def _co_eqn(self, t, sol_adj):
""" compute residuals LHS """
x_adj, y_adj = sol_adj[:, 0].reshape(-1, 1), sol_adj[:,
1].reshape(-1, 1)
eqn1 = diff(x_adj, t) + t * y_adj
eqn2 = diff(y_adj, t) - t * x_adj
return eqn1, eqn2
def adjust(self, x, t):
""" perform initial value adjustment """
x_adj = self.x0 + (1 - torch.exp(-t)) * self.dx_dt0 + (
(1 - torch.exp(-t))**2) * x
dx = diff(x_adj, t)
d2x = diff(dx, t)
return {'pred': x_adj, 'dx': dx, 'd2x': d2x}
def _sir_eqn(self, t, x_adj):
S_adj, I_adj, R_adj = x_adj[:, 0], x_adj[:, 1], x_adj[:, 2]
S_adj, I_adj, R_adj = S_adj.reshape(-1, 1), I_adj.reshape(
-1, 1), R_adj.reshape(-1, 1)
eqn1 = diff(S_adj, t) + self.beta * I_adj * S_adj / self.N
eqn2 = diff(I_adj, t) - (self.beta * I_adj * S_adj /
self.N) + self.gamma * I_adj
eqn3 = diff(R_adj, t) - self.gamma * I_adj
return eqn1, eqn2, eqn3
def adjust(self, y, u):
a = self.bc[0]
b = (self.bc[1] - self.bc[0]) * (y - self.ymin)
c = self.ymax - self.ymin
d = (y - self.ymin) * (y - self.ymax) * u
u_adj = a + b / c + d
du = diff(u_adj, y)
dre = diff(self._reynolds_stress(y, du), y)
d2u = diff(du, y)
return {'pred': u_adj, 'dre': dre, 'd2u': d2u}
def _poisson_eqn(self, u, x, y):
return diff(u, x, order=2) + diff(u, y, order=2) - 2 * x * (y - 1) * (
y - 2 * x + x * y + 2) * torch.exp(x - y)
def adjust(self, x, t):
""" perform initial value adjustment """
x_adj = self.x0 + (1 - torch.exp(-t)) * x
dx_dt = diff(x_adj, t)
return {'pred': x_adj, 'dx': dx_dt}