# Generating Synthetic Vehicle Speed Records Using LSTM

Jiri Vrany, Michal Krepelka, Matej Chumlen

► To cite this version:

Jiri Vrany, Michal Krepelka, Matej Chumlen. Generating Synthetic Vehicle Speed Records Using LSTM. 19th IFIP International Conference on Artificial Intelligence Applications and Innovations (AIAI), Jun 2023, León, Spain. pp.125-136, 10.1007/978-3-031-34111-3_12. hal-05449798

HAL Id: hal-05449798

https://inria.hal.science/hal-05449798v1

Submitted on 9 Jan 2026

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
<figure><img src="image_2.png" /></figure>

ifip

International Federation for Information Processing

This document is the original author manuscript of a paper submitted to an IFIP
conference proceedings or other IFIP publication by Springer Nature. As such, there
may be some differences in the official published version of the paper. Such
differences, if any, are usually due to reformatting during preparation for publication or
minor corrections made by the author(s) during final proofreading of the publication
manuscript.
# Generating Synthetic Vehicle Speed Records Using LSTM

Jiri Vrany(✉)D, Michal KrepelkaD, and Matej ChumlenD

Faculty of Mechatronics, Informatics and Interdisciplinary Studies, Technical University of Liberec, Liberac, Czech Republic

jiri.vrany@tul.cz

**Abstract.** Quality assurance testing of automotive electronic components such as navigation or infotainment displays requires data from genuine car rides. However, traditional static on-site testing methods are time-consuming and costly. To address this issue, we present a novel approach to generating synthetic ride data using Bidirectional LSTM, which offers a faster, more flexible, and environmentally friendly testing process. In this paper, we demonstrate the effectiveness of our approach by generating synthetic vehicle speed along a given route and evaluating the fidelity of the generated output using objective and subjective methods. Our results show that our approach achieves high levels of fidelity and offers a promising solution for quality assurance testing in the automotive industry. This work contributes to the growing research on generative machine learning models and their potential applications in the automotive industry.

**Keywords:** LSTM · generative models · vehicle speed · synthetic data · applied machine learning · digital twin

## 1 Introduction

Our work focuses on the computers used for vehicle-driver interaction, like the dashboard, navigation or infotainment. The current approach for their integration testing is either field testing or on-site Hardware-In-The-Loop simulation. The velocity model described in this paper is part of a larger project that aims to digitise integration testing and create a digital twin of the vehicle section.

A simulation requires data obtained from actual driving. Getting data in this way is time, resource and environmentally intensive. Almost every change to the test scenario then requires another field run. Data synthesis as part of the digital transformation process can reduce these costs. It will also allow testing on new, unfamiliar routes. By unfamiliar, we mean that no previously recorded data are available from rides on such a route.

The primary variable obtained in the measurement is the instantaneous velocity of the vehicle at a given location and time. In addition, the measurement process acquires data from sensors in the car, currently mostly shared via Controller Area Network (CAN) bus. All data obtained in this way are time series.
This paper summarises our approach towards vehicle speed data synthesis based on Global Navigation Satellite System (GNSS) coordinates using Long-Short Term Memory Neural Network (LSTM). The primary desired property of the model results is their realism. We are using objective and subjective tests to evaluate the model fidelity.

Our goal is to create the most credible velocity model possible in terms of the perception of the test equipment operator. We do not address typical traffic simulation, the evolution of traffic density during the day, multi-vehicle interaction or local effects on speed. If the test operator cannot distinguish the origin of the testing data, then our goal is fulfilled.

The main contributions of this paper are 1) a description of specific data preparation method to link actual rides and map data, 2) an evaluation of the possibility of using LSTM to generate geo-referenced time series and 3) a summary of the combined approach to verify the result plausibility by objective and subjective criteria.

## 2 The Problem and Motivation

Vehicle speed is a pseudo-stochastic process influenced by many external phenomena. Specific changes in the recorded velocity cannot be reliably explained by retrospective data analysis as the necessary data might not be available. According to [1], the vehicle speed is, among others, affected by traffic volume during the day, weather or road signals. However, the probe vehicle might not be logging such information.

