DeepONet-accelerated Bayesian inversion for moving boundary problems
Abstract
This work demonstrates that neural operator learning provides a powerful and flexible framework for building fast, accurate emulators of moving boundary systems, enabling their integration into digital twin platforms. To this end, a Deep Operator Network (DeepONet) architecture is employed to construct an efficient surrogate model for moving boundary problems in single-phase Darcy flow through porous media. The surrogate enables rapid and accurate approximation of complex flow dynamics and is coupled with an Ensemble Kalman Inversion (EKI) algorithm to solve Bayesian inverse problems. The proposed inversion framework is demonstrated by estimating the permeability and porosity of fibre reinforcements for composite materials manufactured via the Resin Transfer Moulding (RTM) process. Using both synthetic and experimental in-process data, the DeepONet surrogate accelerates inversion by several orders of magnitude compared with full-model EKI. This computational efficiency enables real-time, accurate, high-resolution estimation of local variations in permeability, porosity, and other parameters, thereby supporting effective monitoring and control of RTM processes, as well as other applications involving moving boundary flows. Unlike prior approaches for RTM inversion that learn mesh-dependent mappings, the proposed neural operator generalises across spatial and temporal domains, enabling evaluation at arbitrary sensor configurations without retraining, and represents a significant step toward practical industrial deployment of digital twins.
Summary
This paper addresses the problem of computationally expensive Bayesian inversion for moving boundary problems, specifically in the context of Resin Transfer Moulding (RTM) for composite material manufacturing. The main research question is how to accelerate this inversion process to enable real-time estimation of material properties like permeability and porosity, which are crucial for process control and digital twin integration. To achieve this, the authors employ a Deep Operator Network (DeepONet) to create a surrogate model of the complex single-phase Darcy flow through porous media that governs the RTM process. This surrogate is then coupled with an Ensemble Kalman Inversion (EKI) algorithm to efficiently solve the Bayesian inverse problem. The DeepONet is trained on data generated from a Control Volume Finite Element Method (CVFEM) solver. The approach is validated using both synthetic and experimental data, focusing on estimating permeability and porosity variations in fiber reinforcements. The key finding is that the DeepONet surrogate significantly accelerates the EKI inversion process by several orders of magnitude compared to using the full CVFEM model directly. This allows for real-time, high-resolution estimation of material properties, enabling effective monitoring and control of RTM processes. A significant contribution is the DeepONet's ability to generalize across spatial and temporal domains, allowing evaluation at arbitrary sensor configurations without retraining, which addresses a limitation of previous mesh-dependent approaches. This research matters because it provides a practical and efficient framework for integrating digital twins into RTM and other moving boundary flow applications.
Key Insights
- •DeepONet-accelerated EKI achieves "several orders of magnitude" speedup compared to full-model EKI for Bayesian inversion in moving boundary problems. This acceleration is crucial for enabling real-time applications.
- •The DeepONet surrogate generalizes across spatial and temporal domains, allowing for evaluation at arbitrary sensor configurations without retraining. This is a significant advantage over previous mesh-dependent approaches for RTM inversion.
- •The framework effectively identifies both material parameters (permeability, porosity) and the geometry of defective regions (e.g., race-tracking channels, central defects).
- •The paper highlights the sensitivity of posterior estimates of scalar parameters (e.g., viscosity, inlet pressure parameters) to the ensemble size used in EKI, even with relatively dense sensor configurations.
- •The authors use an "out-of-sample" ground truth for validation, which tests the robustness and generalization capabilities of the DeepONet surrogate under covariate shift. This is more challenging than using data drawn directly from the prior distribution.
- •The DeepONet is trained on a fixed mesh but can be evaluated at arbitrary spatial locations due to its operator learning nature, making it adaptable to different sensor placements.
Practical Implications
- •The developed framework can be used for real-time monitoring and control of RTM processes, enabling adjustments during manufacturing to improve component quality.
- •The technology facilitates non-destructive evaluation of manufactured parts concurrently with the injection process, potentially leading to certification purposes.
- •Practitioners and engineers can use the DeepONet surrogate to rapidly evaluate different process designs and control strategies (e.g., optimizing inlet configurations, pressure schedules) to minimize deviations from design specifications.
- •The framework opens up future research directions, including extending the DeepONet surrogate to handle anisotropic permeability, multi-phase flows, and more complex defect geometries.
- •The approach can be applied to other computationally intensive RTM tasks, such as optimal process design and both passive and active control strategies.