Torch Forecasting Models

This document was written for darts version 0.15.0 and later.

We assume that you already know about covariates in Darts. If you’re new to the topic we recommend you to read our guide on covariates first.

Content of this section

The first subsection covers the most important points about Torch Forecasting Models (TFMs):

  • How to use TFMs

  • Top-level look at chunks

  • TFM covariates support

  • Time span requirements for target and covariate series

The second subsection gives an in-depth guide of how input data is used when training and predicting with TFMs.

Introduction

In Darts, Torch Forecasting Models (TFMs) are broadly speaking “machine learning based” models, which denote PyTorch-based (deep learning) models.

TFMs train and predict on fixed-length chunks (sub-samples) of your input target and *_covariates series (if supported). Target is the series for which we want to predict the future, *_covariates are the past and / or future covariates.

Each chunk contains an input chunk - representing the sample’s past - and an output chunk - the sample’s future. The sample’s prediction point lies at the end of the input chunk. The length of these chunks has to be specified at model creation with parameters input_chunk_length and output_chunk_length (more on chunks in the next subsection).

# model that looks 7 time steps back (past) and 1 time step ahead (future)
model = SomeTorchForecastingModel(input_chunk_length=7,
                                  output_chunk_length=1,
                                  **model_kwargs)

All TFMs can be trained on single or multiple target series and, depending on their covariate support (covered in this subsection), past_covariates and / or future_covariates. When using covariates you have to supply one dedicated past and / or future covariates series for each target series.

Optionally, you can use a validation set with dedicated covariates during training. If the covariates have the required time spans, you can use the same for training, validation and prediction. (covered in this subsection)

# fit the model on a single target series with optional past and / or future covariates
model.fit(target,
          past_covariates=past_covariates,
          future_covariates=future_covariates,
          val_series=target_val,  # optionally, use a validation set
          val_past_covariates=past_covariates_val,
          val_future_covariates=future_covariates_val)

# fit the model on multiple target series
model.fit([target, target2, ...],
          past_covariates=[past_covariates, past_covariates2, ...],
          ...
          )

You can produce forecasts for any input target TimeSeries or for several targets given as a sequence of TimeSeries. This will also work on series that have not been seen during training, as long as each series contains at least input_chunk_length time steps.

# predict the next n=3 time steps for any input series with `series`
prediction = model.predict(n=3,
                           series=target,
                           past_covariates=past_covariates,
                           future_covariates=future_covariates)

If you want to know more about the training and prediction process of our Torch Forecasting Models and how they work with covariates, read on.

Top level look at training and predicting with chunks

In Figure 1 you can see how your data is distributed to the input and output chunks for each sample when calling fit() or predict(). For this example we look at data with daily frequency. The input chunk extracts values from target and optionally from past_covariates and / or future_covariates that fall into the input chunk time span. These “past” values of future_covariates are called “historic future covariates”.

The output chunk only takes optional future_covariates values that fall into the output chunk time span. The future values of our past_covariates - “future past covariates” - are only used to provide the input chunk of upcoming samples with new data.

All this information is used to predict the “future target” - the next output_chunk_length points after the end of “past target”.

figure0

Figure 1: Top level look at training / predicting on chunks with Torch Forecasting Models

When calling predict() and depending on your forecast horizon n, the model can either predict in one go (if n <= output_chunk_length), or auto-regressively, by predicting on multiple chunks in the future (if n > output_chunk_length). That is the reason why when predicting with past_covariates you might have to supply additional “future values of your past_covariates“.

Torch Forecasting Model Covariates Support

Under the hood, Darts has 5 types of {X}CovariatesModel classes implemented to cover different combinations of the covariate types mentioned before:

Table 1: Darts’ “{X}CovariatesModels” covariate support

Each Torch Forecasting Model inherits from one {X}CovariatesModel (covariate class names are abbreviated by the X-part):

Table 2: Darts’ Torch Forecasting Model covariate support

Required target time spans for training, validation and prediction

The relevant data is extracted automatically by the models, based on the time axes of the series. You can use the same covariates series for both fit() and predict() if they meet the requirements below.

Training only works if at least one sample with an input and output chunk can be extracted from the data you passed to fit(). This applies both to training and validation data. In terms of minimum required time spans, this means:

  • target series of minimum length input_chunk_length + output_chunk_length

  • *_covariates time span requirements for fit() from covariates guide section 2.3.

