code: from pathlib import Path
  import pickle
  import warnings
  
  import numpy as np
  import pandas as pd
  from pandas.core.common import SettingWithCopyWarning
  import pytorch_lightning as pl
  from pytorch_lightning.callbacks import EarlyStopping, LearningRateMonitor
  from pytorch_lightning.loggers import TensorBoardLogger
  import torch
  
  from pytorch_forecasting import EncoderNormalizer, GroupNormalizer, TimeSeriesDataSet
  from pytorch_forecasting.data import NaNLabelEncoder
  from pytorch_forecasting.data.examples import generate_ar_data
  from pytorch_forecasting.metrics import NormalDistributionLoss
  from pytorch_forecasting.models.deepar import DeepAR
  from pytorch_forecasting.utils import profile
  
  warnings.simplefilter("error", category=SettingWithCopyWarning)
  
  
  data = generate_ar_data(seasonality=10.0, timesteps=400, n_series=100)
  data["static"] = "2"
  data["date"] = pd.Timestamp("2020-01-01") + pd.to_timedelta(data.time_idx, "D")
  validation = data.series.sample(20)
  
  max_encoder_length = 60
  max_prediction_length = 20
  
  training_cutoff = data["time_idx"].max() - max_prediction_length
  
  training = TimeSeriesDataSet(
      data[lambda x: ~x.series.isin(validation)],
      time_idx="time_idx",
      target="value",
      categorical_encoders={"series": NaNLabelEncoder().fit(data.series)},
      group_ids=["series"],
      static_categoricals=["static"],
      min_encoder_length=max_encoder_length,
      max_encoder_length=max_encoder_length,
      min_prediction_length=max_prediction_length,
      max_prediction_length=max_prediction_length,
      time_varying_unknown_reals=["value"],
      time_varying_known_reals=["time_idx"],
      target_normalizer=GroupNormalizer(groups=["series"]),
      add_relative_time_idx=False,
      add_target_scales=True,
      randomize_length=None,
  )
  
  validation = TimeSeriesDataSet.from_dataset(
      training,
      data[lambda x: x.series.isin(validation)],
      # predict=True,
      stop_randomization=True,
  )
  batch_size = 64
  train_dataloader = training.to_dataloader(train=True, batch_size=batch_size, num_workers=0)
  val_dataloader = validation.to_dataloader(train=False, batch_size=batch_size, num_workers=0)
  
  # save datasets
  training.save("training.pkl")
  validation.save("validation.pkl")
  
  early_stop_callback = EarlyStopping(monitor="val_loss", min_delta=1e-4, patience=5, verbose=False, mode="min")
  lr_logger = LearningRateMonitor()
  
  trainer = pl.Trainer(
      max_epochs=10,
      gpus=-1,
      gradient_clip_val=0.1,
      limit_train_batches=30,
      limit_val_batches=3,
      # fast_dev_run=True,
      # logger=logger,
      # profiler=True,
      callbacks=[lr_logger, early_stop_callback],
  )
  
  
  deepar = DeepAR.from_dataset(
      training,
      learning_rate=0.1,
      hidden_size=32,
      dropout=0.1,
      loss=NormalDistributionLoss(),
      log_interval=10,
      log_val_interval=3,
      # reduce_on_plateau_patience=3,
  )
  print(f"Number of parameters in network: {deepar.size()/1e3:.1f}k")
  
  # # find optimal learning rate
  # deepar.hparams.log_interval = -1
  # deepar.hparams.log_val_interval = -1
  # trainer.limit_train_batches = 1.0
  # res = trainer.tuner.lr_find(
  #     deepar, train_dataloaders=train_dataloader, val_dataloaders=val_dataloader, min_lr=1e-5, max_lr=1e2
  # )
  
  # print(f"suggested learning rate: {res.suggestion()}")
  # fig = res.plot(show=True, suggest=True)
  # fig.show()
  # deepar.hparams.learning_rate = res.suggestion()
  
  torch.set_num_threads(10)
  trainer.fit(
      deepar,
      train_dataloaders=train_dataloader,
      val_dataloaders=val_dataloader,
  )
  
  # calcualte mean absolute error on validation set
  actuals = torch.cat([y for x, (y, weight) in iter(val_dataloader)])
  predictions = deepar.predict(val_dataloader)
  print(f"Mean absolute error of model: {(actuals - predictions).abs().mean()}")
  
  # # plot actual vs. predictions
  # raw_predictions, x = deepar.predict(val_dataloader, mode="raw", return_x=True)
  # for idx in range(10):  # plot 10 examples
  #     deepar.plot_prediction(x, raw_predictions, idx=idx, add_loss_to_title=True)
  
apis: torch.set_num_threads pandas.to_timedelta pandas.Timestamp