2783


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.1149 - mae: 0.2679

Epoch 45/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.1238 - mae: 0.2861


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.1121 - mae: 0.2666

Epoch 46/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.1197 - mae: 0.2698


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.1077 - mae: 0.2598

Epoch 47/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.0876 - mae: 0.2198


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.1062 - mae: 0.2547

Epoch 48/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 1s 96ms/step - loss: 0.0905 - mae: 0.2384


 6/13 ━━━━━━━━━━━━━━━━━━━━ 0s 11ms/step - loss: 0.0965 - mae: 0.2463


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 8ms/step - loss: 0.1002 - mae: 0.2516

Epoch 49/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.1093 - mae: 0.2580


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.1047 - mae: 0.2577

Epoch 50/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.0912 - mae: 0.2433


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0934 - mae: 0.2430

Epoch 51/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0921 - mae: 0.2444


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0922 - mae: 0.2423

Epoch 52/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0878 - mae: 0.2301


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0894 - mae: 0.2356

Epoch 53/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.1047 - mae: 0.2559


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0944 - mae: 0.2454

Epoch 54/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.1044 - mae: 0.2586


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0845 - mae: 0.2320

Epoch 55/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0822 - mae: 0.2245


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0850 - mae: 0.2325

Epoch 56/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0930 - mae: 0.2417


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0808 - mae: 0.2268

Epoch 57/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0698 - mae: 0.2038


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0759 - mae: 0.2178

Epoch 58/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0918 - mae: 0.2457


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0753 - mae: 0.2176

Epoch 59/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0646 - mae: 0.2048


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0717 - mae: 0.2131

Epoch 60/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.0665 - mae: 0.2022


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0722 - mae: 0.2138

Epoch 61/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 17ms/step - loss: 0.0617 - mae: 0.1936


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0683 - mae: 0.2074

Epoch 62/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0685 - mae: 0.2023


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0663 - mae: 0.2028

Epoch 63/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 17ms/step - loss: 0.0608 - mae: 0.1966


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0611 - mae: 0.1937

Epoch 64/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0664 - mae: 0.2053


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0600 - mae: 0.1948

Epoch 65/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0636 - mae: 0.1938


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0582 - mae: 0.1898

Epoch 66/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0528 - mae: 0.1861


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0508 - mae: 0.1799

Epoch 67/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0525 - mae: 0.1881


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0495 - mae: 0.1775

Epoch 68/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0468 - mae: 0.1697


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0461 - mae: 0.1692

Epoch 69/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0412 - mae: 0.1611


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0415 - mae: 0.1614

Epoch 70/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0501 - mae: 0.1786


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0410 - mae: 0.1594

Epoch 71/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0266 - mae: 0.1292


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0357 - mae: 0.1505

Epoch 72/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 17ms/step - loss: 0.0279 - mae: 0.1300


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0327 - mae: 0.1417

Epoch 73/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.0368 - mae: 0.1531


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0330 - mae: 0.1439

Epoch 74/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0290 - mae: 0.1346


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0305 - mae: 0.1374

Epoch 75/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0315 - mae: 0.1464


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0318 - mae: 0.1422

Epoch 76/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0280 - mae: 0.1333


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0310 - mae: 0.1409

Epoch 77/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0262 - mae: 0.1277


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0296 - mae: 0.1355

Epoch 78/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0343 - mae: 0.1475


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0308 - mae: 0.1393

Epoch 79/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0289 - mae: 0.1357


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0283 - mae: 0.1332

Epoch 80/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0249 - mae: 0.1227


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0282 - mae: 0.1319

Epoch 81/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0193 - mae: 0.1066


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0268 - mae: 0.1282

Epoch 82/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0319 - mae: 0.1436


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0280 - mae: 0.1335

Epoch 83/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 20ms/step - loss: 0.0256 - mae: 0.1208