For prediction you have to supply the target series that you wish to forecast. For any forecast horizon n the minimum time span requirements are:

  • target series of minimum length input_chunk_length

  • *_covariates time span requirements for predict() also from from covariates guide section 2.3.

Side note: Our *RNNModels accept a training_length parameter at model creation instead of output_chunk_length. Internally the output_chunk_length for these models is automatically set to 1. For training, past target must have a minimum length of training_length + 1 and for prediction, a length of input_chunk_length.

In-depth look at how input data is used when training and predicting with TFMs

Training

Let’s have a look at how the models work under the hood.

Let’s assume we run an ice-cream shop and we want to predict sales for the next day. We have one year (365 days) past data of our end-of-day ice-cream sales and of the average measured daily ambient temperature. We also noticed that our ice-cream sales depend on the day of the week so we want to include this in our model.

  • past target: actual past ice-cream sales ice_cream_sales

  • future target: predict the ice-cream sales for the next day

  • past covariates: measured average daily temperatures in the past temperature

  • future covariates: day of the week for past and future weekday

Checking Table 1, a model that would accommodate this kind of covariates would be a SplitCovariatesModel (if we don’t use historic values of future covariates), or MixedCovariatesModel (if we do). We choose a MixedCovariatesModel - the TFTModel.

Imagine that we saw a pattern in our past ice cream sales that repeated week after week. So we set input_chunk_length = 7 days to let the model look back an entire week into the past. The output_chunk_length can be set to 1 day to predict the next day.

Now we can create a model and train it! Figure 2 shows you how TFTModel will use our data.

from darts.models import TFTModel

model = TFTModel(input_chunk_length=7, output_chunk_length=1)
model.fit(series=ice_cream_sales,
          past_covariates=temperature,
          future_covariates=weekday)
figure4

Figure 2: Overview of a single sequence from our ice-cream sales example; Mon1 - Sun1 stand for the first 7 days from our training dataset (week 1 of the year). Mon2 is the Monday of week 2.

When calling fit(), the models will build an appropriate darts.utils.data.TrainingDataset, which specifies how to slice the data to obtain training samples. If you want to control this slicing yourself, you can instantiate your own TrainingDataset and call model.fit_from_dataset() instead of fit(). By default, most models (though not all) will build sequential datasets, which basically means that all sub-slices of length input_chunk_length + output_chunk_length in the provided series will be used for training.

So during training, the torch models will go through the training data in sequences (see Figure 3). Using information from the input chunk and output chunk, the model predicts the future target on the output chunk. The training loss is evaluated between the predicted future target and the actual target value on the output chunk. The model trains itself by minimizing the loss over all sequences.

figure5

Figure 3: Prediction and loss evaluation in a single sequence

After having completed computations on the first sequence, the model moves to the next one and performs the same training steps. The starting point of each sequence is selected randomly from the sequential dataset. Figure 4 shows how this would look like if by pure chance the second sequence started one time step (day) after the first.

This sequence-to-sequence process is repeated until all 365 days were covered.

Side note: Having “long” target series can result in a very large number of training sequences / samples. You can set an upper bound for the number of sequences / samples per target that the model should be trained on with fit()-parameter max_samples_per_ts. This will take the most recent sequences for every target series (sequences closest to target end).

# fit only on the 10 "most recent" sequences
model.fit(target, max_samples_per_ts=10)
figure6

Figure 4: Sequence-to-sequence: Move to next sequence and repeat training steps

Training with a validation dataset

You can also train your models with a validation dataset:

# create train and validation sets
ice_cream_sales_train, ice_cream_sales_val = ice_cream_sales.split_after(training_cutoff)

# train with validation set
model.fit(series=ice_cream_sales_train,
          past_covariates=temperature,
          future_covariates=weekday,
          val_series=ice_cream_sales_val,
          val_past_covariates=temperature,
          val_future_covariates=weekday)

If you split your data, you have to define a training_cutoff (a date or fraction at which to split the dataset) so that both the train and validation datasets satisfy the minimum length requirements from this subsection

Instead of splitting by time, you can also use another subset of time series as validation set.

The model trains itself the same way as before but additionally evaluates the loss on the validation dataset. If you want to keep track of the best performing model on the validation set, you have to enable checkpoint saving as shown next.

