def loss_func(input, prediction):
ret = torch.empty(len(input), 2)
for index in range(len(input)):
xy = input[index]
ts = trial_solution(xy[0], xy[1], prediction[index])
lap = laplace(ts, xy)
ret[index] = lap**2
ret = torch.sum(ret)
return ret
from differentiate import laplace
def trial_solution(x, y, prediction):
return y * torch.sin(math.pi * x) + x * (x - 1) * y * (y - 1) * prediction
def solution(x: tensor, y: tensor):
return (1 / (math.exp(math.pi) - math.exp(-math.pi))) * torch.sin(
math.pi * x) * (torch.exp(math.pi * y) - torch.exp(-math.pi * y))
xy = tensor([.5, .5], dtype=torch.float, requires_grad=True)
prediction = solution(xy[0], xy[1])
# ts = trial_solution(xy[0], xy[1], prediction)
lap = laplace(prediction, xy)
print(lap)
steps = 16
lin_space = np.linspace(0, 1, steps)
with torch.no_grad():
zPredicted = np.zeros((steps, steps))
for ix in range(steps):
for iy in range(steps):
x = torch.tensor(lin_space[ix], dtype=torch.float)
y = torch.tensor(lin_space[iy], dtype=torch.float)
zPredicted[ix][iy] = solution(x, y)
levels = np.linspace(zPredicted.min(), zPredicted.max(), 100)
cs = plt.contourf(lin_space,
lin_space,