2023.11.23
閱讀的deepxde version: 1.9.0

1. train_aux_vars ，即pde當中的第三個參數

這個變量的含義困惑很久。最后發現就是operator learning的PDEs方程parameters。
脈絡：def pde aux_vars->
deepxde目前支持tf1最多，但是對其他框架也有支持，倉庫的主要維護者Lu Lu跟百度應該有合作，目前對paddlepaddle的支持正在提升。因此，實際上對于很多函數，作者寫了4遍，每個框架都寫一遍，基本同樣的功能，但里面的細節不同。

pdeoperator.py 中的PDEoperator坐標類的train_next_batch方法

（注意：我這里命名是按著記憶直接寫的，不是源碼中的真實名稱）

    def train_next_batch(self, batch_size=None):if self.train_x is None:func_feats = self.func_space.random(self.num_func)func_vals = self.func_space.eval_batch(func_feats, self.eval_pts)vx = self.func_space.eval_batch(func_feats, self.pde.train_x[:, self.func_vars])self.train_x = (func_vals, self.pde.train_x)self.train_aux_vars = vxif self.batch_size is None:return self.train_x, self.train_y, self.train_aux_varsindices = self.train_sampler.get_next(self.batch_size)traix_x = (self.train_x[0][indices], self.train_x[1])return traix_x, self.train_y, self.train_aux_vars[indices]

model.py

def set_data_train(self, X_train, y_train, train_aux_vars=None):self.X_train = X_trainself.y_train = y_trainself.train_aux_vars = train_aux_vars

            self.train_state.set_data_train(*self.data.train_next_batch(self.batch_size))

根據這些代碼段順藤摸瓜確定了train_aux_vars的定位：Parameters of PDEs.

        def outputs_losses(training, inputs, targets, auxiliary_vars, losses_fn):self.net.auxiliary_vars = auxiliary_vars# Don't call outputs() decorated by @tf.function above, otherwise the# gradient of outputs wrt inputs will be lost here.outputs_ = self.net(inputs, training=training)# Data losseslosses = losses_fn(targets, outputs_, loss_fn, inputs, self)if not isinstance(losses, list):losses = [losses]# Regularization lossif self.net.regularizer is not None:losses += [tf.math.reduce_sum(self.net.losses)]losses = tf.convert_to_tensor(losses)# Weighted lossesif loss_weights is not None:losses *= loss_weightsreturn outputs_, losses

值得一提的是作者從頭到尾都在使用 TrainState 來儲存訓練當中的各種變量。

class TrainState:def __init__(self):self.epoch = 0self.step = 0# Current dataself.X_train = Noneself.y_train = Noneself.train_aux_vars = Noneself.X_test = Noneself.y_test = Noneself.test_aux_vars = None# Results of current step# Train resultsself.loss_train = Noneself.y_pred_train = None# Test resultsself.loss_test = Noneself.y_pred_test = Noneself.y_std_test = Noneself.metrics_test = None# The best results correspond to the min train lossself.best_step = 0self.best_loss_train = np.infself.best_loss_test = np.infself.best_y = Noneself.best_ystd = Noneself.best_metrics = Nonedef set_data_train(self, X_train, y_train, train_aux_vars=None):self.X_train = X_trainself.y_train = y_trainself.train_aux_vars = train_aux_varsdef set_data_test(self, X_test, y_test, test_aux_vars=None):self.X_test = X_testself.y_test = y_testself.test_aux_vars = test_aux_varsdef update_best(self):if self.best_loss_train > np.sum(self.loss_train):self.best_step = self.stepself.best_loss_train = np.sum(self.loss_train)self.best_loss_test = np.sum(self.loss_test)self.best_y = self.y_pred_testself.best_ystd = self.y_std_testself.best_metrics = self.metrics_testdef disregard_best(self):self.best_loss_train = np.inf

由train state可見pde前兩個變量的含義就是偏微分方程組的坐標輸入和解輸出