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0273 - mae: 0.1298

Epoch 84/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0293 - mae: 0.1359


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0268 - mae: 0.1304

Epoch 85/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0219 - mae: 0.1162


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0273 - mae: 0.1303

Epoch 86/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0243 - mae: 0.1233


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0277 - mae: 0.1305

Epoch 87/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 1s 97ms/step - loss: 0.0248 - mae: 0.1283


 8/13 ━━━━━━━━━━━━━━━━━━━━ 0s 7ms/step - loss: 0.0258 - mae: 0.1285


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 7ms/step - loss: 0.0259 - mae: 0.1281

Epoch 88/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0214 - mae: 0.1168


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0249 - mae: 0.1251

Epoch 89/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0276 - mae: 0.1306


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0250 - mae: 0.1248

Epoch 90/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.0231 - mae: 0.1235


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0232 - mae: 0.1219

Epoch 91/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0296 - mae: 0.1411


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0259 - mae: 0.1286

Epoch 92/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0205 - mae: 0.1096


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0257 - mae: 0.1264

Epoch 93/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0251 - mae: 0.1273


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0248 - mae: 0.1249

Epoch 94/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 21ms/step - loss: 0.0214 - mae: 0.1190


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0221 - mae: 0.1184

Epoch 95/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 1s 97ms/step - loss: 0.0220 - mae: 0.1186


 7/13 ━━━━━━━━━━━━━━━━━━━━ 0s 8ms/step - loss: 0.0241 - mae: 0.1244


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 7ms/step - loss: 0.0241 - mae: 0.1240

Epoch 96/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0249 - mae: 0.1289


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0248 - mae: 0.1260

Epoch 97/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.0242 - mae: 0.1248


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0231 - mae: 0.1210

Epoch 98/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0254 - mae: 0.1265


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0244 - mae: 0.1237

Epoch 99/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.0187 - mae: 0.1101


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0220 - mae: 0.1165

Epoch 100/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0205 - mae: 0.1138


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0229 - mae: 0.1208

Epoch 101/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.0341 - mae: 0.1410


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0244 - mae: 0.1225

Epoch 102/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0241 - mae: 0.1204


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0237 - mae: 0.1210

Epoch 103/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0246 - mae: 0.1281


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0244 - mae: 0.1243

Epoch 104/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.0246 - mae: 0.1259


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0229 - mae: 0.1198

Epoch 105/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 1s 94ms/step - loss: 0.0204 - mae: 0.1157


 6/13 ━━━━━━━━━━━━━━━━━━━━ 0s 11ms/step - loss: 0.0244 - mae: 0.1236


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 10ms/step - loss: 0.0241 - mae: 0.1227

Epoch 106/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.0227 - mae: 0.1194


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0236 - mae: 0.1203

Epoch 107/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0240 - mae: 0.1240


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0242 - mae: 0.1236

Epoch 108/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0173 - mae: 0.1027


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0223 - mae: 0.1184

Epoch 109/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.0219 - mae: 0.1175


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0222 - mae: 0.1174

Epoch 110/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 17ms/step - loss: 0.0195 - mae: 0.1081


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0214 - mae: 0.1149

Epoch 111/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0229 - mae: 0.1151


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0215 - mae: 0.1145

Epoch 112/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0314 - mae: 0.1504


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0245 - mae: 0.1265

Epoch 113/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0206 - mae: 0.1094


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0228 - mae: 0.1184

Epoch 114/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 17ms/step - loss: 0.0250 - mae: 0.1283


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0234 - mae: 0.1208

Epoch 115/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 17ms/step - loss: 0.0250 - mae: 0.1230


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0228 - mae: 0.1190

Epoch 116/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0210 - mae: 0.1169


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0207 - mae: 0.1136

Epoch 117/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 17ms/step - loss: 0.0219 - mae: 0.1179


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0214 - mae: 0.1158

Epoch 118/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0218 - mae: 0.1204


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0197 - mae: 0.1114

Epoch 119/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0190 - mae: 0.1086


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0209 - mae: 0.1156

Epoch 120/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 1s 98ms/step - loss: 0.0230 - mae: 0.1168