The measured data gives the instantaneous car speed at a given position. If we have enough training data from a particular route, creating a model to simulate further runs along that route is undoubtedly possible.

We aim to create a more general model capable of generating a velocity waveform for an unfamiliar route. We use the external map data to enrich the training data to achieve this goal. That is, create plausible speed data for any location worldwide, assuming map data is available.

## 3 Related Work

Predicting the velocity profile along a route could be formulated as a regression problem over a time series. The vehicle velocity model can predict long or short term [3].

Short in this context means a time frame of seconds. For example, the model predicts the speed for the next 10 or 20 s. One of the first works focused on speed prediction using deep learning was [2], where Lemieux and Ma solve short-term prediction even though not precisely named this way. In [5], a feedforward neural network (FNN) can predict short-term vehicle velocity. Furthermore, using road slope data increases the accuracy of the prediction. The [4] states that using LSTM is suitable for vehicle velocity time series and should be preferred over vanilla Recurrent Neural Networks (RNN). In [6], Deufel explores vehicle speed
prediction by using encoder-decoder LSTM, OpenStreetMap (OSM) data and slope data computed from Shuttle Radar Topography Mission (SRTM). Also, [8, 9] and [10] report the successful usage of LSTM for short-term velocity prediction in different scenarios.

However, our target is long-term prediction. Long-term in our context means we are trying to predict speed for the entire itinerary. Time frames can vary from minutes to hours. This prediction type is more challenging than short-term prediction because it can be affected by unexpected traffic events. From the studies we know, only [7] combines FNN with LSTM for effective long-term vehicle velocity prediction.

Generally speaking about time series prediction, [11] shows that Bidirectional LSTM (BiLSTM) significantly improves the precision of stock price forecasting compared to Unidirectional LSTM.

Generative Adversarial Networks (GAN) are state-of-the-art in artificial data creation. These works suggest practical testing methods for generated data authenticity, even for works not focused on GANs like ours. To test the generative properties of the model, i.e., prediction over an unknown route, we need to test the realism of the result. The principle is the same as in the case of GAN. Zhou [24], Lucic [13], Xu [14], Yang [15], and Borji [16] have published their approaches to the problem of validating GAN results and finding objective quality metrics.

# 4 Method

The goal is to create a generalised model to predict the speed profile on a given route. We must create new attributes to train the model to help explain specific speed changes in the measured data. For example, whether the car drives in town, on a motorway or a countryside road, whether the route is straight or contains turns, the radius of those turns, and other information. We denote these new attributes as the geometry of the route. We then use the measured data enriched with these new attributes to train an appropriate machine-learning model. An essential requirement for the resulting synthetic data is then its realism.

Deufel [5] shows that incorporating slope data improves the prediction of short-term vehicle speed and further extends this idea in [6] with map data and encoder-decoder LSTM. A combination of FNN and LSTM was applied in [7] for long-term vehicle speed prediction. Namini [11] shows BiLSTM increases prediction performance over LSTM on stock time series. Combining elevation and map data with BiLSTM could yield good long-term vehicle speed prediction.

## 4.1 Maps and Spatial Information

We use the OSM as a primary map data source and the Open Source Routing Machine (OSRM) as a routing service. We used the speed profile generated by the OSRM as the baseline model for comparison. The velocity calculation in OSRM is based on a vehicle profile defining the maximum speed on different
surfaces and types of roads. At the same time, representing a new profile or modifying an existing one on a local service instance will change the resulting velocity estimate [17].

## 4.2 Dataset, Preprocessing and Feature Engineering

Our research partner organization provided actual ride measurement data for model training. The dataset consists of 2815 drives with a total length of 22179.5 km and a duration of 455 h. Unfortunately, the dataset is currently not publicly available.

The speed on an arbitrary route should be independent of its exact location in the world. The factors influencing the velocity can be divided into driver-related, route-related and traffic-related. As we mentioned before, traffic simulation is not the goal of this work. Therefore we omit the traffic-related factors. Once all the route-related aspects are known, we can synthesize the speed data. We focus on collecting as much route-related data as possible.

We use map-matching algorithms from OSRM to pair measured spatiotemporal data with OSM geographical data. We can merge data from multiple sources by assigning the car ride data to uniquely identified OSM objects.

