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pinn.py
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pinn.py
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########################################################################################################################
# PINN method for HRTF interpolation
#
# Given HRTF from limited number of directions (330 hrtf),
# we wish to interpolate the HRTF over a large direction (930 hrtf)
#
# Fei Ma,
# feima1024@gmail.com
# 4th, Oct, 2023
########################################################################################################################
## if you find the code useful,
## please consider denoting to the Free Sofware Fundation or the Wikimedia Foundation
## https://my.fsf.org/
## https://wikimediafoundation.org/
########################################################################################################################
# the code runs on my macpro with python 3.9, 3.10, tensorflow 2.12 and 2.13
# the numpy version and scipy version should not be a problem if they are compitable with python and tensorflow
# With just 3 hidden layers and <16 nodes in each hidden layer, the Network is small, and can be trained faster on
# powerful CPU rather than GPU.
########################################################################################################################
# import the python packages,
import tensorflow as tf
from tensorflow.keras import activations
from keras import backend as K
import logging
logging.getLogger('tensorflow').setLevel(logging.ERROR)
import numpy as np
from time import time as now
from datetime import datetime
import scipy.optimize
import scipy.io as sio
import random
DTYPE='float32' ## using float64 will result in slightly better results around 1~2 dB, but that will double the training time
tf.keras.backend.set_floatx(DTYPE)
for ii in range(50):
print(">>>")
########################################################################################################################
########################################################################################################################
### the definiton of the PINN model
#############################################################
### neural network initialization
def init_model(num_input=3, layers = 3, neurons=3): ## (x,y,z) input number is 3, layer number = depth L, neuron number = width W
model = tf.keras.Sequential()
model.add(tf.keras.Input(num_input)) ## input layer
for ii in range(layers): ## hidden layers
model.add(tf.keras.layers.Dense(neurons,activation=tf.keras.activations.get('tanh'),kernel_initializer='glorot_normal'))
model.add(tf.keras.layers.Dense(1)) ## output layer
return model
#############################################################
### calculate the PDE loss
def get_pde(model,pde_input,wave_num1):
with tf.GradientTape(persistent=True) as tape:
x1, x2, x3 = pde_input[:,0:1], pde_input[:,1:2], pde_input[:,2:3] # (x1,x2,x3) = (x,y,z)
tape.watch(x1) ## notify tensorflow that we care about the gradient with respect to x1, x2, x3
tape.watch(x2)
tape.watch(x3)
pde_pred = model(tf.stack([x1[:,0],x2[:,0],x3[:,0]],axis=1)) # mode prediction
x1_d1 = tape.gradient(pde_pred,x1) ## first order gradient with respect to x, y, z
x2_d1 = tape.gradient(pde_pred,x2)
x3_d1 = tape.gradient(pde_pred,x3)
x1_d2 = tape.gradient(x1_d1,x1) ## second order gradient with respect to x, y, z
x2_d2 = tape.gradient(x2_d1,x2)
x3_d2 = tape.gradient(x3_d1,x3)
del tape
Laplacian = ( x1_d2 + x2_d2 + x3_d2 )*wave_num1 ## wave_num1 = (1/(omega/c))^2, this normalize the laplacian
loss_pde = tf.reduce_mean(tf.square(Laplacian + pde_pred)) ## this line of code calculate the PDE loss
return loss_pde ## return the PDE loss
#############################################################
### calculate the data loss
def get_data(model,data_input,data_target):
data_pred = model(data_input) ## mode prediction
loss_data = tf.reduce_mean(tf.square(data_pred-data_target)) ## calcualte the difference between training data and the prediction, result in the data loss
return loss_data ## return the data loss
#############################################################
### calculat the gradient with respect to the loss
def get_grad(model,data_input,data_target,pde_input,wave_num1):
with tf.GradientTape(persistent=True) as tape:
