GenNet: A Generative AI-Driven Mobile Network Simulator for Multi-Objective Network Optimization

Q5: Which specific datasets were used for training GenNet? Could this choice potentially limit the system’s generalizability or make it overly dependent on particular datasets?

A5: In the development of GenNet, we used several primary datasets. For example:

1. Mobile network operator dataset: This dataset includes data from a major mobile network operator in China, covering the activity trajectories of 10,000 users over one month in the Beijing area. It contains information about user activities at various locations, such as offices, restaurants, and schools, used for simulating user behavior trajectories.

2. Foursquare dataset: This dataset records activities of 1,000 users over a month, including visits to different types of locations such as arts and entertainment venues, food and drink establishments, and office spaces. It helps in simulating diverse user behavior patterns.

3. RadioMapSeer dataset: This dataset contains building layouts, base station positions, and path loss maps in the form of images. It is primarily used for training the model to understand the relationship between environmental geography and path loss.

4. RSRPSet dataset: The RSRPSet dataset, published by Huawei Technologies, includes data about base station and receiver positions, as well as Reference Signal Received Power (RSRP), with approximately 5 million entries. While specific geographic details were removed for privacy reasons, the dataset was processed to reconstruct the geographical layout for training and testing path loss estimation models.

These datasets play a crucial role in providing realistic environment modeling and effective training support. However, since the data is sourced from specific geographic regions (e.g., the Beijing area and specific Foursquare locations) and application scenarios, this might limit the generalizability of GenNet, making it more reliant on certain environments. Future work could focus on expanding the range of geographic areas and user behavior data to enhance GenNet’s applicability and robustness across diverse scenarios.

Q6: Please discuss how you addressed or mitigated potential overfitting to these specific datasets, and what steps you took to ensure GenNet's applicability to a wide range of network scenarios.

A6: To address the potential risk of overfitting to the specific datasets used for GenNet, we implemented several key strategies to enhance the generalizability and applicability of the model across a wide range of network scenarios:

1. Diverse dataset integration: We combined multiple datasets from different sources, including the mobile network operator dataset, Foursquare data, RadioMapSeer, and RSRPSet. Each dataset has unique characteristics—ranging from user activity data in urban settings to different network path loss scenarios—ensuring that GenNet was exposed to diverse user behaviors and network conditions during training. This helped mitigate overfitting to any one specific dataset and improved the robustness of the model.

2. Cross-validation across datasets: We applied cross-validation across different datasets, such as using RadioMapSeer for training and RSRPSet for validation. This cross-validation approach ensured that GenNet was tested on environments it had not seen during training, thereby helping to assess and improve its performance across different network configurations and reduce overfitting risks.

3. Physics-informed neural networks: In path loss modeling, we incorporated a Physics-Informed Neural Network (PINN) approach by embedding electromagnetic theory into the training process. This involved using the Volume Integral Equation (VIE) as a knowledge-driven component alongside data-driven training, which helped the model to adhere to physical laws governing signal propagation. By incorporating physical knowledge, GenNet could generalize well beyond the specific patterns present in the data, leading to better applicability across various network conditions.

These measures are crucial in mitigating overfitting and ensuring that GenNet could generalize effectively to a wide range of network scenarios and environments.

We thank the reviewer for recognizing our paper’s strengths and giving constructive comments. We would like to address the comments and questions below.

Q1: Please provide specific details on any modifications or innovations they made to the generative models to adapt them for mobile network simulation.

A1: The generative models used in the proposed simulator have undergone specific modifications to better suit mobile network environments. For example, the user mobility model leverages neural differential equations within a generative adversarial imitation learning framework to capture continuous spatiotemporal dynamics, addressing the irregularity and sparsity of user activity patterns. This allows for realistic simulation of individual-level trajectories, important for mobile scenarios. Additionally, for wireless propagation, PEFNet, a physics-informed neural network, integrates Volume Integral Equations (VIE) from Maxwell's equations to model electromagnetic signal propagation with high physical fidelity. PEFNet also uses a data-driven learning component to refine path loss estimates with real-world data, ensuring accuracy and adaptability across different urban environments. These innovations collectively enhance the accuracy and utility of the simulator in accurately representing mobile network dynamics.

Q2: Please add a specific section in the introduction or methodology detailing the key technical challenges in developing GenNet and how you overcame them.