With knowledge of OSM identifiers, we then acquire map metadata. For this purpose, we use Overpass API. Further, we add elevation and slope data from Open-Elevation API, an open-source elevation API based on SRTM data. These attributes are then combined with the measured velocity to form the final model training and validation dataset. We also add those features to each specified route at the time of new data prediction. The list of training data attributes is in Table 1.

<table><caption>**Table 1.** Model input attributes.</caption><thead><tr><td>Name</td><td>Type</td><td>Description</td></tr></thead><tbody><tr><td>azimuth_delta</td><td>continuous</td><td>first difference of forward azimuth</td></tr><tr><td>elevation_delta</td><td>continuous</td><td>first difference of absolute elevation</td></tr><tr><td>way_maxspeed</td><td>continuous</td><td>OSM speed limit</td></tr><tr><td>waysurface</td><td>categorical</td><td>OSM road surface (asphalt, sett, cobblestone, etc.)</td></tr><tr><td>way_type</td><td>categorical</td><td>OSM road type (primary, highway, residential, etc.)</td></tr><tr><td>node</td><td>categorical</td><td>node specific features (level crossing, traffic sign, intersection, traffic signal, etc.)</td></tr></tbody></table>

The training dataset contains three continuous and three categorical attributes. After one hot encoding, the categorical attributes yield 35 features. The total number of model input attributes is 38. The single target variable is called *target_speed*.
From the input attributes, the *way_maxspeed* attribute seems to be essential for limiting the resulting speed and following the traffic rules. However, this parameter is inconsistent and often missing in the OSM data. To train the model, we filled in the missing values during preprocessing by interpolation and analyzing whether the path passes through the settlement or is outside.

The resulting data are multivariate sequences with data points not equally distributed in distance nor time. The sampling frequency of the measured data and the coarseness of OSM nodes determine the distribution. To solve this issue, we resample the data. Every data point forms a new feature vector describing a 1-meter segment of the road. Output sequences are of shape (N, s) where N is the number of samples and s is the route length in meters.

## 4.3 Neural Networks

In the case of time series prediction, temporal information plays an important role. RNN can learn context from already processed sequences and are suitable for time series prediction. Vanilla RNNs suffer from vanishing and exploding gradients, making them hard to train, especially considering long-term dependencies [4]. We use a Long Short-Term Memory Network (LSTM) to solve this issue. The LSTM cell can be described by following equations taken from [12]:

$$ 
\begin{aligned}
i_t &= \sigma(W_{ii}x_t + b_{ii} + W_{hi}h_{t-1} + b_{hi}) \\
f_t &= \sigma(W_{if}x_t + b_{if} + W_{hf}h_{t-1} + b_{hf}) \\
g_t &= tanh(W_{ig}x_t + b_{ig} + W_{hg}h_{t-1} + b_{hg}) \\
o_t &= \sigma(W_{io}x_t + b_{io} + W_{ho}h_{t-1} + b_{ho}) \\
c_t &= f_t \odot c_{t-1} + i_t \odot g_t \\
h_t &= o_t \odot tanh(c_t)
\end{aligned}
$$

where *t* is given time, *x*<sub>*t*</sub> input, *σ* is sigmoid function, ⊙ is element-wise product and *W*<sub>..</sub> are matrices mapping input or hidden state to input *i*<sub>*t*</sub>, forget *f*<sub>*t*</sub>, cell *g*<sub>*t*</sub> and output *o*<sub>*t*</sub> gates respectively. Finally, *c*<sub>*t*</sub> is cell state and *h*<sub>*t*</sub> hidden state.

BiLSTM is an extension of LSTM. As the name suggests, we apply LSTM to the input data twice, in standard and reversed order. Output for a given time step *t* is the concatenation of hidden states from both directions.

## 4.4 Testing the Fidelity of the Result

To test the plausibility of the result, we have been comparing the synthetic results with measured rides. We used Wasserstein distance - *W*<sub>*p*</sub> [18, 19] and kernel Maximum Mean Discrepancy - *MMD* [20, 21] as the discriminative metrics for comparing the similarity of two waveforms.