 7/13 ━━━━━━━━━━━━━━━━━━━━ 0s 9ms/step - loss: 0.0217 - mae: 0.1149


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 7ms/step - loss: 0.0219 - mae: 0.1159

Epoch 121/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0183 - mae: 0.1041


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0215 - mae: 0.1150

Epoch 122/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0245 - mae: 0.1274


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0205 - mae: 0.1147

Epoch 123/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0199 - mae: 0.1130


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0209 - mae: 0.1145

Epoch 124/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.0166 - mae: 0.1008


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0213 - mae: 0.1144

Epoch 125/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0239 - mae: 0.1247


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0210 - mae: 0.1150

Epoch 126/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0196 - mae: 0.1103


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0205 - mae: 0.1126

Epoch 127/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 1s 95ms/step - loss: 0.0237 - mae: 0.1215


 6/13 ━━━━━━━━━━━━━━━━━━━━ 0s 10ms/step - loss: 0.0209 - mae: 0.1127


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 7ms/step - loss: 0.0205 - mae: 0.1120

Epoch 128/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0240 - mae: 0.1261


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0221 - mae: 0.1188

Epoch 129/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.0164 - mae: 0.1049


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0200 - mae: 0.1129

Epoch 130/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0190 - mae: 0.1070


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0197 - mae: 0.1101

Epoch 131/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.0210 - mae: 0.1159


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0198 - mae: 0.1113

Epoch 132/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 1s 88ms/step - loss: 0.0214 - mae: 0.1181


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0189 - mae: 0.1088

Epoch 133/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.0174 - mae: 0.1025


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0192 - mae: 0.1093

Epoch 134/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0245 - mae: 0.1240


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0206 - mae: 0.1133

Epoch 135/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0158 - mae: 0.1000


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0187 - mae: 0.1086

Epoch 136/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 24ms/step - loss: 0.0193 - mae: 0.1099


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0197 - mae: 0.1103

Epoch 137/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0194 - mae: 0.1107


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0187 - mae: 0.1078

Epoch 138/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0204 - mae: 0.1138


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0207 - mae: 0.1139

Epoch 139/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0214 - mae: 0.1123


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0193 - mae: 0.1081

Epoch 140/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0228 - mae: 0.1217


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0211 - mae: 0.1143

Epoch 141/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 1s 103ms/step - loss: 0.0213 - mae: 0.1219


 8/13 ━━━━━━━━━━━━━━━━━━━━ 0s 8ms/step - loss: 0.0190 - mae: 0.1109


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 7ms/step - loss: 0.0191 - mae: 0.1103

Epoch 142/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0155 - mae: 0.1015


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0194 - mae: 0.1110

Epoch 143/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.0220 - mae: 0.1189


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0199 - mae: 0.1121

Epoch 144/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0193 - mae: 0.1100


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0195 - mae: 0.1106

Epoch 145/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0170 - mae: 0.1063


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0188 - mae: 0.1080

Epoch 146/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0232 - mae: 0.1208


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0210 - mae: 0.1147

Epoch 147/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0179 - mae: 0.1044


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0206 - mae: 0.1132

Epoch 148/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0127 - mae: 0.0894


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0174 - mae: 0.1030

Epoch 149/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0169 - mae: 0.1044


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0178 - mae: 0.1059

Epoch 150/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 20ms/step - loss: 0.0221 - mae: 0.1147


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0189 - mae: 0.1093

Epoch 151/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0174 - mae: 0.1040


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0194 - mae: 0.1084

Epoch 152/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 20ms/step - loss: 0.0201 - mae: 0.1108


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0187 - mae: 0.1084

Epoch 153/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0157 - mae: 0.0980


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0187 - mae: 0.1068

Epoch 154/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.0187 - mae: 0.1087


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0188 - mae: 0.1076

Epoch 155/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0166 - mae: 0.1005


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0182 - mae: 0.1052

Epoch 156/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 1s 101ms/step - loss: 0.0147 - mae: 0.0989


