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Significance
Circulating fluidized beds (CFBs) are among the most important reactors in energy and chemical engineering, but their internal flow and combustion states are extremely difficult to perceive in real time. Inside a CFB boiler, dense gas-solid motion, heat transfer, species transport, and chemical reactions are strongly coupled. Local changes in solids circulation, temperature, or gas composition may affect the whole reactor, yet only sparse measurement signals can usually be obtained from accessible positions. These limited signals are not sufficient to directly reveal the full internal flow and combustion conditions. Computational fluid dynamics (CFD) can provide detailed full-field information, but its computational cost is too high for online prediction and operational early warning. This gap creates the need for a digital twin (DT): a virtual-real mapping system that connects physical measurements with a digital model, reconstructs the hidden internal field, and predicts its future evolution fast enough to support real-time decision making.
In a recent study published in Chemical Engineering Science, Mr. Xiaofei Li, A/Prof. Shuai Wang, Prof. Kun Luo, and Prof. Jianren Fan from Zhejiang University developed a novel enhanced compressed sensing-temporal convolutional neural network-reduced order model (ECS-TCN-ROM) for CFB real-time prediction. This work represents a milestone toward digital twins of complex gas-solid reacting systems, establishing a direct route from sparse physical measurements to real-time digital reconstruction. The importance of this work lies not only in accelerating simulation, but also in providing a breakthrough for virtual-real fusion in complex energy-chemical reactors.
The first highlight of the work is the construction of a physics-informed reduced representation of the complex reactor field. Based on full-order simulation data, proper orthogonal decomposition (POD) is used to extract dominant spatial modes and their corresponding time-dependent mode coefficients, thereby decomposing the high-dimensional gas-solid reacting flow into a limited number of physically meaningful modes. In this way, the complex full-field reactor dynamics are projected from the original high-dimensional space into a compact reduced order model (ROM). This transformation is a key breakthrough, because it makes an otherwise inaccessible full-field reacting flow describable by a low-dimensional physical representation while retaining the dominant structures that govern reactor behavior. With this reduced representation, the model no longer needs to predict every grid point directly; instead, it predicts the evolution of the mode coefficients and then reconstructs the full field through the retained POD modes. This strategy makes real-time prediction computationally feasible.
The second highlight is the virtual-real fusion enabled by enhanced compressed sensing (ECS). A digital twin cannot rely on complete CFD fields as online input; it must work with limited physical measurements. The authors therefore innovatively developed ECS to establish the mapping from sparse measurement data in physical space to mode coefficients in digital space. The discrete empirical interpolation method (DEIM) is adopted to determine informative sensor positions, while an adaptive Savitzky-Golay (S-G) filtering strategy is introduced to suppress noise in the reconstructed mode coefficients. This step is critical because it allows limited, noisy measurement information to drive the digital model and reconstruct the hidden full-field reactor state. In this sense, the ECS strategy turns sparse measurements from isolated local observations into effective gateways for full-field digital perception.
The third highlight is ahead-of-time full-field prediction through a temporal convolutional neural network (TCN). The TCN learns the nonlinear temporal dependence hidden in the mode coefficient sequences, allowing the reduced model to infer how dominant physical structures will evolve without repeatedly solving the full multiphase governing equations online. By embedding artificial intelligence (AI) into the evolution of mode coefficients, the framework transforms the reduced order model from a fast reconstruction tool into a predictive engine for future reactor states. After the current mode coefficients are reconstructed from sparse information, the TCN predicts their future evolution. These predicted mode coefficients are then combined with POD modes to reconstruct future distributions of CO2 mass fraction, temperature, and particle volume fraction. The resulting ECS-TCN-ROM therefore goes beyond current-state reconstruction. It provides future full-field prediction, which is the key capability required by a CFB digital twin.
The reported results demonstrate the strength of this framework. The ECS-TCN-ROM captures the main characteristics of the reactor fields while achieving a speedup of approximately 4-5 orders of magnitude compared to the full-order CFD computation for a single variable. For industrial CFB operation, this rapid prediction capability provides more than a numerical advantage. It demonstrates the feasibility of transforming sparse physical measurements into real-time, full-field digital states of a complex gas-solid reacting system.
By integrating POD-based reduced modelling, ECS-based virtual-real fusion, and TCN-based future prediction, this work develops a breakthrough physical AI-driven digital twin framework for industrial fluidized beds. More than a fast prediction tool, this framework marks an important step toward the deep integration of physical reactors and their digital counterparts, enabling complex gas-solid reacting systems to be perceived, predicted, and updated in real time. This digital twin framework therefore provides a powerful pathway for future virtual-real interaction and lays a solid foundation for real-time full-field optimization and control of complex energy-chemical systems.
Reference
Xiaofei Li, Shuai Wang, Kun Luo*, Jianren Fan, A novel reduced order model of circulating fluidized beds coupled with enhanced compressed sensing and temporal convolutional neural networks, Chemical Engineering Science, Volume 317, 2025, 122003,
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