More studies pointed out that human-based evaluation is insufficient for general conclusions [22, 23]. However, the end user of the results of our model will be a human tester working at the testbed. Therefore, we decided also to use a user Turing test to verify the fidelity of the result. In designing our human-based evaluation approach, we followed the rules described in the HYPE work [24].
# 5 Experiments and Discussion

## 5.1 The Baseline Model - OSRM Speed

Using OSRM as a part of the data preprocessing gives us the ETA and the calculated travel speed between the nodes of the route. The primary question was if the OSRM result could serve as a speed model for our final goal.

## 5.2 The LSTM Model

We have complete information about the route's geometry during model training and prediction time. Considering the sequential nature of the data, we decided to use BiLSTM to take advantage of both past and future contexts and implemented it in Python with Pytorch standard LSTM class [12]. We assume this is similar to actual driving, where the driver can see the route situation far ahead or know the route details from the past.

We tested different combinations of hyperparameters, and for the final model, we used 5 layers of LSTM with a hidden dimension of 512 and a single linear output layer. We add an activation function (ReLU) to the output value and found it to improve the training results. The data for training were batches (size 128) of sequences of length 128 sampled with stride 16 from the measured drives. We trained the model for 30 epochs with a fixed learning rate of 1e-5. We used MSE loss function with Adam optimizer.

## 5.3 Objective Evaluation of the Model

Since many factors affect the resulting speed profile, let's assume that no two rides on an identical route in real life will have an identical speed profile record. And although such two waveforms will be different, both will be real. We first examined how the actual data differ from each other to develop a metric for objectively evaluating the quality and realism of the modelled data.

First, we chose a test route and then found all rides on it using dynamic time warping (DTW) [25] applied to GNSS coordinates. We defined the combined DTW score as follows:

$$dtw_{comb} = dtw(lat) + dtw(lon) \quad (1)$$

We consider two routes similar when $dtw_{comb} < 0.1$. Our dataset's most extensive group of repetitive test drives consists of 20 measurements. This most repetitive route includes urban areas, a main road and a motorway and is approximately 17 km long.

Figure 1 shows five randomly selected measured speed records along the most repetitive route. It is visible that the speed waveforms are different for each ride.

After a series of experiments, we selected Wasserstein distance $W_p$ and Maximum Mean Discrepancy $MMD$ as the primary metrics to describe the similarity of the measurements. We used the Radial-basis function kernel $rbf$ [26] for MMD.
<figure><img src="image_3.png" /><figcaption>Fig. 1. Captured speed profiles of five randomly selected rides on the test route.</figcaption></figure>

By computing all 2-element non-repeating combinations from 20 rides, we obtained 190 ride pairs. For each ride, we had the measured velocity *v* and can calculate acceleration *a*. The acceleration is a significant indicator of the speed profile fidelity because of the car's physical limits. We then calculated *W*<sub>*p*</sub> and *MMD* of *v* and *a* for each of the 190 ride pairs. This gives four metrics denoted as *W*<sub>*p*</sub>*v*, *W*<sub>*p*</sub>*a*, *MMD*<sub>*v*</sub> and *MMD*<sub>*a*</sub>.

All four metrics have a normal-like distribution, so we used the basic empirical rule to evaluate if a generated ride can be considered real-like. We consider the generated data realistic if, for each observation X the 3σ-rule is valid:

$$ Pr(\mu - 3\sigma \le X \le \mu + 3\sigma) \qquad (2) $$

The Table 2 contains the calculated values. It should be noted that the minimum real value for both *W*<sub>*p*</sub> and *MMD* is zero, since in this case the two compared rides are identical. Thus, the negative lower bound value of the interval of the 3σ-rule results is replaced by zero.

<table><caption>Table 2. Wasserstein distance and Maximum Mean Discrepancy of actual rides.</caption><thead><tr><th>Real rides</th><th><i>W</i><sub>p</sub> μ</th><th><i>W</i><sub>p</sub> σ</th><th>MMD μ</th><th>MMD σ</th></tr></thead><tbody><tr><td>acceleration <i>a</i></td><td>0.640031</td><td>0.273252</td><td>0.00079216</td><td>0.00010252</td></tr><tr><td>velocity <i>v</i></td><td>6.120097</td><td>2.145314</td><td>0.019162</td><td>0.009737</td></tr></tbody></table>

For the model evaluation, we first generated the coordinates of the test route using the OSM web application and saved the result in KML format. After
preprocessing this basic route skeleton, we got the route dataframe with the same sampling frequency as for the measured data (0.1 s).

