TemperatureToy.py

import torch

t_c = [0.5,  14.0, 15.0, 28.0, 11.0,  8.0,  3.0, -4.0,  6.0, 13.0, 21.0]
t_u = [35.7, 55.9, 58.2, 81.9, 56.3, 48.9, 33.9, 21.8, 48.4, 60.4, 68.4]
t_c = torch.tensor(t_c)
t_u = torch.tensor(t_u)

def model(t_u, w, b):
    return w * t_u + b

def loss_fn(t_p, t_c):
    squared_diffs = (t_p - t_c)**2
    return squared_diffs.mean()

w = torch.ones(1)
b = torch.zeros(1)
t_p = model(t_u, w, b)
t_p


loss = loss_fn(t_p, t_c)
loss

delta = 0.1
loss_rate_of_change_w = \
    (loss_fn(model(t_u, w + delta, b), t_c) -
     loss_fn(model(t_u, w - delta, b), t_c)) / (2.0 * delta)

learning_rate = 1e-2
w = w - learning_rate * loss_rate_of_change_w

loss_rate_of_change_b = \
    (loss_fn(model(t_u, w, b + delta), t_c) -
     loss_fn(model(t_u, w, b - delta), t_c)) / (2.0 * delta)

def dloss_fn(t_p, t_c):
    dsq_diffs = 2 * (t_p - t_c)
    return dsq_diffs


def dmodel_db(t_u, w, b):
    return 1.0

def model(t_u, w, b):
    return w * t_u + b

def dmodel_dw(t_u, w, b):
    return t_u

def grad_fn(t_u, t_c, t_p, w, b):
    dloss_dw = dloss_fn(t_p, t_c) * dmodel_dw(t_u, w, b)
    dloss_db = dloss_fn(t_p, t_c) * dmodel_db(t_u, w, b)
    return torch.stack([dloss_dw.mean(), dloss_db.mean()])

def training_loop(n_epochs, learning_rate, params, t_u, t_c):
    for epoch in range(1, n_epochs + 1):
        w, b = params
        t_p = model(t_u, w, b)
        loss = loss_fn(t_p, t_c)
        grad = grad_fn(t_u, t_c, t_p, w, b)
        params = params - learning_rate * grad
        print('Epoch %d, Loss %f' % (epoch, float(loss)))
        print("    Params:", params)
        print("    Grad:", grad)
    return params

Result = training_loop(
    n_epochs = 100,
    learning_rate = 1e-4,
    params = torch.tensor([1.0, 0.0]),
    t_u = t_u,
    t_c = t_c)

t_un = 0.1 * t_u
Result = training_loop(n_epochs=5000, learning_rate=1e-2, params = torch.tensor([1.0, 0.0]), t_u = t_un, t_c = t_c)