An Advanced Physics-Informed Neural Operator for Comprehensive Design Optimization of Highly-Nonlinear Systems: An Aerospace Composites Processing Case Study

TL;DR

This work tackles learning solution operators for highly nonlinear, multiphysics PDEs with multiple input functions in aerospace composites processing. It introduces an advanced physics-informed DeepONet (PIDON) featuring nonlinear decoders, multi-input branches, domain decomposition, decoupled multi-output operators, and curriculum learning to span broad design spaces. The approach yields zero-shot, real-time predictive capability with substantial accuracy gains (e.g., ~2.3°C temperature error and ~0.022 DoC error) and up to ~20× speedups over high-fidelity FE simulations, enabling rapid process design optimization. The method generalizes via local coordinates and interface-loss-driven continuity, offering a scalable framework for complex nonlinear design problems beyond composites manufacturing.

Abstract

Deep Operator Networks (DeepONets) and their physics-informed variants have shown significant promise in learning mappings between function spaces of partial differential equations, enhancing the generalization of traditional neural networks. However, for highly nonlinear real-world applications like aerospace composites processing, existing models often fail to capture underlying solutions accurately and are typically limited to single input functions, constraining rapid process design development. This paper introduces an advanced physics-informed DeepONet tailored for such complex systems with multiple input functions. Equipped with architectural enhancements like nonlinear decoders and effective training strategies such as curriculum learning and domain decomposition, the proposed model handles high-dimensional design spaces with significantly improved accuracy, outperforming the vanilla physics-informed DeepONet by two orders of magnitude. Its zero-shot prediction capability across a broad design space makes it a powerful tool for accelerating composites process design and optimization, with potential applications in other engineering fields characterized by strong nonlinearity.

Figures (11)

• Figure 1: Schematic of composite-tool system in an autoclave with local coordinates $x_1$ and $x_2$.
• Figure 2: Schematic of proposed multi-input PIDON with NDs. Two branch nets are integrated to process time-dependent and time-independent input functions. NDs are responsible for learning the solution operators at different subdomains.
• Figure 3: Schematic of proposed multi-input PIDON with nonlinear decoder for thermochemical analysis of composites curing process.
• Figure 4: Temperature (a) and DoC (b) prediction performance of PIDON at composite part mid-point for two curing scenarios: thin tooling ($T$ maximum absolute error = 3.2°C, $\alpha$ maximum error = 0.024) and thick tooling ($T$ maximum error = 0.9°C, $\alpha$ maximum absolute error = 0.021). An identical two-hold cure cycle was used for both scenarios (shown in gray.)
• Figure 5: Effect of implementing ND in the architecture of DeepONet. The model with ND (dark red) results in considerably smaller training loss and exhibits a more stable behavior.