tape.watch(model.trainable_variables)
loss_data = get_data(model,data_input,data_target) ## data loss
loss_pde = get_pde(model,pde_input,wave_num1) ## pde loss
loss = loss_data + loss_pde ## total loss
g = tape.gradient(loss,model.trainable_variables) ## take the gradient of the trainable parameters with respect to the loss
del tape
return loss_data, loss_pde, g ## return the data_loss, pde_loss, and the gradient
#############################################################
### predict the HRTF for the test_input coordiantes
def get_test(model,test_input):
test_pred = model(test_input) ## model prediction
return test_pred ## return the prediction
##############################################################################################################
########################################################################################################################
# some global variables
speed = 343; # speed of sound
lr = 1e-3; # adam learning rate
num_epochs = 100*1000; # training epoches
layers = 3 # PINN depth
########################################################################################################################
########################################################################################################################
## this is the training process
for human in range(40,41): ## human denote the ID of subjects, iterative over subject 11 to 50
################################################################################################################
### prepare the training data
file = str(human)+'.mat'
data = sio.loadmat(file);
#######################################
total_hrtf = data['total_hrtf']; ## known HRTF + unknown HRTF = total HRTF,
## total HRTF is a [7 , 2 , 1260] tensor
## 7 is the number of frequency bins of interest
## total_hrtf[ ff, 0, 0:1260] is the real part of total HRTF at frequency ff
## total_hrtf[ ff, 1, 0:1260] is the imag part of total HRTF at frequency ff
## total_hrtf[ ff, 0, 0:630] is the real and left part of total HRTF at frequency ff
## total_hrtf[ ff, 0, 0:630] is the real and right part of total HRTF at frequency ff
## total_hrtf[ ff, 1, 630:1260] is the imag and left part of total HRTF at frequency ff
## total_hrtf[ ff, 1, 630:1260] is the imag and right part of total HRTF at frequency ff
total_est = np.copy(total_hrtf); ## a tensor the same size as total_hrtf, it will store the total_hrtf estimation
train_hrtf = data['train_hrtf']; ## known HRTF only
## train HRTF is a [7 , 2 , 330] tensor
## 7 is the number of frequency bins of interest
## train_hrtf[ ff, 0, 0:330] is the real part of train HRTF at frequency ff
## train_hrtf[ ff, 1, 0:330] is the imag part of train HRTF at frequency ff
## train_hrtf[ ff, 0, 0:165] is the real and left part of train HRTF at frequency ff
## train_hrtf[ ff, 0, 0:165] is the real and right part of train HRTF at frequency ff
## train_hrtf[ ff, 1, 165:330] is the imag and left part of train HRTF at frequency ff
## train_hrtf[ ff, 1, 165:330] is the imag and right part of train HRTF at frequency ff
total_coor = data['total_coor']; ## coordiantes of the known and unkown HRTFs
## total_coor is a [1260,8] tensor
## total_coor[ii,0:8] is the coordiantes of the ii-th hrtf
## total_coor[ii,0:3] = [x, y, z]
## total_coor[ii,3:6] = [r, theta, phi] in radian
## total_coor[ii,6:8] = [ theta, phi] in degree
train_coor = data['train_coor']; ## coordiantes of the known HRTF only
## train_coor is a [330,8] tensor
## train_coor[ii,0:8] is the coordiantes of the ii-th hrtf
## train_coor[ii,0:3] = [x, y, z]
## train_coor[ii,3:6] = [r, theta, phi] in radian
## train_coor[ii,6:8] = [ theta, phi] in degree
########################################
freq_bb = data['freq_bins']; ## vectors saved by matlab into mat format will be 2D arrays when read by python
## var[0] will get the value of the vector
freq_bins = freq_bb[0] ## a vector of frequency bins we are going to evaluate
## [2.1 4.1 6.2 8.2 10.3 12.3 14.4] kHz
########################################
total_num = data['total_num']; ## total number of known and unknown HRTFs = 1260
train_num = data['train_num']; ## number of known HRTF = 330
total_num = total_num[0][0] ## variables saved by matlab into mat format will be 2D arrays when read by python
train_num = train_num[0][0] ## var[0][0] will get the value of the variable