A2: The key technical challenges in developing GenNet included:

1. Scalable user behavior simulation: Simulating millions of mobile users realistically was a significant challenge. We used advanced generative AI techniques (GANs and VAEs) to create detailed and diverse user movement and communication patterns, ensuring high scalability and accuracy.

2. High-fidelity network component modeling: Modeling network elements like base stations and wireless environments required capturing detailed configurations and environmental factors. We used operator data combined with stochastic, deterministic and e data-driven model to achieve accurate simulations of signal propagation.

3. Efficient parallel processing: Handling real-time interactions of millions of users required efficient computation. We addressed this by implementing parallelization strategies with synchronous updates, mutual exclusion, and coroutines to allow concurrent simulation tasks, thus enhancing scalability and efficiency.

These solutions allowed GenNet to overcome scalability, fidelity, and efficiency challenges, resulting in a robust digital twin for mobile network optimization.

Q3: Please provide specific examples or use cases where reduced computation time in network simulations leads to tangible benefits in research or industry applications.

A3: Reduced computation time in network simulations has significant reality benefits, especially in scenarios involving reinforcement learning (RL). In RL algorithms, the agent needs to interact with the simulator tens of thousands of times to learn optimal strategies. Improved simulation efficiency drastically accelerates this iterative process, leading to faster training and convergence of the RL model. This means that new network optimization policies can be developed, tested, and deployed much more quickly, providing substantial advantages in both research exploration and industrial applications where rapid iteration is important.

Q4: For the experimental results in Figures 7, 8, and 9, how should these be interpreted? please provide a clear interpretation guide for these figures in the main text, explaining how to read the graphs and what conclusions can be drawn from them.

A4: The experimental results in Figures 7, 8, and 9 illustrate the trends in different performance metrics during the iterative process of each corresponding algorithm. It is important to note that none of the algorithms have fully converged in these figures. These figures are intended to show how key metrics evolve over time with different algorithms. From these results, we observe that in large-scale mobile network environments, existing multi-objective reinforcement learning algorithms struggle significantly to achieve convergence, indicating the challenges of applying these methods to complex, dynamic mobile network scenarios.

We thank the reviewer for recognizing our paper’s strengths and giving constructive comments. We would like to address the comments and questions below.

Q1: Please explain the accuracy of the generated information.

A1: The accuracy of the generated information is supported by the experimental results of the algorithms used in our simulator. For example, in the activity trajectory generation, the framework based on generative adversarial imitation learning, achieved over 50% reduction in MAPE when simulating COVID-19 spread compared to baseline models, indicating a high level of accuracy. For the path loss estimation, the PEFNet model achieved an R² of 0.9731, a MAE of 0.7759 dB, and a RMSE of 2.1733 dB on the RadioMapSeer dataset, demonstrating better accuracy compared to other baseline models. These results validate the high accuracy and reliability of the information generated by our simulator.

Q2: The simulation experiment uses GPU and generative AI to simulate system functions, compared to traditional simulation software that uses CPU. If GPU acceleration is used in both cases, what conclusion would the author draw about the performance comparison?

A2: Our simulator supports GPU acceleration, unlike traditional simulation software which typically lacks GPU acceleration capabilities. This fundamental difference is important for the performance comparison, as the ability to leverage GPU acceleration can significantly enhance simulation efficiency and scalability, providing a major advantage over conventional CPU-based simulators.

Q3: Could the authors explain how many control parameters, performance metrics, and functions need to be retained in a comprehensive simulator, such as NS-3, OPNET, OMNET++, to be generally applicable to most simulation experiments?

A3: To address the question regarding the number of control parameters, performance metrics, and functions in a comprehensive simulator like NS-3, OPNET, or OMNeT++, it should be noted that these numbers depend on the network type and use case. However, a generally versatile simulator should include around 20 to 30 control parameters covering protocol settings, node mobility, channel, and link characteristics. It should also offer 10 to 15 key performance metrics, such as throughput, delay, jitter, packet delivery ratio, and energy consumption. Additionally, hundreds of functions are needed to model various network protocols, routing algorithms, and traffic generation features, ensuring the simulator’s adaptability to a wide range of network scenarios.

Q4: Please clarify the statement about MATLAB in the INTRODUCTION Section. The author mentioned in the related work that MATLAB is a link-level simulator. As we know, MATLAB provides a scientific computing tool. Based on this tool, link-level simulators and system-level simulators can be developed. For example, the well-known Vienna Platform can implement the protocol stack for LTE and 5G systems and complete system-level simulations.