Next, we used the OSRM speed profile from the route dataframe as the baseline velocity model and computed the acceleration for it. We also predicted velocity and acceleration for the test route with our trained LSTM model.

For visual comparison, we include a graph of the resulting speed from both models and the *way_maxspeed*. From Fig. 2, we can see that the baseline OSRM model gives different results at first glance. We assume that the *way_maxspeed* attribute influences the OSRM speed value. If the *way_maxspeed* is not present in a specific location in the OSM data, the OSRM speed can differ from the actual speed significantly.

<figure><img src="image_4.png" /><figcaption>Fig. 2. Comparison of models and way max speed on the test route.</figcaption></figure>

Next we randomly selected 10 routes from the test set, and for each of them, we computed $W_p$ and MMD between the actual data and the models for v and a. This gives us $W_{pa}$, $MMD_a$, $W_{pv}$, $MMD_v$ for each model. The mean result calculated from 10 tests for each model are shown in Tables 3 and 4.

<table><caption>Table 3. Mean result for 10 random test routes predicted by OSRM model.</caption><tr><td>$W_{pv}$</td><td>84.598625</td><td>0.486241</td><td>0.000000 - 12.556039</td></tr><tr><td>$W_{pa}$</td><td>2.564519</td><td>0.091275</td><td>0.000000 - 1.459787</td></tr><tr><td>$MMD_v$</td><td>0.359960</td><td>0.017533</td><td>0.000000 - 0.048373</td></tr><tr><td>$MMD_a$</td><td>0.135979</td><td>0.016274</td><td>0.000485 - 0.001100</td></tr></table>

The resulting metrics for the OSRM model were outside the specified range in all ten cases. The mean value in Table 3 shows, that the OSRM results cannot be considered realistic according to our criterion. They do not fit inside the given
interval neither for velocity nor for acceleration. Hence the model is insufficient to generate further CAN bus data tied to the car speed. This baseline model is applicable for estimating the ETA during navigation. However, it does not achieve the necessary sensitivity for our purposes.

<table><caption>**Table 4.** Mean result for 10 random test routes predicted by LSTM model.</caption><thead><tr><th>LSTM</th><th>μ</th><th>σ</th><th>3σ-rule interval</th></tr></thead><tbody><tr><td>W<sub>p</sub>v</td><td>6.653617</td><td>4.224982</td><td>0.000000 - 12.556039</td></tr><tr><td>W<sub>p</sub>a</td><td>0.707986</td><td>0.538143</td><td>0.000000 - 1.459787</td></tr><tr><td>MMDv</td><td>0.021584</td><td>0.019176</td><td>0.000000 - 0.048373</td></tr><tr><td>MMDa</td><td>0.0008177</td><td>0.0002019</td><td>0.000485 - 0.001100</td></tr></tbody></table>

The LSTM satisfies the 3σ-rule for all four metrics. In all ten test cases, $W_p$ and $MMD$ for velocity and acceleration were within the defined range. This is demonstrated by the mean result shown in the Table 4. Thus, we consider the LSTM results realistic by objective metrics.

## 5.4 Subjective Evaluation of LSTM Model

The baseline OSRM model did not pass the objective test. Therefore, we used only the LSTM model for subjective testing with a group of pre-selected and instructed evaluators. Evaluators worked voluntarily, without reward.

Evaluators were shown a plot of randomly selected speed profiles and asked whether the speed was measured or synthesized. Two figures represented each instance: a linear plot of speed over time and a heat map of speed as a route line in the map.

<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Example of actual profile.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Example of synthetic profile.</figcaption></figure>

Figures 3 and 4 show examples of the actual and synthetic speed profiles displayed to the testers. For this particular pair of speed profiles, the $W_p$ and
$MMD_v$ values were 5.11879 and 0.036183. However, we did not disclose the objective metrics to the testers.

