Link-adaptive digital twin for robust physical-layer modeling in hybrid-amplified ultra-wideband optical networks

Ultra-wideband optical networks represent a practical solution for expanding communication capacity and supporting emerging applications such as artificial intelligence data center interconnection and 6G-oriented intelligent networks. Accurate physical-layer modeling has become increasingly essential to ensure reliable ultra-wideband network operation and capacity optimization, particularly under the intensified inter-channel stimulated Raman scattering (ISRS) effect.

The paper identifies several critical challenges in physical-layer modeling for ultra-wideband optical networks. First, the ISRS effect becomes non-negligible with the introduction of new bands, leading to power transfer from high-frequency to low-frequency channels and degrading transmission performance. Second, hybrid-amplified links combining Raman amplifiers (RAs) and doped fiber amplifiers (DFAs) are widely deployed, which introduces complex pump–signal interactions that further complicate physical-layer modeling. Third, link parameters such as fiber length, launch power, Raman pump power, and insertion loss vary significantly across different transmission scenarios, requiring robust models that maintain high accuracy under diverse conditions. Finally, practical network operation requires real-time feedback, demanding modeling approaches that are both accurate and computationally efficient.

Existing modeling approaches struggle to simultaneously meet the requirements of accuracy, computational efficiency, and cross-scenario generalization. Analytical models, such as GN-based extensions, provide valuable theoretical insights but often involve high computational complexity and depend on precise link parameter measurements. Machine learning (ML)–based methods offer fast inference and the capability to capture complex nonlinear effects, but conventional ML models often generalize poorly across diverse link configurations.

The paper proposes the link-adaptive digital twin (LA-DT) that enables robust physical-layer modeling in hybrid-amplified ultra-wideband links, addressing key modeling challenges of limited generalization, high computational complexity, and slow inference speed. LA-DT is capable of adapting to diverse link conditions, accounting for variations in fiber length, launch power, Raman pump power, and insertion losses. It explicitly considers the variation of insertion loss induced by Raman pumps for the first time, a factor that is often overlooked but has a non-negligible impact on practical network performance.

1. EDFA Heterogeneity-Driven Decomposed GSNR Modeling: To mitigate the accuracy degradation of GSNR modeling caused by EDFA heterogeneity in practical ultra-wideband networks, the authors adopt a decomposed strategy that predicts three key physical-layer powers before entering EDFA—namely, amplified spontaneous emission (ASE) noise power, nonlinear interference (NLI) power, and signal power—rather than modeling GSNR directly. This approach ensures accurate GSNR estimation under varying EDFA gain and noise figure (NF) settings, while enhancing interpretability across diverse link conditions.

2. DeepModNet-Based DT Architecture: To enhance generalization in cross-scenario power prediction, three dedicated DT models were developed: DeepModNet-NLI, DeepModNet-ASE, and DeepModNet-Sig. These DeepModNet models are built on a novel neural network architecture that introduces linear modulation layers (LMLs), enabling dynamic conditional modeling through a shared backbone and cross-domain regression. Each LML performs dynamic conditioning by learning domain-dependent scaling and shifting functions. Given an intermediate feature vector h and an embedded domain label z, the LML applies the transformation: h̃ = gamma(z) ⊙ h + beta(z), where gamma(z) and beta(z) are learnable functions that generate modulation parameters conditioned on the domain z, and ⊙ denotes element-wise multiplication.

3. Domain Discriminator–Guided Few-Shot Fine-Tuning: To further support rapid adaptation to previously unseen scenarios with only limited data, three domain discriminators are designed to guide the few-shot fine-tuning of the DeepModNet-based DT models. The domain discriminators perform domain identification by evaluating the consistency of functional mappings, selecting the training domain whose functional mapping exhibits the highest consistency with that of the target samples under the current model architecture.

