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Started writing about GRU model

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Victor Mylle
2024-04-22 15:54:25 +02:00
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2
Reports/Thesis/sections/background.tex
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@@ -4,6 +4,8 @@
% -> enkel forecast is vaak brak -> reinforcement learning is lastig -> generatief modelleren, veel generaties om mee te trainen
% - Achtergrond electrititetismarkt
% - Achtergrond Generatief modelleren (van NRV)
% - TODO: Achtergrond RNN?
\subsection{Electricity market}
The electricity market consists of many different parties who all work together and want to make a profit in the end. An overview of the most important parties can be found in Table \ref{tab:parties}.

108
Reports/Thesis/sections/nrv_prediction.tex
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@@ -70,7 +70,7 @@ The NRV value for a quarter can be sampled from the reconstructed cumulative dis
TODO: Explain non autoregressive and autoregressive models\\\\
Two methods exist to sample full-day NRV values. The first method is a non-autoregressive model. This model outputs the quantiles for every quarter. For each quarter, the cumulative distribution function is reconstructed and sampled. The model is conditioned on the NRV timeline of the previous day. This consists of 96 values. The second method is an autoregressive model. This model outputs the quantiles for the next quarter for which the NRV distribution is wanted. This model is conditioned on the 96 previous NRV values. When a full-day sample of the NRV is wanted, the model is used recursively. The model predicts the quantiles for the next quarter, the cumulative distribution function is reconstructed and the NRV value is sampled. This value can then be used as input for the next quarter. This process is repeated until a full-day sample is obtained. Autoregressive problems suffer from the problem that errors in the prediction of early quarters, propagate through the model and can lead to larger errors in later quarters.
\\\\
\subsubsection{Training}
\subsubsection{Training} \label{subsubsec:quantile_regression_training}
The quantile regression model is trained using the pinball loss function, also known as the quantile loss. The model outputs the quantile values for the NRV. The quantile values themselves are not available in the training data. Only the real NRV values are known. The loss function is defined as:
\begin{equation}
L_\tau(y, \hat{y}) = \begin{cases}
@@ -361,9 +361,20 @@ Because of error propagation in the autoregressive model, the outputted quantile
% TODO: Talk about the over/underestimation of the quantiles for the models. Plots have been made for this.
\subsubsection{Non-linear Model}
More complex models can also be used to model the NRV. The same training and evaluation process can be used as the linear model. The training loop is the same but the model architecture is different. Quantile regression is still used so the model outputs the quantiles for the NRV. The model is trained using the pinball loss function and the MAE, MSE, CRPS metrics are calculated on the test set. A simple feedforward neural network is used as a non-linear model. The model architecture used is shown in Table \ref{tab:non_linear_model_architecture}. First, if the inputs include the quarter of the day, the quarter embedding is calculated and concatenated with the other input features. These features are then passed to a linear layer with a chosen hidden size. The output of this layer is passed through a ReLu activation function and a dropout layer. This process is repeated N times to increase the depth of the model. The output of the last linear layer is the quantiles for the NRV prediction. For an autoregressive model, this is just the quantiles for one quarter. If the model is non-autoregressive, the quantiles for every quarter are outputted. The number of outputs is then the number of quarters in a day multiplied by the number of quantiles used.
More complex models, such as non-linear neural networks, offer the possibility of capturing more complex patterns in the NRV data. These patterns can include nonlinear relationships between the input features and the NRV. The training and evaluation process for these non-linear models follows the same procedure as that used for the linear model. This ensures the different models can be compared to one another using the same metrics.
\\\\
\begin{table}[h]
In this context, a simple feedforward neural network is trained to predict the quantiles for the NRV. The quantiles are then used to reconstruct the cumulative distribution function (CDF) for the NRV of a quarter. Predictions for the NRV can then be sampled from this reconstructed CDF. The neural network is trained using the pinball loss function explained in section \ref{subsubsec:quantile_regression_training}.