We used a method similar to the cost-effective approximation from the HYPE paper [24]. Each evaluator got 10 actual and 10 generated velocity profiles randomly selected from 1000 measured and 1000 generated runs.

In selecting the evaluators, we approached the volunteers and personnel who performed component testing on the mentioned testbeds. We first explained the problem and showed several edge cases. Next, all evaluator candidates performed the qualification test. The test aimed to check whether the candidates understood the problem and were sufficiently motivated to solve it. The test consisted of ten pre-selected rides, and candidates must successfully identify at least six to pass.

A total of 23 volunteers passed the qualification test for subjective testing. We obtained ratings for 447 of 460 given profiles, as some volunteers did not rate all given samples. The question for each sample was whether it was an actual measurement. Correctly classifying the displayed profile as measured or synthetic led to true positive and true negative results. Classification of the generated profile as measured resulted in a false positive. And finally, false negatives mean that the measured profile was marked as synthetic.

<table><caption>**Table 5.** Confusion matrix for the subjective test of LSTM fidelity.</caption><thead><tr><td>Truth/Prediction</td><td>Real</td><td>Synthetic</td></tr></thead><tbody><tr><td>Real</td><td>123</td><td>109</td></tr><tr><td>Synthetic</td><td>101</td><td>114</td></tr></tbody></table>

Table 5 shows the confusion matrix obtained from this analysis. The Accuracy was 53.02%, Precision 54.91% and Recall 53.01%. This means that the testers were unable to reliably distinguish whether the results were generated or measured. In terms of subjective evaluation, the LSTM results can be considered realistic and applicable for further development.

# 6 Conclusion and Future Work

We created a system for preprocessing and encoding the georeferenced information usable for general speed profile generation on any given route. The BiLSTM model is functional and realistic both in objective metrics and when tested by real users.

The model will be used to synthesise other CAN bus data in the project. Some of these parameters correlate with speed and route geometry. Using synthetic speed data, we can generate data like wheel rotation speed, brake pressure or throttle pedal pressure.

The developed model generates a single speed profile for each route. Nevertheless, for some simulation scenarios, we need more dynamic behaviour. Therefore,
our future work will focus on the GAN domain. We aim to generate multiple velocity profiles for a single route using configurable hyperparameters.

**Acknowledgements.** This paper was supported by the Technology Agency of the Czech Republic project CK01000020, "Development of a GNSS route generator and CANBUS signal with machine learning using Software Defined Radio."

## References

1. Lin, H., Zito, R.: A review of travel-time prediction in transport and logistics. In: Proceedings of the Eastern Asia Society for Transportation Studies, vol. 5 (2005)

2. Lemieux, J., Ma, Y.: Vehicle Speed Prediction Using Deep Learning, 2015 IEEE Vehicle Power and Propulsion Conference (VPPC), (2015), pp. 1–5, https://doi.org/10.1109/VPPC.2015.7353037

3. Bratsas, C., Koupidis, K., Salanova, J.-M., Giannakopoulos, K., Kaloudis, A., Aifadopoulou, G.: A comparison of machine learning methods for the prediction of traffic speed in urban places. Sustainability 12, 142 (2020). https://doi.org/10.3390/su12010142

4. Du, Y., et al.: The Vehicle’s Velocity Prediction Methods Based on RNN and LSTM Neural Network, 2020 Chinese Control And Decision Conference (CCDC), (2020), pp. 99–102, https://doi.org/10.1109/CCDC49329.2020.9164532

5. Deufel, F., Gießler, M., Gauterin, F.: A generic prediction approach for optimal control of electrified vehicles using artificial intelligence. Vehicles 4(1), 182–198 (2022). https://doi.org/10.3390/vehicles4010012

6. Deufel, F., Jhaveri, P., Harter, M., Gießler, M., Gauterin, F.: Velocity Prediction Based on Map Data for Optimal Control of Electrified Vehicles Using Recurrent Neural Networks (LSTM). Vehicles 4, 808–824. (2022) 10.3390/vehicles4030045