Saving and Loading Model States

Per default, the models don’t automatically save any checkpoints. If you want to keep track of the best performing model on the validation set and the latest 5 epochs, you have to enable checkpoint saving at model creation:

model = SomeTorchForecastingModel(..., model_name='MyModel', save_checkpoints=True)

# checkpoints are saved automatically
model.fit(...)

# load the model state that performed best on validation set
best_model = model.load_from_checkpoint(model_name='MyModel', best=True)

You can also save or load manually:

model.save_model(model_path)
loaded_model = model.load_model(model_path)

/!Warning /!At this stage of Darts development, we are not (yet) ensuring backward compatibility, so it might not always be possible to load a model saved by an older version of the library.

Forecast/Prediction

After having trained the model, we want to predict the future ice-cream sales for any number of days after our 365 days training data.

The actual prediction works very similar to how we trained the data on sequences. Depending on the number of days we want to predict - the forecast horizon n - we distinguish between two cases:

  • If n <= output_chunk_length: we can predict n in one go (using one “internal model call”)

    • in our example: predict the next day’s ice-cream sales (n = 1)

  • If n > output_chunk_length: we must predict n by calling the internal model multiple times. Each call outputs output_chunk_length prediction points. We go through as many calls as needed until we get to the final n prediction points, in an auto-regressive fashion.

    • in our example: predict ice-cream sales for the next 3 days at once (n = 3)

    To do this we have to supply additional past_covariates for the next n - output_chunk_length = 2 time steps (days) after the end of our 365 days training data. Unfortunately, we do not have measured temperature for the future. But let’s assume we have access to temperature forecasts for the next 2 days. We can just append them to temperature and the prediction will work!

    temperature = temperature.concatenate(temperature_forecast, axis=0)
    
prediction = model.predict(n=n,
                           series=ice_cream_sales_train,
                           past_covariates=temperature,
                           future_covariates=weekday)
figure7

**Figure 5: Forecast with a single sequence for n <= output_chunk_length**

figure8

**Figure 6: Auto-regressive forecast for n > output_chunk_length**

Performance Recommendations

This section recaps the main factors impacting the performance when training and using torch-based models.

Build your TimeSeries using 32-bits data

The models in Darts will dynamically cast themselves (to 64 or 32-bits) to follow the dtype in the TimeSeries. Large performance and memory gains can often be obtained when everything (data and model) is in float32. To achieve this, it is enough to build your TimeSeries from arrays (or Dataframe-backing array) having dtype np.float32, or simply call my_series32 = my_series.astype(np.float32). Calling my_series.dtype gives you the dtype of your TimeSeries.

Use a GPU

In many cases using a GPU will provide a drastic speedup compared to CPU. It can also incur some overheads (for transferring data to/from the GPU), so some testing and tuning is often necessary. We refer to our GPU/TPU guide for more information on how to setup a GPU (or a TPU) via PyTorch Lightning.

Tune the batch size

A larger batch size tends to speed up the training because it reduces the number of backward passes per epoch and has the potential to better parallelize computation. However it also changes the training dynamics (e.g. you might need more epochs, and the convergence dynamics is affected). Furthermore larger batch sizes increase memory consumption. So here too some testing is required.

Tune num_loader_workers

All deep learning models in Darts have a parameter num_loader_workers in their fit() and predict() functions, which configures the num_workers parameter in the PyTorch DataLoaders. By default it is set to 0, which means that the main process will also take care of loading the data. Setting num_workers > 0 will use additional workers to load the data. This typically incurs some overhead (notably increasing memory consumption), but in some cases it can also substantially improve performance. The ideal value depends on many factors such as the batch size, whether you are using a GPU, the number of CPU cores available, and whether loading the data involved I/O operations (if the series are stored on disk).

Small models first

Of course one of the main factors affecting performance is the model size (number of parameters) and the number of operations required by forward/backward passes. Models in Darts can be tuned (e.g. number of layers, attention heads, widths etc), and these hyper-parameters tend to have a large impact on performance. When starting out, it is a good idea to build models of modest size first.

Data in Memory and I/O bottlenecks

It’s helpful to load all your TimeSeries in memory upfront if you can. Darts offers the possibility to train models on any Sequence[TimeSeries], which means that for big datasets, you can write your own Sequence implementation, and read the time series lazily from disk. This will typically incur a high I/O cost, though. So when training on multiple series, first try to build a simple List[TimeSeries] upfront, and see if it holds in the computer memory.