 6/13 ━━━━━━━━━━━━━━━━━━━━ 0s 11ms/step - loss: 0.0168 - mae: 0.1032


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 9ms/step - loss: 0.0175 - mae: 0.1052


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 11ms/step - loss: 0.0176 - mae: 0.1053

Epoch 157/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0169 - mae: 0.1040


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0182 - mae: 0.1063

Epoch 158/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 17ms/step - loss: 0.0254 - mae: 0.1292


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0212 - mae: 0.1163

Epoch 159/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 1s 102ms/step - loss: 0.0135 - mae: 0.0898


 7/13 ━━━━━━━━━━━━━━━━━━━━ 0s 9ms/step - loss: 0.0163 - mae: 0.0998


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 7ms/step - loss: 0.0176 - mae: 0.1039

Epoch 160/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0215 - mae: 0.1153


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0186 - mae: 0.1067

Epoch 161/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0200 - mae: 0.1135


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0196 - mae: 0.1104

Epoch 162/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0198 - mae: 0.1128


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0200 - mae: 0.1126

Epoch 163/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0208 - mae: 0.1138


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0190 - mae: 0.1089

Epoch 164/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0236 - mae: 0.1156


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0194 - mae: 0.1092

Epoch 165/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.0161 - mae: 0.0990


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0181 - mae: 0.1051

Epoch 166/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0182 - mae: 0.1114


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0187 - mae: 0.1086

Epoch 167/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0184 - mae: 0.1007


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0178 - mae: 0.1032

Epoch 168/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0126 - mae: 0.0860


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0167 - mae: 0.1016

Epoch 169/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0230 - mae: 0.1249


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0188 - mae: 0.1086

Epoch 170/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.0120 - mae: 0.0880


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0164 - mae: 0.1011

Epoch 171/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 20ms/step - loss: 0.0145 - mae: 0.0959


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0160 - mae: 0.0997

Epoch 172/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.0159 - mae: 0.0971


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0181 - mae: 0.1058

Epoch 173/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0173 - mae: 0.1049


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0172 - mae: 0.1038

Epoch 174/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 1s 93ms/step - loss: 0.0213 - mae: 0.1154


 6/13 ━━━━━━━━━━━━━━━━━━━━ 0s 11ms/step - loss: 0.0207 - mae: 0.1153


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 8ms/step - loss: 0.0194 - mae: 0.1110

Epoch 175/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0155 - mae: 0.0965


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0176 - mae: 0.1046

Epoch 176/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0203 - mae: 0.1131


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0192 - mae: 0.1113

Epoch 177/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0160 - mae: 0.0978


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0163 - mae: 0.1010

Epoch 178/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0226 - mae: 0.1172


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0185 - mae: 0.1074

Epoch 179/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 17ms/step - loss: 0.0140 - mae: 0.0949


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0171 - mae: 0.1031

Epoch 180/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0137 - mae: 0.0914


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0175 - mae: 0.1028

Epoch 181/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0204 - mae: 0.1102


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0182 - mae: 0.1059

Epoch 182/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 17ms/step - loss: 0.0155 - mae: 0.0903


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0167 - mae: 0.1011

Epoch 183/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0180 - mae: 0.1081


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0166 - mae: 0.1020

Epoch 184/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0192 - mae: 0.1094


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0169 - mae: 0.1025

Epoch 185/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0192 - mae: 0.1084


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0180 - mae: 0.1057

Epoch 186/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0154 - mae: 0.0967


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0173 - mae: 0.1032

Epoch 187/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.0225 - mae: 0.1200


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0197 - mae: 0.1110

Epoch 188/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0184 - mae: 0.1080


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0175 - mae: 0.1038

Epoch 189/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0153 - mae: 0.0985


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0162 - mae: 0.1009

Epoch 190/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0162 - mae: 0.0987


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0160 - mae: 0.0988

Epoch 191/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0135 - mae: 0.0897


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0160 - mae: 0.1000

Epoch 192/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 1s 99ms/step - loss: 0.0157 - mae: 0.0968


