EM-GANSim: Real-time and Accurate EM Simulation Using Conditional GANs for 3D Indoor Scenes

W: We appreciate the reviewer’s comments and as mentioned in Section 4.1, the dataset was generated using state-of-the-art EM simulation tools, specifically WinProp and DCEM, which are well-established in the field for their accuracy to simulate electromagnetic wave propagation. These tools ensure that the ground truth (GT) labels are highly reliable and adhere to physical principles. The dataset spans a variety of 3D indoor environments, including complex floor plans, varying material properties (e.g., concrete, glass, wood), and multiple room configurations. This diversity ensures robust model performance and generalizability. The source code and dataset will be made publicly available upon publication, as stated in the paper.

Q: We acknowledge the effectiveness of Wasserstein loss in improving GAN stability and convergence. While we have not explicitly implemented the Wasserstein loss in the current study, we chose the binary cross-entropy loss due to its computational simplicity and established efficacy in our application context.

We conducted an initial analysis of the impact of material properties on GAN performance. Variations in material (e.g., concrete, glass, wood) are incorporated in the training dataset to ensure robust predictions across diverse scenarios. While our results indicate that the GAN generalizes well, we noticed minor discrepancies in accuracy for highly reflective materials like glass. The dataset was generated synthetically using established EM simulators like WinProp and DCEM, which compute signal propagation based on known material properties and geometries. Therefore, no physical sensors were employed for data collection in this study. The accuracy of the synthetic data is validated against physical principles of EM propagation, such as adherence to Maxwell's equations and established models for reflection, diffraction, and attenuation. Furthermore, benchmarking against traditional ray-tracing methods demonstrates the fidelity of our training data.

W1: We had comparison results with both DCEM and WinProp, as shown in heatmap plots Figure 2,6,7. While it is true that our method has a slightly higher MSE compared to DCEM (~0.8 dbm^2), we emphasize that EM-GANSim achieves a significant efficiency improvement (5X speedup). We can include more quantitative results Table in the revised work. The mentioned papers Vaganova et al., 2023; Haron et al., 2021; Gómez et al., 2023 are different in focus and we did not find released source codes for reference.

W2: We included a detailed discussion of this real-time efficiency in Section 5.2, specifically highlighting the performance for each data point. The key advantage of our method lies in its ability to generate predictions for a given point in milliseconds (approximately 1 ms), which is significantly faster than traditional RT-based methods that require 5X the time. This 5X improvement is a major advancement because it transforms EM simulations from a computationally intensive process into one capable of supporting dynamic scenarios. Such scenarios often involve constantly changing transmitter locations or environmental configurations, where rapid recalculations are essential. As discussed in the paper, our method's capability to handle these dynamic conditions makes it particularly advantageous for applications like 5G network planning and real-time decision-making in complex indoor environments.

W3: The benefits of GAN are mentioned in the Introduction. The main results section and discussed in detail in Section 3.2. We believe that discussing the benefits of GANs without providing sufficient background could lead to a lack of clarity or context for readers unfamiliar with the technology.

W4: The phrase "more pronounced areas of both high and low signal strength" aimed to convey that the GAN-based heatmaps capture a broader dynamic range of power levels, which aligns with the expected physics of signal attenuation and multipath effects in complex environments. The histogram Figure 3 shows this pattern more clearly. We will revise the writeup to minimize confusion.

MW1: We have a flowchart with many details in Figure 5, but due to space limits and for a brief introduction, we used Figure 1 to only provide a simple overview. We can add more information to Figure 1 to make it more comprehensive.

MW2: Thank you for your observation. However, the use of {enumerate} and {itemize} is intentional and necessary for the clarity and systematic presentation of our contributions and results.

MW3: We will make sure that our use of terminology is consistent.

MW4: This is to show the calculation in milliseconds.

Q1: We intended to include more results in the main scripts but due to space limits, we presented them in the Appendix.

Q2: We report the average MSE to provide a single, standardized metric for evaluating overall model accuracy across diverse scenarios, offering a clear and concise comparison against traditional methods while reflecting the model's generalization capabilities.

Q3: Traditional RT methods are introduced and cited in the second paragraph of the Introduction.

W1: While the heatmaps displayed are 2D slices, the height information is encoded and utilized within the model (simulated at different heights). The generator receives a 3D encoding of the environment geometry, including vertical features, which can be found in the provided sample data. We will make sure to clarify this and add 3d simulation results in the revised version.

W2: The "2K+ models and 64M heatmaps" were generated using WinProp and the DCEM simulator, as mentioned in Section 4.1. We generated rooms with different layouts with WinProp and ran ray-tracing to get corresponding heatmaps for each acne. More details can be found in the provided sample data. To facilitate reproducibility, we will release the dataset and code upon acceptance.

W3: We have provided the detailed GAN structure illustration in Figure 5 in the Appendix, and a detailed discussion about the parameters and training process in Section 3.2. We balanced the weights of physical regularizations through experiments with various weighting factors for direct propagation, reflection, and diffraction losses to assess their impact on training stability and accuracy. Starting with baseline values based on electromagnetic theory, we refined the weights using grid search to optimize convergence and output fidelity. This systematic approach ensured a stable and accurate model.