The considered condition is a C+L band system with a total bandwidth of 12 THz, divided into 120 WDM channels at 100 GHz spacing. Standard single-mode fiber (SSMF) is employed with an attenuation of 0.2 dB/km, dispersion of 16.7 ps/nm/km at 1550 nm, and dispersion slope of 0.08 ps/nm2/km. Six Raman pumps are employed at wavelengths of 1425 nm, 1435 nm, 1445 nm, 1465 nm, 1480 nm, and 1500 nm, each randomly sampled from 0 to 200 mW with 1 mW steps.

A comprehensive domain pool comprising 35 transmission scenarios was constructed with diverse ultra-wideband link conditions, including variations in fiber length (40-80 km), per-channel launch power (-3 to 2 dBm), fiber insertion loss (0.25-0.75 dB), and Raman pump insertion loss (0-0.5 dB). Training data were generated using GNPy, which adopts a semi-analytical GN/EGN framework for physical layer modeling. For each scenario, 500 samples were collected, with 300 used for training and 200 for testing, forming a multi-domain dataset comprising 10,500 training samples and 7,000 test samples.

DeepModNet-NLI consists of 3 hidden layers with a total of 336 neurons, employs the Tanh activation function, and incorporates 1 LML along with a 32-dimensional domain embedding. Both DeepModNet-ASE and DeepModNet-Sig employ 4 hidden layers. The former uses a total of 512 neurons with Tanh activation, while the latter uses a total of 2528 neurons with ReLU activation. Each contains 4 LMLs, with domain embeddings of 32 and 64 dimensions, respectively. All models are trained using the Adam optimizer with a learning rate of 0.001.

A static conditional modeling approach, referred to as BaseCondNet, was adopted as the baseline. Instead of applying dynamic feature modulation, the baseline method directly incorporates scenario-specific parameters into the input features, consisting of 10 features including six-dimensional Raman pump powers and four link parameters: fiber length, per-channel launch power, fiber insertion loss, and Raman pump insertion loss.

DeepModNet-based DT models consistently outperform the baseline BaseCondNet-based models across all three power prediction tasks, despite being trained with the same amount of data.

For the NLI power prediction task, the mean and standard deviation (mu ± sigma) of the RMSE are 0.151 ± 0.187 dBm for DeepModNet-NLI and 0.343 ± 0.259 dBm for BaseCondNet-NLI. The corresponding MaxAE values are 0.262 ± 0.265 dBm and 0.630 ± 0.366 dBm, respectively.

For the ASE power prediction task, the RMSE values are 0.111 ± 0.073 dBm for DeepModNet-ASE and 0.267 ± 0.162 dBm for BaseCondNet-ASE. The corresponding MaxAE values are 0.228 ± 0.145 dBm and 0.447 ± 0.234 dBm, respectively.

For the signal power prediction task, the RMSE values are 0.113 ± 0.209 dBm for DeepModNet-Sig and 0.239 ± 0.232 dBm for BaseCondNet-Sig. The corresponding MaxAE values are 0.191 ± 0.295 dBm and 0.369 ± 0.317 dBm, respectively.

By taking the average RMSE over all 7,000 test samples as the primary indicator of prediction accuracy, DeepModNet-NLI improves the prediction accuracy by 56.0% compared to BaseCondNet-NLI in the NLI power modeling task. Similarly, DeepModNet-ASE and DeepModNet-Sig achieve accuracy improvements of 58.4% and 52.7%, respectively, in the ASE and signal power prediction tasks.

Domain-wise evaluations across all 35 scenarios confirm that DeepModNet-based DT models consistently outperform the baseline models in every individual link condition, demonstrating both stable and robust prediction performance across diverse domains. The observed accuracy improvement is primarily attributed to the dynamic conditional modeling strategy adopted by DeepModNet architecture, which enables the model to effectively capture variations induced by different link configurations, achieving dynamic adjustment and adaptive modeling across diverse transmission scenarios.