total_mid = total_num//2 ## total_hrtf[ ff, 0, 0:total_mid] real and left part of total hrtf
## total_hrtf[ ff, 0, total_mid:total_num] real and right part of total hrtf
## total_hrtf[ ff, 1, 0:total_mid] imagl and left part of total hrtf
## total_hrtf[ ff, 1, total_mid:total_num] imagl and right part of total hrtf
train_mid = train_num//2 ## train_hrtf[ ff, 0, 0:train_mid] real and left part of train hrtf
## train_hrtf[ ff, 0, train_mid:train_num] real and right part of train hrtf
## train_hrtf[ ff, 1, 0:train_mid] imagl and left part of train hrtf
## train_hrtf[ ff, 1, train_mid:train_num] imagl and right part of train hrtf
################################################################################################################
for ff in range(0,7): ## iterative over frequency
###############################
### the wave number
freq = freq_bins[ff]; ## the current frequency
wave_num = 2*np.pi*freq/speed; ## the wave number
wave_num1 = 1.0/(wave_num**2); ## a factor used for normalizing the Laplacian
###############################
### the node number ## calculate the number of neurons in hidden layer according the frequency
nodes = 0;
if freq<3000: ## f<3000, neuron = f/500
nodes = int(np.ceil(freq/500));
elif freq>6000:
nodes = int(np.ceil(freq/1000)); ## f>6000, neuron = f/1000
else:
nodes = 6; ## else neuron = 6
##########################################################################################################################################
for dd in range(4): ## 4 pinn methods to model the [real left], [real right], [imaginary left], [imaginar right] part of HRTF
if dd==0: ## real left
####################################################################################################
data_train = np.zeros((train_mid,1)); ### use the real and left known HRTF as training data
xyz_train = np.zeros((train_mid,3)) ### the real and left known HRTF's cartesian coordinates
xyz_total = np.zeros((total_mid,3)) ### the real and left [known + unknown] total HRTF's cartesian coordinates
for ii in range(train_mid):
data_train[ii,0] = train_hrtf[ff,0,ii] ### get the traning data
xyz_train[ii,0:3] = train_coor[ii,0:3] ### and the corresponding coordinates
for ii in range(total_mid):
xyz_total[ii,0:3] = total_coor[ii,0:3] ### get the coordiantes used for PDE loss calculation
####################################################################################################
elif dd==1: ## real right
####################################################################################################
data_train = np.zeros((train_num-train_mid,1)); ### same as above but for the real and right part
xyz_train = np.zeros((train_num-train_mid,3))
xyz_total = np.zeros((total_num-total_mid,3))
for ii in range(train_mid,train_num):
data_train[ii-train_mid,0] = train_hrtf[ff,0,ii]
xyz_train[ii-train_mid,0:3] = train_coor[ii,0:3]
for ii in range(total_mid,total_num):
xyz_total[ii-total_mid,0:3] = total_coor[ii,0:3]
####################################################################################################
elif dd==2: ## imag left
####################################################################################################
data_train = np.zeros((train_mid,1)); ### same as above but for the imaginary and left part
xyz_train = np.zeros((train_mid,3))
xyz_total = np.zeros((total_mid,3))
for ii in range(train_mid):
data_train[ii,0] = train_hrtf[ff,1,ii]
xyz_train[ii,0:3] = train_coor[ii,0:3]
for ii in range(total_mid):
xyz_total[ii,0:3] = total_coor[ii,0:3]
####################################################################################################
else: ## imag right
####################################################################################################
data_train = np.zeros((train_num-train_mid,1)); ### same as above but for the imaginary and right part
xyz_train = np.zeros((train_num-train_mid,3))
xyz_total = np.zeros((total_num-total_mid,3))
for ii in range(train_mid,train_num):
data_train[ii-train_mid,0] = train_hrtf[ff,1,ii]
xyz_train[ii-train_mid,0:3] = train_coor[ii,0:3]
for ii in range(total_mid,total_num):
xyz_total[ii-total_mid,0:3] = total_coor[ii,0:3]
#########################################################################################################################################