\\\\
The architecture of the non-linear model is illustrated in Table \ref{tab:non_linear_model_architecture}. The model begins with an input layer that converts the quarter of the day into an embedding. This layer concatenates the other input features with the quarter embedding. These combined features are then processed through a sequence of layers:
\begin{itemize}
\item Linear layer: Transforms input features to higher-dimensional space defined by hidden size.
\item ReLU Activation Function: Introduces non-linearity to the model to learn complex patterns. This also helps with the vanishing gradient problems with deep neural networks.
\item Dropout Layer: Regularizes the model to prevent overfitting. During training, random neurons are set to zero.
\end{itemize}
This sequence of layers is repeated N times to increase the depth of the model and enhance its ability to learn complex patterns. The final layer of the network is a linear layer that outputs the quantiles for the NRV prediction. For an autoregressive model, this is just the quantiles for a single quarter, whereas for a non-autoregressive model, the quantiles for every quarter of the day are outputted. The number of outputs is then the number of quarters in a day multiplied by the number of quantiles used.
\\\\
\begin{table}[H]
\centering
\begin{tabularx}{\textwidth}{Xr} % Set the table width to the text width
\toprule
@@ -380,16 +391,14 @@ Dropout (Regularization) & [B, Hidden Size] \\
Linear (Linear) & [B, Number of quantiles] \\
\bottomrule
\end{tabularx}
\caption{Non-linear Quantile Regression Model Architecture Details}
\caption{Non-linear Quantile Regression Model Architecture}
\label{tab:non_linear_model_architecture}
\end{table}
This is still a quite simple model with not too many hyperparameters to experiment with. The hidden size of the linear layers and the number of layers can be experimented with. The same quantiles will be that were used for the linear quantile regression model. The model is trained using the Adam optimizer with a learning rate of 1e-4. Early stopping is used with a patience of 5 epochs. The results of the non-linear model are shown in Table \ref{tab:autoregressive_non_linear_model_results}.
While this non-linear model is still quite simple, it offers the flexibility in tuning a limited set of hyperparameters. The hidden size of the linear layers and the number of layers can be experimented with, which can significantly influence the model's performance. The experiments are executed with the same quantiles as the linear model. The results of the non-linear model are shown in Table \ref{tab:autoregressive_non_linear_model_results}.
\begin{table}[ht]
\begin{table}[H]
\centering
\caption{Comparison of autoregressive models with various configurations}
\label{tab:model_comparison}
\begin{adjustbox}{width=\textwidth,center}
\begin{tabular}{@{}cccccccccc@{}}
\toprule
@@ -401,6 +410,7 @@ NRV & & & & & & & & \\
& 2 & 256 & 32982.64 & 38117.43 & 138.92 & 147.55 & 82.10 & 86.42 \\
& 4 & 256 & 33317.10 & 37817.78 & 139.42 & 146.90 & 82.17 & 85.63 \\
& 8 & 256 & 32727.90 & 36346.57 & 139.21 & 144.80 & 81.86 & 84.51 \\
& 16 & 256 & 35076.57 & 38624.83 & 143.28 & 148.61 & 84.70 & 87.05 \\
\midrule
NRV + Load + PV\\ + Wind & & & & & & & & \\
& 2 & 256 & 28860.10 & 42983.21 & 130.46 & 156.65 & 75.47 & 92.15 \\
@@ -416,11 +426,89 @@ NRV + Load + PV\\ + Wind + Net Position\\ + QE (dim 5) & & & & & & & & \\
\bottomrule
\end{tabular}
\end{adjustbox}
\caption{Autoregressive non-linear quantile regression model results. All the models used a dropout of 0.2 .}
\label{tab:autoregressive_non_linear_model_results}
\end{table}
\subsubsection{GRU Model}
% TODO: Talk more about the results in the table.
