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Physics-Informed Neural Network for Modelling the Thermochemical Curing Process of Composite-Tool Systems During Manufacture
Sina Amini Niaki, Ehsan Haghighat, Trevor Campbell, Anoush Poursartip, Reza Vaziri
TL;DR
The paper addresses efficient simulation of coupled heat transfer and resin cure in composite-tool systems, where repeated high-fidelity modelling is costly and the processes have distinct behaviours. It develops a modified PINN with decoupled subnetworks, interface-aware physics constraints, adaptive loss weighting, surrogate inputs, and transfer learning. The method produces small surrogate-model errors across cases and supports real-time simulation over problem settings.
Problem
Repeated high-fidelity simulations are costly, while composite curing couples heat conduction and resin kinetics with distinct behaviours.
Method
A modified PINN uses decoupled subnetworks, explicit interface discontinuities, physics-based loss terms, adaptive weighting, surrogate parameters, and transfer learning.
Results
The PINN surrogate has averaged absolute errors below 1.6 K for temperature, 0.007 for degree of cure, and 1.6 K for thermal lag across the reported cases.
Takeaways & Limitations
The framework supports real-time simulation across problem settings and transfer learning can reduce training time for similar settings.
Takeaways & Limitations
The formulation assumes an initially uniform system temperature and zero or very small initial resin cure, while boundary conditions may use prescribed or convective heat transfer.
Abstract
from arXiv · showhide
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.
1. Introduction
Composite curing requires computationally solving coupled heat-transfer and resin-cure PDEs, while repeated high-fidelity simulations can be costly. The paper develops PINN modifications for efficient, realistic modelling and surrogate simulation of composite-tool systems.
- Coupled nonlinear PDEs describe heat conduction and resin cure kinetics during composite manufacture, but their solutions require computational approximation.
- Repeated simulations for optimization, control, or monitoring motivate more computationally efficient solution approaches.
- DNNs can directly approximate PDE solutions and be efficiently trained and evaluated using automatic differentiation and stochastic optimization.
- Theory-guided machine learning requires expensive high-fidelity simulation data, whereas PINNs enforce PDE, initial-condition, and boundary-condition residuals directly.
- The proposed approach addresses distinct thermal-conduction and cure behaviours using decoupled DNN training, interface discontinuities, and physics-based boundary enforcement.
2. Exothermic Heat Transfer in Curing Composite Materials
The paper formulates coupled heat-transfer and resin-cure equations for a composite-tool system with evolving temperature, cure, material discontinuities, and autoclave thermal boundaries.
- Exothermic heat transfer is governed by a PDE with internal heat generation, while resin cure follows a temperature- and cure-dependent ordinary differential equation.
- Together, the equations predict temperature T(x, t) and degree of cure α(x, t) subject to initial and boundary conditions.
- The composite-tool interface creates discontinuous material properties at x = L_t, requiring separate composite and tool descriptions.
- Autoclave air temperature T_a evolves during processing and can impose either prescribed or convective boundary conditions.
- Initial conditions specify system temperature T_0 and an initially zero or very small resin degree of cure α_0.
3. Physics-Informed Neural Network for Thermochemical Cure Process
The PINN approximates temperature and degree of cure from space-time inputs by minimizing physics-based residuals and initial, boundary, and interface losses. Separate subnetworks with sequential training, discontinuity-aware architecture, and constrained activations address coupled thermochemical behavior and material interfaces.
- PINN formulation: The network maps space-time inputs (x, t) to temperature and degree-of-cure outputs (T, α).The feed-forward DNN represents the dependent solution variables from independent spatial and temporal coordinates.
- PINN formulation: The total loss combines PDE, initial-condition, and boundary-condition residual terms evaluated at collocation points.Automatic differentiation supplies derivatives of the DNN approximations for these physics-based losses.
- Training strategy: Two separate subnetworks for α and T are trained sequentially because joint and simultaneous training fail to reduce all losses adequately.The procedure alternates optimization of the cure network and temperature network while holding the other network fixed, iterating until convergence.