xyz_train = tf.convert_to_tensor(xyz_train, dtype=tf.float32) ### transfer the numpy data into tensorflow data, float32 format
data_train = tf.convert_to_tensor(data_train, dtype=tf.float32)
xyz_total = tf.convert_to_tensor(xyz_total, dtype=tf.float32)
wave_num1 = tf.convert_to_tensor(wave_num1, dtype=tf.float32)
#########################################################################################################################################
## the core training process
now_err = 0 ### record the current data loss
### the PINN training is sensitive to network initialization, the training is repeated five times
### we select the training with the least data loss as the training result
for cc in range(5):
#####################################################################################################
### this line of code will clear the memory used by a model after it finish
### with out it, you will run out of memory quickly
tf.keras.backend.clear_session()
#####################################################################################################
### tell tensorflow to build up a static graph for the model_fit function
### the core model fitting/traning function
@tf.function
def model_fit(model,data_input,data_target,pde_input,wave_num1):
loss_data,loss_pde,grad=get_grad(model,data_input,data_target,pde_input,wave_num1)
optim.apply_gradients(zip(grad,model.trainable_variables))
return loss_data, loss_pde
#####################################################################################################
model = init_model(3,layers,nodes) ## initialize a model with input number, hidden layer number, and nodes number
optim = tf.keras.optimizers.legacy.Adam(learning_rate = lr) ### we use the ADAM optimizer
db_true = 10*np.log10(tf.reduce_mean(tf.square(data_train)))/0.1/10 ### energy of the training HRTF in dB
#####################################################################################################
### let us train
for jj in range(1,num_epochs):
loss_data,loss_pde=model_fit(model,xyz_train,data_train,xyz_total,wave_num1)
#####################################################################################################
loss_data_db = (10*np.log10(loss_data) - db_true)//0.1/10 ## the data loss
loss_pde_db = 10*np.log10(loss_pde)//0.1/10 ## pde loss
now = datetime.now() ## current date and time
now = now.strftime("%H:%M:%S")
## print data loss, pde loss, layer number, neuron number, for subject huamn at frequency ff
print(ff,'ID',human,'T',now,'L',layers,'N',nodes,'R',dd,loss_data_db,loss_pde_db)
#######################################################################################################
### if the current data loss is smaller
if loss_data_db < now_err:
#########################################################
now_err = loss_data_db; ### store the data loss
pinn_pred = get_test(model,xyz_total); ### predict the HRTF at [known + unknown] total HRTF coordinates
pinn_pred = pinn_pred.numpy(); ### transfer the prediction into numpy format
#########################################################
if dd==0:
for ii in range(total_mid): ### store the real left HRTF prediction into the total_est
total_est[ff,0,ii] = pinn_pred[ii][0]
elif dd==1:
for ii in range(total_mid,total_num): ### store the real right HRTF prediction into the total_est
total_est[ff,0,ii] = pinn_pred[ii-total_mid][0]
elif dd==2:
for ii in range(total_mid): ### store the imag left HRTF prediction into the total_est
total_est[ff,1,ii] = pinn_pred[ii][0]
else:
for ii in range(total_mid,total_num): ### store the imag right HRTF prediction into the total_est
total_est[ff,1,ii] = pinn_pred[ii-total_mid][0]
#######################################################################################################
### good enough, stop
if now_err<-29.0: ### if the current data loss is small enough, we do not repeat the training 5 times, stop it.
break;
print('------------------------------------------')
##################################################################################################
### save the result into a file
newfile = str(human) + '_L' + str(layers) + '.mat'
sio.savemat(newfile,{'total_hrtf':total_hrtf,'total_est':total_est,'total_coor':total_coor,'train_coor':train_coor});
####################################################################################################################