The results of the non-linear quantile regression model, as shown in Table \ref{tab:autoregressive_non_linear_model_results}, show valuable insights into the performance of the models with different hyperparameters and input feature sets. Increasing the number of layers and hidden size in the model does not necessarily lead to better performance on the test set. The model doesn't generalize well anymore and tends to overfit the training data. The input feature set plays a huge role in the performance of the model. The model with the input features NRV, Load, PV, Wind, Net Position, and the quarter embedding with 5 dimensions performs the best.
\subsubsection{Comparison}
\begin{figure}[H]
\centering
\begin{subfigure}[b]{0.49\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_linear_model_samples/AQR_NRV_Load_Wind_PV_NP_QE-Sample_864.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.49\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_non_linear_model_samples/AQR_NL_NRV_Load_Wind_PV_NP_QE-Sample_864.png}
\end{subfigure}
\begin{subfigure}[b]{0.49\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_linear_model_samples/AQR_NRV_Load_Wind_PV_NP_QE-Sample_4320.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.49\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_non_linear_model_samples/AQR_NL_NRV_Load_Wind_PV_NP_QE-Sample_4320.png}
\end{subfigure}
\begin{subfigure}[b]{0.49\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_linear_model_samples/AQR_NRV_Load_Wind_PV_NP_QE-Sample_6336.png}
\caption{Autoregressive linear model}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.49\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_non_linear_model_samples/AQR_NL_NRV_Load_Wind_PV_NP_QE-Sample_6336.png}
\caption{Autoregressive non-linear model}
\end{subfigure}
\caption{Comparison for examples from test set between the autoregressive linear and non-linear models. The plots show the confidence intervals calculated from 1000 generated full-day NRV samples. The samples were generated using input features NRV, Load, Wind, PV, Net Position and the quarter embedding. The non-linear model used 8 layers with a hidden size of 256 and a dropout rate of 0.2.}
\label{fig:linear_non_linear_sample_comparison}
\end{figure}
TODO: better comparison
Figure \ref{fig:linear_non_linear_sample_comparison} shows a comparison between the samples of autoregressive linear and non-linear models for certain examples of the test set. The non-linear model has a small increase in variance in the samples compared to the linear model. This results in some wider confidence intervals. This can be seen in example 2 of the figure.
TODO: non autoregressive non-linear model for quantile regression
\subsubsection{GRU Model}
Another more complex model that can be used is a Recurrent Neural Network (RNN). The RNN can be used to model the NRV data because of the sequential nature of the input features. The RNN keeps a hidden state that is updated at every time step using the new input data. The hidden state is then used to make the prediction. At each time step, the data needed to predict the NRV of the following quarter is fed into the model. This is done for the 96 quarters in a day. The last hidden state can then be extracted from the GRU model and be used to make a prediction for the quantiles of the next quarter.
\\\\
The two most common types of RNNs are the Long Short-Term Memory (LSTM) and the Gated Recurrent Unit (GRU). The GRU is a simpler version of the LSTM. The GRU has fewer parameters which results in faster training times. The GRU still can capture long-term dependencies in the data and can achieve similar performance to the LSTM.
\\\\
\begin{figure}[H]
\centering
\includegraphics[width=0.8\textwidth]{images/quantile_regression/rnn/RNN_diagram.png}
\caption{RNN model input and output visualization}
\label{fig:rnn_model_visualization}
\end{figure}
The input features for the RNN model are carefully structured to capture the relevant information from the previous quarters and the forecasted values. Each input feature vector represents a quarter and consists of the following components:
\begin{itemize}
\item The actual NRV value from the current quarter (T-1), which provides the model with the historical context of the NRV.
\item The forecasted or real values for the next quarter (T), including load, PV, wind, and net position. If the next quarter is not the quarter to predict, the real values for that quarter are used. If the next quarter is the quarter to predict, the forecasted values are used.