7. Yufang, L., Mingnuo, C., Wanzhong, Z.: Investigating long-term vehicle speed prediction based on BP-LSTM algorithms. IET Intell. Transp. Syst. 13, 1281–1290 (2019). https://doi.org/10.1049/iet-its.2018.5593

8. Maa, X., et al.: Long short-term memory neural network for traffic speed prediction using remote microwave sensor data. Transportation Research Part C: Emerging Technologies, vol. 54, 2015, pp. 187–197. Elsevier Ltd. https://doi.org/10.1016/j.trc.2015.03.014

9. Yeon, K., Min, K., Shin, J., Sunwoo, M., Han, M.: Ego-vehicle speed prediction using a long short-term memory based recurrent neural network. Int. J. Automot. Technol. 20(4), 713–722 (2019). https://doi.org/10.1007/s12239-019-0067-y

10. Zhao, J., Gao, Y., Bai, Z., Wang, H., Lu, S.: Traffic Speed Prediction Under Non-Recurrent Congestion: Based on LSTM Method and BeiDou Navigation Satellite System Data, in IEEE Intelligent Transportation Systems Magazine, vol. 11, no. 2, pp. 70–81, Summer (2019) https://doi.org/10.1109/MITS.2019.2903431

11. Siami-Namini, S., Tavakoli, N., Namin, A.S.: The performance of LSTM and BiLSTM in forecasting time series. IEEE Int. Conf. Big Data (Big Data) 2019, 3285–3292 (2019). https://doi.org/10.1109/BigData47090.2019.9005997

12. Pytorch LSTM Documentation. Accessed 12 Jan 2023. https://pytorch.org/docs/stable/generated/torch.nn.LSTM.html

13. Lucic, M., Kurach, K., Michalski, M., Gelly, S., Bousquet, O.: Are gans created equal? a large-scale study. In: Advances in Neural Information Processing Systems, pp. 700–709 (2019)
14. Xu, Q., et al.: An empirical study on evaluation metrics of generative adversarial networks. arXiv preprint arXiv:1806.07755 (2018)

15. Yang, L., Lerch, A.: On the evaluation of generative models in music. Neural Com- put. Appl. 32 (9), 4773–4784 (2020)

16. Borji, A.: Pros and cons of gan evaluation measures. Comput. Vision Image Underst. 179, 41–65 (2018)

17. Huber, S., Rust, C.: Calculate Travel Time and Distance with Openstreetmap Data Using the Open Source Routing Machine (OSRM). Stata J. 2016/16(2):416–423 (2016) https://doi.org/10.1177/1536867X1601600209

18. Arjovsky, M., Soumith, C., Bottou, L.: Wasserstein generative adversarial net- works. International conference on machine learning, PMLR (2017)

19. Wacha, B., Belilovsky, E., Blaschko, M., Antonoglou, I., Gretton, A.: A test of relative similarity for model selection in generative models. arXiv preprint arXiv:1511.04581 (2015)

20. Vallender, S.S.: Calculation of the Wasserstein distance between probability dis- tributions on the line. Theor. Probab. Appl. 18 (4), 784–786 (1974)

21. Borgwardt, K.M., et al.: Integrating structured biological data by kernel maximum mean discrepancy. Bioinformatics 22 (14), e49–e57 (2006)

22. Ariza, C.: The interrogator as critic: the turing test and the evaluation of generative music systems. Comput. Music. J. 33 (2), 48–70 (2009)

23. Pease, A., Colton, S.: On impact and evaluation in computational creativity: a discussion of the turing test and an alternative roposal. In: Proceedings of the AISB symposium on AI and philosophy, p 39. York, United Kingdom (2011)

24. Zhou, S., et al.: Hype: A benchmark for human eye perceptual evaluation of gen- erative models. In: Advances in Neural Information Processing Systems, vol. 32 (2019)

25. Salvador, S., Chan, P.: FastDTW: toward accurate dynamic time warping in linear time and space. Intell. Data Anal. 11 (5), 561–580 (2007)

26. Rasmussen, C.E., Williams, C.K.I.: Gaussian Processes for Machine Learning, the MIT Press, 2006, ISBN 026218253X. c 2006 Massachusetts Institute of Technology. https://www.GaussianProcess.org/gpml