A wall-clock runtime comparison was conducted between GNPy propagation simulations and the trained DeepModNet-based models under identical link configurations. GNPy requires approximately 8 seconds to complete 20 runs for each domain configuration. In contrast, the trained DeepModNet-based models complete 20 inference runs within milliseconds. Across all five domains tested, the total runtime of the ML-based models is substantially lower than that of GNPy, demonstrating the computational advantage of the proposed approach for repeated evaluations. All time measurements were conducted on a local computing system equipped with a 12th Gen Intel Core i7-1260P CPU running at 2.10 GHz and 32 GB of RAM.

To assess the adaptation capability of the domain discriminator–guided DT models to previously unseen scenarios, 12 new ultra-wideband scenarios were constructed outside the training domain pool, covering variations in fiber length (45-75 km), per-channel launch power (-2.5 to 1.5 dBm), pump insertion loss (0-0.6 dB), and fiber insertion loss (0.4-0.9 dB). For each scenario, 20 samples were collected for fine-tuning and 200 samples for testing, resulting in a total of 2,400 independent test samples.

In the NLI power prediction task, the mean and standard deviation (mu ± sigma) of RMSE and MaxAE for DeepModNet-NLI before fine-tuning are 0.675 ± 0.365 dBm and 1.001 ± 0.431 dBm, respectively. After fine-tuning with 20 samples, these values are reduced to 0.218 ± 0.241 dBm and 0.372 ± 0.323 dBm, respectively.

In the ASE power prediction task, the RMSE and MaxAE values for DeepModNet-ASE before fine-tuning are 0.378 ± 0.266 dBm and 0.540 ± 0.416 dBm, respectively. After fine-tuning, they decrease to 0.117 ± 0.075 dBm and 0.241 ± 0.144 dBm, respectively.

In the signal power prediction task, the RMSE and MaxAE values for DeepModNet-Sig before fine-tuning are 0.454 ± 0.259 dBm and 0.921 ± 0.442 dBm, respectively. After fine-tuning, they are reduced to 0.160 ± 0.205 dBm and 0.276 ± 0.285 dBm, respectively.

Based on the average RMSE across 2,400 test samples, the modeling accuracy is improved by 67.7%, 69.0%, and 64.8% for the NLI, ASE, and signal power prediction tasks, respectively. These results validate the effectiveness of the proposed domain discriminator in identifying new scenarios and confirm that the DeepModNet-based DT models possess strong cross-domain generalization capability, enabling rapid adaptation to unseen scenarios even with extremely limited data.

The GSNR estimation performance was evaluated under both operating modes. For the domain-aware prediction mode across 35 scenarios, the estimated GSNR was calculated using the predicted NLI, ASE, and signal powers substituted into Eq. (8), considering a variety of EDFA configurations to adapt to heterogeneity in practical optical networks. For the 60 channels in the L-band, the gain of EDFA is set to compensate for the fiber attenuation, resulting in a gain range of 8 dB to 16 dB. In the C-band, the EDFA gain is increased by an additional 2 dB to compensate for the power transfer caused by ISRS, resulting in a gain range of 10 dB to 18 dB. The noise figure is set to 5 for C-band EDFAs and 6 for L-band EDFAs.

For DeepModNet, the mean and standard deviation (mu ± sigma) of RMSE are 0.114 ± 0.166 dB, while those of MaxAE are 0.197 ± 0.227 dB. In comparison, BaseCondNet-based models produce significantly larger errors, with RMSE values of 0.258 ± 0.196 dB and MaxAE values of 0.408 ± 0.263 dB. DeepModNet-based DT models achieve a 55.8% improvement compared to BaseCondNet in GSNR estimation. This improvement is primarily attributed to the accurate modeling of signal power by DeepModNet-Sig, which plays a dominant role in GSNR estimation as the signal power is generally much greater than the other two powers during transmission.

For the few-shot fine-tuning mode across 12 unseen scenarios, before fine-tuning, the mean and standard deviation (mu ± sigma) of RMSE and MaxAE are 0.410 ± 0.231 dB and 0.870 ± 0.398 dB, respectively. After fine-tuning with 20 samples per domain, these values are reduced to 0.159 ± 0.179 dB for RMSE and 0.278 ± 0.244 dB for MaxAE. RMSE is reduced by 61.2%, and MaxAE decreases by 68.0%. Domain-wise heatmap analysis shows that all 12 domains exhibit significant improvements in RMSE distribution after fine-tuning, with RMSE values shifting toward lower ranges and high-probability regions becoming more concentrated in the low-error intervals.