Do not use all possible sub-series for training

By default, when calling fit(), the models in Darts will build a TrainingDataset instance that is suitable for the model that you are using (e.g., PastCovariatesTorchModel, FutureCovariatesTorchModel, etc.). By default, these training datasets will often contain all possible consecutive (input, output) subseries present in each TimeSeries. If your TimeSeries are long, this can result in a large amount of training samples, which directly (linearly) impacts the time required to train the model for one epoch. You have two options to limit this:

  • Specify some max_samples_per_ts argument to the fit() function. This will use only the most recent max_samples_per_ts samples per TimeSeries for training.

  • If this option does not do what you want, you can implement your own TrainingDataset instance, and define how to slice your TimeSeries for training yourself. We suggest to have a look at this submodule to see examples of how to do it.


Early Stop

Early stopping can be an efficient way to cut down on the training time. Using early stopping trains the model for fewer epochs by stopping the training when the validation loss does not improve for a set number of nr_epochs_val_period.

Early stopping can be easily implemented on all Darts neural networks based models, by leveraging PyTorch Lightning’s EarlyStopping callback, as shown in the example code below.

from darts.models import NBEATSModel
from darts.datasets import AirPassengersDataset
from pytorch_lightning.callbacks import EarlyStopping
from torchmetrics import MeanAbsolutePercentageError
import pandas as pd
from darts.dataprocessing.transformers import Scaler

# Read data:
series = AirPassengersDataset().load()

# Create training and validation sets:
train, val = series.split_after(pd.Timestamp(year=1957, month=12, day=1))

# Normalize the time series (note: we avoid fitting the transformer on the validation set)
transformer = Scaler()
transformer.fit(train)
train = transformer.transform(train)
val = transformer.transform(val)

# A TorchMetric or val_loss can be used as the monitor
torch_metrics = MeanAbsolutePercentageError()

# Early stop callback
my_stopper = EarlyStopping(
    monitor="val_MeanAbsolutePercentageError",  # "val_loss",
    patience=5,
    min_delta=0.05,
    mode='min',
)
pl_trainer_kwargs = {"callbacks": [my_stopper]}

# Create the model
model = NBEATSModel(
    input_chunk_length=24,
    output_chunk_length=12,
    n_epochs=500,
    torch_metrics=torch_metrics,
    pl_trainer_kwargs=pl_trainer_kwargs)

model.fit(
    series=train,
    val_series=val,
)

Hyperparameter Tuning with Ray Tune

Hyperparameter tuning is a great way to find the best parameters for your model. Ray Tune provides a convenient way to speed this process up with automatic pruning.

Here is an example of how to use Ray Tune to with the NBEATSModel model using the Asynchronous Hyperband scheduler.

from darts.models import NBEATSModel
from darts.datasets import AirPassengersDataset
from pytorch_lightning.callbacks import EarlyStopping
import pandas as pd
from darts.dataprocessing.transformers import Scaler
from torchmetrics import MetricCollection, MeanAbsolutePercentageError, MeanAbsoluteError
from ray import tune
from ray.tune import CLIReporter
from ray.tune.integration.pytorch_lightning import TuneReportCallback
from ray.tune.schedulers import ASHAScheduler

def train_model(model_args, callbacks, train, val):
    torch_metrics = MetricCollection([MeanAbsolutePercentageError(), MeanAbsoluteError()])
    # Create the model using model_args from Ray Tune
    model = NBEATSModel(
        input_chunk_length=24,
        output_chunk_length=12,
        n_epochs=500,
        torch_metrics=torch_metrics,
        pl_trainer_kwargs={"callbacks": callbacks, "enable_progress_bar": False},
        **model_args)

    model.fit(
        series=train,
        val_series=val,
    )

# Read data:
series = AirPassengersDataset().load()

# Create training and validation sets:
train, val = series.split_after(pd.Timestamp(year=1957, month=12, day=1))

# Normalize the time series (note: we avoid fitting the transformer on the validation set)
transformer = Scaler()
transformer.fit(train)
train = transformer.transform(train)
val = transformer.transform(val)

# Early stop callback
my_stopper = EarlyStopping(
    monitor="val_MeanAbsolutePercentageError",
    patience=5,
    min_delta=0.05,
    mode='min',
)

# set up ray tune callback
tune_callback = TuneReportCallback(
    {
        "loss": "val_Loss",
        "MAPE": "val_MeanAbsolutePercentageError",
    },
    on="validation_end",
)