\item A quarter embedding vector representing the current quarter (T-1). The embedding vector gives the model information about the time of day, which can help it learn the daily patterns in the NRV data.
\end{itemize}
The input feature structure is designed to provide the model with a comprehensive view of the previous quarters and the forecasted values for the current quarter. By incorporating both historical and forecasted information sequentially, the model can learn to predict the NRV quantiles for the next quarter more accurately.
\\\\
The GRU model architecture is shown in Table \ref{tab:gru_model_architecture}. The model starts with an embedding layer that converts the quarter of the day into an embedding. This layer concatenates the other input features with the quarter embedding. The input of the TimeEmbedding is of shape (Batch Size, Time Steps, Input Features Size). The output of this layer is then passed to the GRU layer. The GRU layer outputs the hidden state for every time step. This results in a tensor of shape (Batch Size, Time Steps, Hidden Size). Only the last hidden state is relevant for the prediction of the NRV quantiles for the next quarter. The last hidden state should contain all the necessary information from the previous quarters to make the prediction. The last hidden state is then passed through a linear layer to output the quantiles for the NRV prediction.
\\\\
TODO: Zielige visualisatie van model nu
\begin{table}[H]
\centering
\begin{tabularx}{\textwidth}{Xr} % Set the table width to the text width
\toprule
\textbf{Layer (Type)} & \textbf{Output Shape} \\ \midrule
\midrule
Time Embedding & [B, Time Steps, Input + Time Embedding Size] \\
\midrule
GRU & [B, Time Steps, Hidden Size] \\
\multicolumn{2}{c}{\textit{Last state of GRU passed [B, Hidden Size]}} \\
Linear & [B, Number of quantiles] \\
\bottomrule
\end{tabularx}
\caption{GRU Model Architecture}
\label{tab:gru_model_architecture}
\end{table}
\newpage
\subsection{Diffusion}

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@@ -36,6 +36,7 @@
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Example of quantile regression output for one-quarter of the NRV, showing interpolated values for quantiles at 1\%, 5\%, 10\%, 15\%, 30\%, 40\%, 50\%, 60\%, 70\%, 85\%, 90\%, 95\%, and 99\%. These quantiles are used to reconstruct the cumulative distribution function.\relax }}{13}{figure.caption.5}\protected@file@percent }
\newlabel{fig:quantile_regression_example}{{3}{13}{Example of quantile regression output for one-quarter of the NRV, showing interpolated values for quantiles at 1\%, 5\%, 10\%, 15\%, 30\%, 40\%, 50\%, 60\%, 70\%, 85\%, 90\%, 95\%, and 99\%. These quantiles are used to reconstruct the cumulative distribution function.\relax }{figure.caption.5}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.2.1}Training}{14}{subsubsection.5.2.1}\protected@file@percent }
\newlabel{subsubsec:quantile_regression_training}{{5.2.1}{14}{Training}{subsubsection.5.2.1}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.2.2}Evaluation}{15}{subsubsection.5.2.2}\protected@file@percent }
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@@ -69,16 +70,21 @@
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9
Reports/Thesis/verslag.out
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@@ -16,9 +16,8 @@
\contentsline {subsubsection}{\numberline {5.2.2}Evaluation}{15}{subsubsection.5.2.2}%
\contentsline {subsubsection}{\numberline {5.2.3}Linear Model}{16}{subsubsection.5.2.3}%
\contentsline {subsubsection}{\numberline {5.2.4}Non-linear Model}{22}{subsubsection.5.2.4}%
