# Copyright 2022 Huawei Technologies Co., Ltd
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
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# ============================================================================
"""Burgers 1D problem"""
import numpy as np
from sympy import diff, Function, symbols
from .sympy_pde import PDEWithLoss
from ..loss import get_loss_metric
[文档]class Burgers(PDEWithLoss):
r"""
Base class for Burgers 1-D problem based on PDEWithLoss.
Args:
model (mindspore.nn.Cell): Network for training.
loss_fn (str): Define the loss function. Default: mse.
Supported Platforms:
``Ascend`` ``GPU``
Examples:
>>> from mindflow.pde import Burgers
>>> from mindspore import nn, ops
>>> class Net(nn.Cell):
... def __init__(self, cin=2, cout=1, hidden=10):
... super().__init__()
... self.fc1 = nn.Dense(cin, hidden)
... self.fc2 = nn.Dense(hidden, hidden)
... self.fcout = nn.Dense(hidden, cout)
... self.act = ops.Tanh()
...
... def construct(self, x):
... x = self.act(self.fc1(x))
... x = self.act(self.fc2(x))
... x = self.fcout(x)
... return x
>>> model = Net()
>>> problem = Burgers(model)
>>> print(problem.pde())
burgers: u(x, t)Derivative(u(x, t), x) + Derivative(u(x, t), t) - 0.00318309897556901Derivative(u(x, t), (x, 2))
Item numbers of current derivative formula nodes: 3
{'burgers': u(x, t)Derivative(u(x, t), x) + Derivative(u(x, t), t) - 0.00318309897556901Derivative(u(x, t),
(x, 2))}
"""
def __init__(self, model, loss_fn="mse"):
self.mu = np.float32(0.01 / np.pi)
self.x, self.t = symbols('x t')
self.u = Function('u')(self.x, self.t)
self.in_vars = [self.x, self.t]
self.out_vars = [self.u]
super(Burgers, self).__init__(model, self.in_vars, self.out_vars)
if isinstance(loss_fn, str):
self.loss_fn = get_loss_metric(loss_fn)
else:
self.loss_fn = loss_fn
[文档] def pde(self):
"""
Define Burgers 1-D governing equations based on sympy, abstract method.
Returns:
dict, user defined sympy symbolic equations.
"""
burgers_eq = diff(self.u, (self.t, 1)) + self.u * diff(self.u, (self.x, 1)) - \
self.mu * diff(self.u, (self.x, 2))
equations = {"burgers": burgers_eq}
return equations