A4: MATLAB itself is not a simulator for system-level network simulations; rather, it is a scientific computing tool that excels at numerical analysis and matrix computations. Its capabilities are more suited for link-level analysis, where individual connections and their behaviors can be modeled in detail. The Vienna platform is indeed developed based on MATLAB, but it extends beyond MATLAB’s standard capabilities by incorporating additional modules and complex implementations to support both link-level and system-level simulations for technologies like LTE and 5G. Therefore, while MATLAB provides the foundation for link-level analysis, it lacks the built-in functionalities for comprehensive system-level simulations without significant extensions like those provided by the Vienna Platform.

Q5: The author claims in the introduction that the simulation speed of NS-3/OPNET/MATLAB/OMNET++ is slower than real networks. Please provide evidence or citations supporting their claim about simulation speeds.

A5: The statement in the introduction regarding the simulation speed of NS-3, OPNET, MATLAB, and OMNeT++ being slower than real networks is supported by [1]. These simulators often execute 3-4 orders of magnitude slower than real-time networks due to the intricacies involved in modeling packet-level processes, such as congestion control and queueing mechanisms, under pre-defined simulation rules. This nature although essential for accurate emulation, leads to significant computational overhead, making them inefficient for real-time or large-scale simulations.

[1] Linbo Hui, Mowei Wang, Liang Zhang, Lu Lu, and Yong Cui. Digital twin for networking: A data-driven performance modeling perspective. IEEE Network, 2022.

We thank the reviewer for recognizing our paper’s strengths and giving constructive comments. We would like to address the comments and questions below.

Q1: How can you justify that the optimization problem in (1) can indeed work for real-world systems like 5G or 6G?

A1: The optimization problem defined in equation (1) involves variables of base station transmission power, antenna tilt, and antenna azimuth that are directly applicable to real-world systems. The optimization objectives focus on coverage, throughput, and energy consumption, which are important performance metrics for 5G and 6G networks. These variables and objectives are representative of real-world challenges in optimizing modern mobile networks.

Q2: How can you handle the realistic propagation environment characteristics like interference?

A2: For interference modeling, we use Physics-informed Electromagnetic Field Network (PEFNet) which utilizes a data-driven refinement phase, which learns from measured data to account for residual errors, including interference effects. By integrating a knowledge-driven estimate with data-driven corrections, this approach captures both deterministic physical properties and stochastic elements like interference, leading to improved accuracy in modeling realistic propagation environments.

Q3: Can you explain what are the contributions of this work to the field of AI or machine learning?

A3: We present a platform for multi-objective optimization in mobile networks, which also includes an interface for reinforcement learning integration. This contribution significantly advances the capabilities for optimizing mobile network environments, providing a testbench for the application and evaluation of various reinforcement learning algorithms in this domain.

Q4: The results in the experiments do not show a smooth behavior, can you explain why?

A4: The analysis of the experimental results is provided in the appendix. The suboptimal experimental outcomes are mainly due to the complexity of the optimization scenario. Existing multi-objective algorithms struggle to effectively extract relevant information from large-scale base stations, and their update mechanisms may not be suitable for addressing the current multi-objective optimization challenges.

Q5: How many mobile users and base stations can your simulator support?

A5: In our simulator, the simulated mobile network includes 183 base stations and 8,000 mobile users.

Q3: The considered optimization problem is rather simple as it has no non-convex quality of service rate constraints.

A3: Thank you for your comment. While the optimization problem may appear simple, we would like to clarify that when non-convex quality of service rate constraints are introduced, the problem can be reformulated as a multi-objective optimization problem using methods like the Karush-Kuhn-Tucker (KKT) conditions.

In this case, the inequality constraints are incorporated into the optimization framework, and the problem can be solved by optimizing the trade-offs between multiple objectives, while respecting the imposed constraints. The KKT conditions provide the necessary conditions for optimality under inequality constraints, and the Pareto front can then be used to evaluate and select the best solution based on the desired balance between conflicting objectives.

This approach allows the model to not only learn optimal strategies based on different input preferences but also to respect the constraints and provide solutions that effectively balance the trade-offs between multiple objectives.

Q4: The reliability of the ray tracing results and how well they match with the platforms reported in Table-1.

A4: We use the PEFNet to simulate ray tracing. The reliability of PEFNet, is supported by the performance metrics from experiments in [1]. In the RadioMapSeer dataset, PEFNet achieved an R2 value of 0.9731, and in the RSRPSet dataset, it reached an R2 value of 0.9314. These high R2 values, which are very close to 1, indicate a very good fit between our model's predictions and the actual path loss data. This demonstrates the accuracy and reliability of PEFNet in estimating path loss.