\contentsline {subsubsection}{\numberline {5.2.5}GRU Model}{22}{subsubsection.5.2.5}%
\contentsline {subsubsection}{\numberline {5.2.6}Comparison}{22}{subsubsection.5.2.6}%
\contentsline {subsection}{\numberline {5.3}Diffusion}{23}{subsection.5.3}%
\contentsline {section}{\numberline {6}Policies for battery optimization}{23}{section.6}%
\contentsline {subsection}{\numberline {6.1}Baselines}{23}{subsection.6.1}%
\contentsline {subsection}{\numberline {6.2}Policies using NRV predictions}{23}{subsection.6.2}%
\contentsline {subsubsection}{\numberline {5.2.5}GRU Model}{25}{subsubsection.5.2.5}%
\contentsline {subsection}{\numberline {5.3}Diffusion}{27}{subsection.5.3}%
\contentsline {section}{\numberline {6}Policies for battery optimization}{27}{section.6}%
\contentsline {subsection}{\numberline {6.1}Baselines}{27}{subsection.6.1}%
\contentsline {subsection}{\numberline {6.2}Policies using NRV predictions}{27}{subsection.6.2}%

48
src/training_scripts/autoregressive_quantiles.py
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@@ -2,9 +2,7 @@ from src.utils.clearml import ClearMLHelper
#### ClearML ####
clearml_helper = ClearMLHelper(project_name="Thesis/NrvForecast")
task = clearml_helper.get_task(
task_name="AQR: Non-Linear (8 - 512 - 0.2) + Load + PV + Wind + Net Position + QE (dim 5)"
)
task = clearml_helper.get_task(task_name="AQR: GRU (2 - 256)")
task.execute_remotely(queue_name="default", exit_process=True)
from src.policies.PolicyEvaluator import PolicyEvaluator
@@ -30,19 +28,19 @@ data_config = DataConfig()
data_config.NRV_HISTORY = True
data_config.LOAD_HISTORY = True
data_config.LOAD_FORECAST = True
data_config.LOAD_HISTORY = False
data_config.LOAD_FORECAST = False
data_config.WIND_FORECAST = True
data_config.WIND_HISTORY = True
data_config.WIND_FORECAST = False
data_config.WIND_HISTORY = False
data_config.PV_FORECAST = True
data_config.PV_HISTORY = True
data_config.PV_FORECAST = False
data_config.PV_HISTORY = False
data_config.QUARTER = True
data_config.QUARTER = False
data_config.DAY_OF_WEEK = False
data_config.NOMINAL_NET_POSITION = True
data_config.NOMINAL_NET_POSITION = False
data_config = task.connect(data_config, name="data_features")
@@ -70,8 +68,8 @@ else:
model_parameters = {
"learning_rate": 0.0001,
"hidden_size": 512,
"num_layers": 8,
"hidden_size": 256,
"num_layers": 2,
"dropout": 0.2,
"time_feature_embedding": 5,
}
@@ -84,25 +82,25 @@ time_embedding = TimeEmbedding(
# time_embedding = TrigonometricTimeEmbedding(data_processor.get_time_feature_size())
# lstm_model = GRUModel(
# time_embedding.output_dim(inputDim),
# len(quantiles),
# hidden_size=model_parameters["hidden_size"],
# num_layers=model_parameters["num_layers"],
# dropout=model_parameters["dropout"],
# )
non_linear_model = NonLinearRegression(
lstm_model = GRUModel(
time_embedding.output_dim(inputDim),
len(quantiles),
hiddenSize=model_parameters["hidden_size"],
numLayers=model_parameters["num_layers"],
hidden_size=model_parameters["hidden_size"],
num_layers=model_parameters["num_layers"],
dropout=model_parameters["dropout"],
)
# non_linear_model = NonLinearRegression(
# time_embedding.output_dim(inputDim),
# len(quantiles),
# hiddenSize=model_parameters["hidden_size"],
# numLayers=model_parameters["num_layers"],
# dropout=model_parameters["dropout"],
# )
# linear_model = LinearRegression(time_embedding.output_dim(inputDim), len(quantiles))
model = nn.Sequential(time_embedding, non_linear_model)
model = nn.Sequential(time_embedding, lstm_model)
model.output_size = 1
optimizer = torch.optim.Adam(model.parameters(), lr=model_parameters["learning_rate"])