neuralop.losses.LpLoss

class neuralop.losses.LpLoss(d=1, p=2, measure=1.0, reduction='sum')[source]

LpLoss provides the L-p norm between two discretized d-dimensional functions. Note that LpLoss always averages over the spatial dimensions.

Note

In function space, the Lp norm is an integral over the entire domain. To ensure the norm converges to the integral, we scale the matrix norm by quadrature weights along each spatial dimension.

If no quadrature is passed at a call to LpLoss, we assume a regular discretization and take 1 / measure as the quadrature weights.

Parameters:

dint, optional

dimension of data on which to compute, by default 1

pint, optional

order of L-norm, by default 2 L-p norm: [sum_{i=0}^n (x_i - y_i)**p] ** (1/p)

measurefloat or list, optional

measure of the domain, by default 1.0 either single scalar for each dim, or one per dim

To perform quadrature, LpLoss scales measure by the size of each spatial dimension of x, and multiplies them with ||x-y||, such that the final norm is a scaled average over the spatial dimensions of x.

reductionstr, optional

whether to reduce across the batch and channel dimensions by summing (‘sum’) or averaging (‘mean’)

Warning

LpLoss always reduces over the spatial dimensions according to self.measure. reduction only applies to the batch and channel dimensions.

Attributes:

name

Methods

__call__(y_pred, y, **kwargs)	Call self as a function.
abs(x, y[, quadrature])	absolute Lp-norm
reduce_all(x)	reduce x across the batch according to self.reduction
rel(x, y)	rel: relative LpLoss computes ||x-y||/||y||
uniform_quadrature(x)	uniform_quadrature creates quadrature weights scaled by the spatial size of x to ensure that LpLoss computes the average over spatial dims.

Examples

```

uniform_quadrature(x)[source]

uniform_quadrature creates quadrature weights scaled by the spatial size of x to ensure that LpLoss computes the average over spatial dims.

Parameters:

xtorch.Tensor

input data

Returns:

quadraturelist

list of quadrature weights per-dim

reduce_all(x)[source]

reduce x across the batch according to self.reduction

abs(x, y, quadrature=None)[source]

absolute Lp-norm

Parameters:

xtorch.Tensor

inputs

ytorch.Tensor

targets

quadraturefloat or list, optional

quadrature weights for integral either single scalar or one per dimension

rel(x, y)[source]

rel: relative LpLoss computes ||x-y||/||y||

Parameters:

xtorch.Tensor

inputs

ytorch.Tensor

targets