[1] Fenyu Jiang, Tong Li, Xingzai Lv, Hua Rui, and Depeng Jin. Physics-informed neural networks for path loss estimation by solving electromagnetic integral equations. IEEE Transactions on Wireless Communications, 2024.

Q5: Constraint violation probability should be included in the results.

A5: We would like to clarify that our simulator has action constraints, with the multi-objective optimization algorithm reading the action bounds directly from the simulator. Thus, the action constraints are always satisfied, and no violations occur. Additionally, for constraints on the optimization objectives, we show the multi-objective optimization results on a pareto front and select solutions that meet the constraints directly from the front. Therefore, constraint violations are not observed in our results.

Q6: MORL algorithms can be easily implemented using OpenAIGym, is there an interface available for OpenAI Gym?

A6: Thank you for your comment regarding the use of OpenAI Gym for implementing MORL algorithms. We currently do not have an interface available for OpenAI Gym. We would like to clarify that our approach is compatible with the majority of the interfaces supported by Gym. Additionally, our framework allows users to define custom interfaces, giving them the flexibility to specify the outputs they wish to obtain. In the future, we aim to achieve full compatibility with Gym, providing a seamless integration for MORL algorithm implementations.

We thank the reviewer for recognizing our paper’s strengths and giving constructive comments. We would like to address the comments and questions below.

Q1: It is not clear why multi-objective reinforcement learning techniques are beneficial compared to multi-objective optimization techniques and how envelope outperforms other RL solutions.

A1: Multi-objective reinforcement learning (MORL) is particularly well-suited for dynamic, large-scale environments such as mobile networks, where objectives need to be balanced in real time and can change over time. In contrast, multi-objective optimization (MOO) excels in static, well-defined scenarios with a clear set of objectives, where detailed system modeling and offline computations can be effectively applied.

MOO is effective for optimizing objectives such as energy efficiency and spectrum efficiency in scenarios that involve well-structured, fixed problems. It relies on mathematical frameworks like ε-constraint methods and iterative block coordinate descent to solve trade-offs between objectives. However, MOO's reliance on offline computation, system modeling, and iterative techniques makes it less adaptable to dynamic, real-time conditions, particularly in large-scale, evolving networks. This limits its application in mobile networks, where network conditions and user demands are constantly changing.

On the other hand, MORL introduces a learning-based approach that can dynamically adapt to changing network conditions and user preferences without requiring retraining. By using methods such as envelope-based learning and generalized Bellman equations, MORL optimizes trade-offs like reliability, latency, and throughput in real time. envelope-based learning, in particular, allows MORL to efficiently handle multiple conflicting objectives by learning a generalized policy that balances these objectives without reducing them to a single scalarized metric. This flexibility makes MORL highly effective for dynamic networks, where conditions are unpredictable and decisions need to be made on the fly.

Unlike traditional reinforcement learning (RL), which typically optimizes a single cumulative reward, MORL is designed to handle multi-objective problems by modeling and learning the trade-offs between objectives. Techniques like hindsight experience replay and convex envelope optimization further enhance MORL's ability to explore diverse preferences and learn optimal policies that perform well under various scenarios. These features make MORL an ideal solution for next-generation cellular networks, where the ability to balance conflicting goals such as ultra-reliable low-latency communication (URLLC), energy efficiency, and seamless connectivity is critical.

In summary, while MOO is effective for static, well-defined problems that require detailed modeling, MORL offers a more adaptive and flexible solution for the dynamic and complex environments of modern mobile networks.

Q2: The presented results are not comprehensive and it is hard to gain any insights in terms of the computation or time complexity or dimension of the Generative AI based proposed simulator.

A2: Thank you for your comment. We have provided a detailed discussion of the runtime comparisons between GenNet and traditional simulators in Table 2: Simulation Efficiency of GenNet and Existing Environments. This table presents a comprehensive analysis of the simulation efficiency, including tasks related to mobile user behaviors and wireless transmission.

Our results show that for both tasks, GenNet's computational efficiency significantly outperforms traditional simulators. Specifically, the simulation time is reduced by more than an order of magnitude—over 10 times faster—compared to conventional simulators. This reduction in runtime proves GenNet's better performance in handling complex simulations, particularly in large-scale, dynamic network scenarios, where traditional simulators often struggle with scalability and efficiency.