# define the hyperparameter space
config = {
    "batch_size": tune.choice([16, 32, 64, 128]),
    "num_blocks": tune.choice([1, 2, 3, 4, 5]),
    "num_stacks": tune.choice([32, 64, 128]),
    "dropout": tune.uniform(0, 0.2),
}

reporter = CLIReporter(
    parameter_columns=list(config.keys()),
    metric_columns=["loss", "MAPE", "training_iteration"],
)

resources_per_trial = {"cpu": 8, "gpu": 1}

# the number of combinations to try
num_samples = 10

scheduler = ASHAScheduler(max_t=1000, grace_period=3, reduction_factor=2)

train_fn_with_parameters = tune.with_parameters(
    train_model, callbacks=[my_stopper, tune_callback], train=train, val=val,
)

analysis = tune.run(
    train_fn_with_parameters,
    resources_per_trial=resources_per_trial,
    # Using a metric instead of loss allows for
    # comparison between different likelihood or loss functions.
    metric="MAPE",  # any value in TuneReportCallback.
    mode="min",
    config=config,
    num_samples=num_samples,
    scheduler=scheduler,
    progress_reporter=reporter,
    name="tune_darts",
)

print("Best hyperparameters found were: ", analysis.best_config)

Example Benchmark

As an example, we show here the time required to train one epoch on the first 80% of the energy dataset (darts.datasets.EnergyDataset), which consists of one multivariate series that is 28050 timesteps long and has 28 dimensions. We train two models; NBEATSModel and TFTModel, with default parameters and input_chunk_length=48 and output_chunk_length=12 (which results in 27991 training samples with default sequential training datasets). For the TFT model, we also set the parameter add_cyclic_encoder='hour'. The tests are made on a Intel CPU i9-10900K CPU @ 3.70GHz, with an Nvidia RTX 2080s GPU, 32 GB of RAM. All TimeSeries are pre-loaded in memory and given to the models as a list.

Model

Dataset

dtype

CUDA

Batch size

num workers

time per epoch

NBEATSModel

Energy

64

no

32

0

283s

NBEATSModel

Energy

64

no

32

2

285s

NBEATSModel

Energy

64

no

32

4

282s

NBEATSModel

Energy

64

no

1024

0

58s

NBEATSModel

Energy

64

no

1024

2

57s

NBEATSModel

Energy

64

no

1024

4

58s

NBEATSModel

Energy

64

yes

32

0

63s

NBEATSModel

Energy

64

yes

32

2

62s

NBEATSModel

Energy

64

yes

1024

0

13.3s

NBEATSModel

Energy

64

yes

1024

2

12.1s

NBEATSModel

Energy

64

yes

1024

4

12.3s

NBEATSModel

Energy

32

no

32

0

117s

NBEATSModel

Energy

32

no

32

2

115s

NBEATSModel

Energy

32

no

32

4

117s

NBEATSModel

Energy

32

no

1024

0

28.4s

NBEATSModel

Energy

32

no

1024

2

27.4s

NBEATSModel

Energy

32

no

1024

4

27.5s

NBEATSModel

Energy

32

yes

32

0

41.5s

NBEATSModel

Energy

32

yes

32

2

40.6s

NBEATSModel

Energy

32

yes

1024

0

2.8s

NBEATSModel

Energy

32

yes

1024

2

1.65

NBEATSModel

Energy

32

yes

1024

4

1.8s

TFTModel

Energy

64

no

32

0

78s

TFTModel

Energy

64

no

32

2

72s

TFTModel

Energy

64

no

32

4

72s

TFTModel

Energy

64

no

1024

0

46s

TFTModel

Energy

64

no

1024

2

38s

TFTModel

Energy

64

no

1024

4

39s

TFTModel

Energy

64

yes

32

0

125s

TFTModel

Energy

64

yes

32

2

115s

TFTModel

Energy

64

yes

1024

0

59s

TFTModel

Energy

64

yes

1024

2

50s

TFTModel

Energy

64

yes

1024

4

50s

TFTModel

Energy

32

no

32

0

70s

TFTModel

Energy

32

no

32

2

62.6s

TFTModel

Energy

32

no

32

4

63.6

TFTModel

Energy

32

no

1024

0

31.9s

TFTModel

Energy

32

no

1024

2

45s

TFTModel

Energy

32

no

1024

4

44s

TFTModel

Energy

32

yes

32

0

73s

TFTModel

Energy

32

yes

32

2

58s

TFTModel

Energy

32

yes

1024

0

41s

TFTModel

Energy

32

yes

1024

2

31s

TFTModel

Energy

32

yes

1024

4

31s