Physics-Informed Neural Network for Modelling the Thermochemical Curing Process of Composite-Tool Systems During Manufacture (2011.13511v2)

Abstract: We present a Physics-Informed Neural Network (PINN) to simulate the thermochemical evolution of a composite material on a tool undergoing cure in an autoclave. In particular, we solve the governing coupled system of differential equations -- including conductive heat transfer and resin cure kinetics -- by optimizing the parameters of a deep neural network (DNN) using a physics-based loss function. To account for the vastly different behaviour of thermal conduction and resin cure, we design a PINN consisting of two disconnected subnetworks, and develop a sequential training algorithm that mitigates instability present in traditional training methods. Further, we incorporate explicit discontinuities into the DNN at the composite-tool interface and enforce known physical behaviour directly in the loss function to improve the solution near the interface. We train the PINN with a technique that automatically adapts the weights on the loss terms corresponding to PDE, boundary, interface, and initial conditions. Finally, we demonstrate that one can include problem parameters as an input to the model -- resulting in a surrogate that provides real-time simulation for a range of problem settings -- and that one can use transfer learning to significantly reduce the training time for problem settings similar to that of an initial trained model. The performance of the proposed PINN is demonstrated in multiple scenarios with different material thicknesses and thermal boundary conditions.

• The paper develops a PINN approach that integrates physical constraints with neural networks to model coupled thermal conduction and resin cure kinetics.
• It introduces a decoupled network architecture with adaptive loss weighting to enhance training stability and accuracy in multi-objective settings.
• The method is validated against FEM simulations, showing minimal errors in temperature and cure predictions for reliable real-time use.

Insightful Overview of "Physics-Informed Neural Network for Modeling the Thermochemical Curing Process of Composite-Tool Systems During Manufacture"

The paper presents a sophisticated approach leveraging Physics-Informed Neural Networks (PINNs) for simulating the complex thermochemical curing process of composite materials on tooling systems. The methodology integrates deep learning with domain-specific physics, effectively solving the coupled system of differential equations governing the heat and cure kinetics during the manufacture of composite tools in an autoclave environment.

Technical Discussion and Methodological Innovations

1. Modeling Framework: The paper develops a PINN framework explicitly designed to tackle the multiphysics challenge present in composite tool curing processes. The ability of PINNs to incorporate domain knowledge through a physics-based loss function offers a distinct advantage over traditional numerical methods such as the finite element method (FEM), especially concerning computational efficiency and flexibility in parameter space sampling.
2. Decoupled Network Architecture: Central to the paper's contributions is a novel approach for designing the network architecture. The authors propose a decoupled setup where separate subnetworks independently model thermal conduction and resin cure kinetics. Sequential training is employed to address training instability issues arising from coupling dynamics, which enhances the PINN's stability and accuracy.
3. Interface Discontinuities: The paper extends the standard formulation of PINNs by incorporating explicit discontinuities at the composite-tool interface. This capability is critical for accurately capturing the physical behaviors expected in real-world applications where material properties such as thermal conductivity exhibit discontinuous behavior across interfaces.
4. Adaptive Training Techniques: An innovative adaptive loss weighting scheme is introduced. This scheme dynamically adjusts the importance of various loss components—governing equations' residuals, initial conditions, and boundary conditions—ensuring balanced training that is crucial for multi-objective optimization.
5. Efficient Training Strategies: The research also highlights the use of transfer learning strategies to expedite training times significantly. By reusing learned models from similar problem settings, training new models becomes computationally more efficient, which is particularly beneficial in scenarios requiring numerous simulations across similar configurations.

Numerical Validation and Implications

The PINN approach is comprehensively validated against high-fidelity FEM simulations under diverse scenarios with variable material thicknesses and thermal boundary conditions. The results show excellent agreement, with errors in both temperature and cure predictions kept minimal, showcasing the efficacy of PINNs in capturing complex curing dynamics. This agreement underscores the potential of using PINNs not only for modeling but also as surrogate models for real-time applications and uncertainty quantification in manufacturing processes.

Future Directions and Research Potential

As demonstrated, PINNs provide a robust framework which could transform current practices in composite manufacturing simulations. Future avenues of research could focus on extending the application of PINNs to more complex multiphysics problems, potentially integrating other phenomena such as fluid flow or chemical reactions. Moreover, the integration of data-driven approaches with PINNs could enhance model generalization and predictive capabilities even further, broadening the scope of real-world engineering problems addressable by this methodology.

In conclusion, this paper contributes substantially to the toolbox of techniques available for efficiently solving complex, coupled partial differential equations in manufacturing contexts. The methodological innovations and results presented have significant implications for both the theoretical advancement of PINNs and their practical applications in composite material manufacturing domains.