Physicsinformed

continuiti.pde.physicsinformed

PDEs and physics-informed loss functions.

PDE

PDE base class.

Example

In general, we can implement a PDE like \(\nabla v = u\) as follows:

def pde(x, u, y, v):  # v = op(x, u, y)
    v_y = grad(y, v)
    return mse(v_y, u)

loss_fn = PhysicsInformedLoss(pde)

__call__(x, u, y, v) abstractmethod

Computes PDE loss.

Usually, we have v = op(x, u, y), e.g., in the physics-informed loss.

PARAMETER	DESCRIPTION
x	Tensor of sensor positions of shape (batch_size, x_dim, num_sensors...). TYPE: Tensor
u	Tensor of sensor values of shape (batch_size, u_dim, num_sensors...). TYPE: Tensor
y	Tensor of evaluation coordinates of shape (batch_size, y_dim, num_evaluations...). TYPE: Tensor
v	Tensor of predicted values of shape (batch_size, v_dim, num_evaluations...). TYPE: Tensor

Source code in src/continuiti/pde/physicsinformed.py

@abstractmethod
def __call__(
    self,
    x: torch.Tensor,
    u: torch.Tensor,
    y: torch.Tensor,
    v: torch.Tensor,
) -> torch.Tensor:
    """Computes PDE loss.

    Usually, we have `v = op(x, u, y)`, e.g., in the physics-informed loss.

    Args:
        x: Tensor of sensor positions of shape (batch_size, x_dim, num_sensors...).
        u: Tensor of sensor values of shape (batch_size, u_dim, num_sensors...).
        y: Tensor of evaluation coordinates of shape (batch_size, y_dim, num_evaluations...).
        v: Tensor of _predicted_ values of shape (batch_size, v_dim, num_evaluations...).

    """

PhysicsInformedLoss(pde)

Physics-informed loss function for training operators in continuiti.

loss = pde(x, u, y, op(x, u, y))

PARAMETER	DESCRIPTION
pde	Maps evaluation coordinates \(y\) and callable \(v\) to PDE loss. TYPE: PDE

Source code in src/continuiti/pde/physicsinformed.py

def __init__(self, pde: PDE):
    self.pde = pde

__call__(op, x, u, y, _)

Evaluate loss.

PARAMETER	DESCRIPTION
op	Operator object. TYPE: Operator
x	Tensor of sensor positions of shape (batch_size, x_dim, num_sensors...). TYPE: Tensor
u	Tensor of sensor values of shape (batch_size, u_dim, num_sensors...). TYPE: Tensor
y	Tensor of evaluation coordinates of shape (batch_size, y_dim, num_evaluations...). TYPE: Tensor
v	Ignored.

Source code in src/continuiti/pde/physicsinformed.py

def __call__(
    self,
    op: Operator,
    x: torch.Tensor,
    u: torch.Tensor,
    y: torch.Tensor,
    _: torch.Tensor,
) -> torch.Tensor:
    """Evaluate loss.

    Args:
        op: Operator object.
        x: Tensor of sensor positions of shape (batch_size, x_dim, num_sensors...).
        u: Tensor of sensor values of shape (batch_size, u_dim, num_sensors...).
        y: Tensor of evaluation coordinates of shape (batch_size, y_dim, num_evaluations...).
        v: Ignored.
    """
    # Call operator
    v_pred = op(x, u, y)

    # Get pde loss
    return self.pde(x, u, y, v_pred)

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Last update: 2024-08-20
Created: 2024-08-20