 7/13 ━━━━━━━━━━━━━━━━━━━━ 0s 9ms/step - loss: 0.0152 - mae: 0.0976


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 9ms/step - loss: 0.0160 - mae: 0.0996

Epoch 193/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0136 - mae: 0.0924


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0161 - mae: 0.0997

Epoch 194/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 1s 101ms/step - loss: 0.0243 - mae: 0.1232


 7/13 ━━━━━━━━━━━━━━━━━━━━ 0s 9ms/step - loss: 0.0207 - mae: 0.1134


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 7ms/step - loss: 0.0191 - mae: 0.1089

Epoch 195/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 56ms/step - loss: 0.0190 - mae: 0.1094


 7/13 ━━━━━━━━━━━━━━━━━━━━ 0s 9ms/step - loss: 0.0182 - mae: 0.1073


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 9ms/step - loss: 0.0178 - mae: 0.1059

Epoch 196/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0180 - mae: 0.1058


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0165 - mae: 0.1009

Epoch 197/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.0180 - mae: 0.1052


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0171 - mae: 0.1029

Epoch 198/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.0164 - mae: 0.1011


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0166 - mae: 0.1021

Epoch 199/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 1s 102ms/step - loss: 0.0139 - mae: 0.0944


 6/13 ━━━━━━━━━━━━━━━━━━━━ 0s 10ms/step - loss: 0.0150 - mae: 0.0970


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 9ms/step - loss: 0.0155 - mae: 0.0987

Epoch 200/200

 1/13 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.0144 - mae: 0.0959


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0187 - mae: 0.1079

phase apprentissage: 18.36 seconds

modele_lstm.summary()

Model: "sequential"

┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓
┃ Layer (type)                    ┃ Output Shape           ┃       Param # ┃
┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩
│ lstm (LSTM)                     │ (None, 14)             │           896 │
├─────────────────────────────────┼────────────────────────┼───────────────┤
│ dense (Dense)                   │ (None, 14)             │           210 │
├─────────────────────────────────┼────────────────────────┼───────────────┤
│ dense_1 (Dense)                 │ (None, 7)              │           105 │
├─────────────────────────────────┼────────────────────────┼───────────────┤
│ dense_2 (Dense)                 │ (None, 7)              │            56 │
└─────────────────────────────────┴────────────────────────┴───────────────┘

 Total params: 3,803 (14.86 KB)

 Trainable params: 1,267 (4.95 KB)

 Non-trainable params: 0 (0.00 B)

 Optimizer params: 2,536 (9.91 KB)

ypred = modele_lstm.predict(Xlearn, verbose=True)
print(Xlearn.shape,ypred.shape)
Ylearn = ylearn.reshape(ylearn.shape[0],nap,)
print("R2 score {:.2f}".format(r2_score(Ylearn, ypred)))
print("model evaluate loss/mae")
modele_lstm.evaluate(Xlearn,ylearn)

 1/13 ━━━━━━━━━━━━━━━━━━━━ 1s 107ms/step


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 9ms/step


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 10ms/step

(400, 14, 1) (400, 7)
R2 score 0.97
model evaluate loss/mae

 1/13 ━━━━━━━━━━━━━━━━━━━━ 2s 174ms/step - loss: 0.0207 - mae: 0.1164


13/13 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0171 - mae: 0.1028

[0.01707562804222107, 0.10179268568754196]

# prediction à partir de t2
t2 = t0 
Xpred  = np.array([ys[t2-nav:t2]]).reshape(1,nav,1)
ypred = modele_lstm.predict(Xpred, verbose=True)
print(Xpred.shape,ypred.shape)

1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step


1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 25ms/step

(1, 14, 1) (1, 7)

Xpred = Xpred.reshape(1,nav,)
ypred = ypred.reshape(nap)
plot_pred()

../../_images/1046419498248682d34c201965bd0d5acd75026e47e83738505893670a716e3d.png

6.7. bibliographie#

Initiez-vous au Deep Learning (openclassroom)