W4: We mentioned the hardware specifications and resources in Section 3.3. The preprocessing cost includes generating the geometry and power prediction data using ray-tracing tools, namely, WinProp and DCEM simulators, which is about 2 weeks of work. While this step is computationally intensive, it is a one-time cost. The gap between training (3 dBm²) and testing (8.5 dBm²) MSE reflects the diversity of unseen test scenarios, as the model generalizes across complex layouts and material configurations. And 8.5 dBm^2 MSE means ~3dBm RMSE in power prediction: this level of error suggests that EM-GANSim achieves reasonably high accuracy in modeling received power distributions, especially given the complexity of 3D indoor environments.

Q1: Answered in W1

Q2: Answered in W2. Our dataset is designed to reflect diverse real-world indoor environments, with a distribution including small (<16m^2, 30%), medium (<100m^2, 50%), and large ( <144m^2, 20%) rooms, various configurations (40% single-room, 40% multi-room, 20% complex floor plans), and material types (90% concrete, 5% glass windows, 5% wood door).

Q3: The weights (α, β, γ) in the physics loss function are determined through a combination of theoretical considerations and empirical tuning. Specifically, we started with baseline weights informed by theoretical insights from electromagnetic wave propagation, for example, direct path loss models, reflection coefficients, and UTD diffraction modeling, and iteratively adjusted these values using a grid search methodology to optimize both convergence and output fidelity.

To ensure training stability, we employ Gaussian noise injection, progressive training from simple to complex environments, and adaptive learning rates. Varying room sizes are handled by normalizing spatial dimensions, dividing larger spaces into sub-regions for simulation, and leveraging a diverse dataset to ensure generalization. The criteria for computing sub-regions include the room's overall dimensions, material composition, and the desired resolution for simulation. Typically, sub-regions are standardized to approximately 2m × 2m, as this size is optimal for capturing detailed EM wave behaviors while maintaining manageable computational overhead.

For main: Thank you for the thoughtful feedback. We address concerns about mode collapse and stability as follows:

Random Input Justification: Gaussian noise is important in terms of breaking weight symmetry during training, promoting diversity in generator outputs. As shown in our ablation studies (Table 5, Fig. 7), removing noise leads to less varied, oversmoothed heatmaps, indicating reduced accuracy and a higher risk of mode collapse.

Mitigation of Mode Collapse in cGANs: We mitigate mode collapse using these approaches: First, a large, diverse dataset of 2,000+ indoor scenes, ensuring the model generalizes across scenarios. Second, incremental training (as described in Section 4.2), starting with simple environments and gradually introducing complexity, allows the generator to learn fundamental signal propagation before tackling intricate layouts. Third, a dynamic learning rate schedule to balance the generator-discriminator interplay during training. We will include an ablation analysis of the effects of these techniques in GAN training in the final submission.

Physical Regularizations: We carefully balanced the weights of physical regularizations by conducting experiments with a range of weighting factors for each physical constraint (direct propagation, reflection, and diffraction losses) to evaluate their impact on the stability of training and the accuracy of predictions. Specifically, we started with baseline weights informed by theoretical insights from electromagnetic wave propagation and iteratively adjusted these values using a grid search methodology to optimize both convergence and output fidelity. Each configuration was evaluated based on metrics such as MSE and training loss dynamics to ensure stability. These constraints improve prediction accuracy (as shown in Figure 2 qualitatively, and in Table 4 quantitatively) while avoiding excessive penalization, which could destabilize the generator.

The results demonstrate that these strategies effectively mitigate mode collapse and ensure model stability. We appreciate the reviewer’s comments, which align with our plans for deeper analysis and refinement.

For minor: Representation of Conditional Geometry (Line 162): The encoded geometry represents the 3D spatial layout, including 2d information at every sample height and material properties of the environment. Further details are available in the provided code.

Labeling and Interpretation of Figure 2: The requested labeling information is included clearly in the figure caption. We can highlight the differences in each subfigure as suggested by the reviewer for a better presentation.

We thank the reviewer for their thoughtful feedback and for recognizing our efforts to address the concerns raised previously. We appreciate the opportunity to provide additional clarifications and details to strengthen the paper. While we can not post a revised paper now, we ware trying to adress the remaining concerns in this detailed response:

Our approach has been evaluated across multiple complex models, achieving consistent and high-quality results. This robustness across diverse layouts would be unlikely if the model were experiencing significant mode collapse or overfitting issues. The outputs also underscore the stability of the proposed method. We have ensured through cross-validations and evaluations that the method generalizes well beyond the training data.

A another detailed explanation of hyper-parameters in the loss function and GAN architecture is provided below:

Hyper-Parameter Tuning: We employed a structured and systematic approach to hyper-parameter tuning. Specifically: Grid Search and Sensitivity Analysis: We conducted a grid search to identify optimal ranges for key parameters. Once a promising range was identified, we applied a finer search within that range to converge on the final values.

Validation-Based Optimization: Hyper-parameters were tuned based on performance on a held-out validation set, ensuring the generalizability of the approach and mitigating overfitting.

Regularization: Physical regularization, combined with architectural constraints, was instrumental in maintaining stability during training, further preventing mode collapse.

GAN-Specific Hyper-Parameters: For GAN-related parameters such as learning rates, beta values for optimizers, and the weight of the adversarial loss, we leveraged best practices from the literature, starting with commonly accepted default values as well as from simple to complex senarios, and iteratively refining based on observed stability and performance trends.

According to the request for additional qualitative results, while we understand the reviewer’s interest in further qualitative results, we are constrained by the submission format and guideline now, and will add more results upon final revision.