- Bi-material interface: The bi-material architecture combines separate T− and T+ networks with a Heaviside step function so the approximated solution can be discontinuous at the interface.The construction targets discontinuous solution variables and derivatives caused by discontinuous material properties.
- Output constraints: Softplus is used for the temperature output to enforce T > 0, while a modified Sigmoid is used for degree of cure constrained to α ∈ (0, 1).These output activations encode known physical ranges directly in the network design.
- Surrogate modeling: Including problem parameters as additional inputs creates a PINN surrogate that predicts responses across parameter ranges without high-fidelity simulation data.The augmented model duplicates physics-based losses across parameter values and can provide almost real-time predictions once trained.
4. Case studies
The case studies evaluate PINN predictions against FEM across composite-tool thicknesses and thermal boundary conditions, then examine adaptive loss weighting, transfer learning, and surrogate-model performance.
- Case-study design: Four case studies vary composite-tool thicknesses and boundary conditions, including prescribed-temperature and convective boundaries.Cases 1 and 2 use Lc = 30 mm and Lt = 20 mm; cases 3 and 4 use Lc = 300 mm and Lt = 200 mm.
- PINN-FEM comparison: PINN temperature and degree-of-cure fields are compared with FEM predictions using discretizations of 35 or 260 elements and 926 time-steps.Figures 7 and 8 report PINN predictions, FEM predictions, absolute errors, and governing-equation residuals.
- Temperature and cure predictions: The model captures the composite exotherm and convective thermal lag, including stronger lag in the tool because its convective heat-transfer coefficient is lower.These behaviors are examined at the tool boundary, tool-composite interface, composite midpoint, and composite top boundary.
- Adaptive loss weights: Adaptive loss weighting yields significantly better convergence and accuracy than constant weights, with errors about 8 and 10 times higher for temperature and degree of cure, respectively, under constant weights.The adaptive scheme updates loss weights at each iteration to balance training across initial and boundary conditions.
- Transfer learning: Transfer learning makes related PINN problems converge much faster by initializing new models with trained weights and biases from similar cases.Weights from cases 1 and 3 initialize cases 1a and 3a, respectively.
- Surrogate modeling: The PINN surrogate evaluates temperature and degree of cure across tool heat-transfer coefficients, taking about 0.5 seconds on a 34 × 926 grid versus about 5 seconds for FEM.Average absolute errors remain below 1.6 K for temperature and 0.007 for degree of cure, within the stated practical error ranges.
5. Conclusions
The study presents a PINN framework for solving coupled exothermic heat-transfer and resin-reaction equations in composite-tool systems across a full cure cycle. Its architecture and training methods address material-interface discontinuities and differing thermal and cure behaviors, while supporting accurate surrogate modeling.
- The PINN solves coupled differential equations governing temperature and degree of cure in composite and tool materials during a full cure cycle.The equations represent exothermic heat transfer and resin reaction.
- Independent subnetworks model temperature and degree of cure, with sequential training designed to overcome PINN instability.The network parameters are constrained using physics-based loss functions.
- The modified PINN captures material-induced discontinuities and maintains physical quantities such as heat flux through additional loss terms.Adaptive loss weighting based on scaling gradients supports robust neural-network training.
- Because it avoids large pre-generated labeled datasets and domain discretization, the PINN can support surrogate modeling and related composite-processing analyses.The stated applications include probabilistic modeling, optimization, uncertainty quantification, and real-time monitoring.
Appendix A. An unrealistically thick composite-tool example
An extreme composite-tool system with Lc = 300 mm and Lt = 200 mm is used to test the PINN over a wide material-size range. The reported figures compare PINN and FEM cure predictions and show temperature distributions for prescribed boundary temperatures at two times.
- The appendix examines an extreme and unrealistic composite-tool system with Lc = 300 mm and Lt = 200 mm.The example corresponds to case studies 3 and 4 in Table 3.
- Figures A.16 and A.17 present PINN and FEM degree-of-cure predictions for case studies 3 and 4.
- Figure A.18 shows temperature distributions for case study 3 with prescribed boundary temperatures at t = 90 min and t = 190 min.