mhjensen
76 lines
2.5 KiB
Python
76 lines
2.5 KiB
Python
import matplotlib.pyplot as plt
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import numpy as np
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import tensorflow.compat.v1 as tf
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tf.disable_v2_behavior()
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#tf.reset_default_graph()
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import keras
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from keras.models import Model
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from keras.layers import Dense, Input
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from keras import optimizers
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from keras import backend as K
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## Creates a trial function g = y0 + x * N(x, P)
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def trial_func(x, y, y0 = 1):
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func = tf.exp(-x)*y0 + x * y
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return func
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## Computes Right Side of differential eq; -k/m * g
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def right_side(trial, k = 1, m = 1):
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return -trial
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## Here we define the loss function
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def loss_wrapper(input_tensor):
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def loss_function(y, y_pred):
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## Find the trial solution and right-side
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trial = trial_func(input_tensor, y_pred)
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right = right_side(trial)
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# For coupled second-order we may need to have two loss function
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left = tf.gradients(trial, input_tensor)
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loss = tf.reduce_mean(tf.math.squared_difference(left, right))
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return loss
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return loss_function
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def create_input_data(a = 0, b = 5, n = 100):
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input_data = np.linspace(a,b,n)
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input_data = input_data.reshape(1,n)
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return input_data
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def create_model(data, n_inputs, n_hidden_layer = 50):
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input_tensor = Input(shape=(n_inputs,))
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hidden = Dense(30, activation='tanh',
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kernel_initializer='random_uniform', bias_initializer='zeros')(input_tensor)
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hidden2 = Dense(200, activation='tanh',
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kernel_initializer='random_uniform', bias_initializer='zeros')(hidden)
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hidden3 = Dense(50, activation='tanh',
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kernel_initializer='random_uniform', bias_initializer='zeros')(hidden2)
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hidden4 = Dense(30, activation='tanh',
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kernel_initializer='random_uniform', bias_initializer='zeros')(hidden3)
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out = Dense(n_inputs)(hidden2)
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model = Model(input_tensor, out)
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sgd = optimizers.SGD(lr=0.001, decay = .1)
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model.compile(loss=loss_wrapper(input_tensor), optimizer='sgd')
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model.fit(data, np.zeros((data.shape[0])), epochs = 5000)
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res = model.predict(data)
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del model
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return res
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data = create_input_data(0, 1, 10)
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shape = data.shape
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res = create_model(data, shape[1], 50)
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results = trial_func(data[0], res)
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euler = euler_cromer(tf = 1, gam = 0, mass = 1)
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plt.plot(data[0], results[0], label = 'Neural Differential Equation')
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plt.plot(euler[0], np.exp(-euler[0]), label = 'Euler-Cromer Method (Numerical)')
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plt.legend()
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plt.title('Neural ODE vs Analytical Method')
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plt.xlabel('Time')
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plt.xlabel('X-Position')
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