The proposed LA-DT provides a promising solution for generalized and scalable physical-layer modeling of hybrid-amplified ultra-wideband optical networks. By providing real-time and accurate modeling results, LA-DT can directly support GSNR optimization in such networks and enhance overall network reliability, while also supplying feedback for adaptive resource allocation. Future work will focus on extending the proposed framework to support heterogeneous multi-span scenarios by incorporating span-level parameter modeling and mechanisms to capture cascaded power evolution across multiple spans. Additionally, incorporating broader system-level factors such as varying channel configurations, modulation formats, traffic loading conditions, and ROADM filtering effects constitutes an important direction for further development. Future work will also employ high-precision Split-Step Fourier Method (SSFM)-based simulations and experimental measurements to strengthen the physical rigor of the framework and verify its consistency with fundamental propagation physics under realistic conditions.

Improvements to AI Systems:

1. Domain-Adaptive Neural Network Architecture with Linear Modulation Layers (LMLs): Implement a dynamic conditioning mechanism where a shared backbone network receives domain-specific modulation parameters (γ(z), β(z)) generated from embedded domain labels. This enables the AI to adjust its internal feature representations based on context without retraining, improving cross-domain generalization for regression tasks.

2. Decomposed Prediction Strategy for Composite Metrics: Instead of directly predicting a composite target (e.g., GSNR), decompose it into physically meaningful intermediate components (signal power, ASE noise, NLI). This improves accuracy, interpretability, and robustness when downstream components (e.g., EDFA gain/NF) vary across deployment conditions.

3. Domain Discriminator–Guided Few-Shot Fine-Tuning: Add a discriminator module that identifies which training domain has the most consistent functional mapping with new target samples. Use this to guide selective fine-tuning with minimal data (e.g., 20 samples), achieving rapid adaptation to unseen scenarios while avoiding catastrophic forgetting.

4. Hybrid Analytical-ML Hybridization: Combine physics-based analytical models (e.g., GN/EGN frameworks) with ML inference to generate training data and validate predictions, ensuring physical consistency while gaining ML’s speed (milliseconds vs. seconds) for real-time network control.

5. Parameter-Aware Feature Engineering: Explicitly incorporate previously overlooked operational parameters (e.g., Raman pump insertion loss) into the model input space, enabling the AI to capture subtle but impactful physical effects that degrade performance if ignored.

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What the Improved AI System Can Do:

• Real-Time Physical-Layer Modeling: Predict signal, ASE noise, and nonlinear interference powers across diverse ultra-wideband optical links in milliseconds, enabling instantaneous GSNR estimation for dynamic network optimization.

• Cross-Scenario Generalization: Maintain high accuracy across varying fiber lengths (40–80 km), launch powers (-3 to 2 dBm), insertion losses, and Raman pump configurations without retraining, reducing the need for per-scenario model development.

• Rapid Adaptation to New Environments: Fine-tune to previously unseen link configurations with as few as 20 samples, achieving >60% error reduction, making it deployable in field conditions where exhaustive data collection is impractical.

• Robust Performance Under Heterogeneous Hardware: Accurately estimate GSNR even when EDFA gain and noise figure settings vary between C-band and L-band, supporting mixed-amplifier deployments common in real networks.

• Scalable Network Control Feedback: Provide fast, accurate feedback loops for adaptive resource allocation, capacity optimization, and fault detection in ultra-wideband systems, supporting AI-driven data center interconnects and 6G intelligent networks.

• Interpretable Predictions: Offer decomposed power predictions that align with physical intuition, enabling engineers to diagnose which impairment (noise, nonlinearity, or signal loss) dominates in a given link condition.