Advanced Deep Operator Networks to Predict Multiphysics Solution Fields in Materials Processing and Additive Manufacturing

TL;DR

This work demonstrates that advanced DeepONet architectures, including S-DeepONet for time-dependent inputs and a ResUNet-based DeepONet for variable geometries, can learn accurate, full-field thermo-mechanical solutions for steel solidification in continuous casting and sequential deposition in additive manufacturing. By training on high-fidelity Abaqus simulations and topology-optimized designs, the models predict entire temperature and residual-stress fields for unseen inputs orders of magnitude faster than traditional FEA, enabling rapid design exploration, optimization, and potential digital-twin applications. The approach yields high accuracy (temperature errors on the order of <1°C; stress errors in MPa range) and up to tens of thousands of times speedups, with direct implications for online control and preliminary optimization in vital industrial processes. The work also provides quantitative benchmarks and demonstrates practical insights into process-parameter effects on residual stresses, highlighting the potential for transfer to broader 3D, micro-/mesoscale, and real-time contexts.

Abstract

Unlike classical artificial neural networks, which require retraining for each new set of parametric inputs, the Deep Operator Network (DeepONet), a lately introduced deep learning framework, approximates linear and nonlinear solution operators by taking parametric functions (infinite-dimensional objects) as inputs and mapping them to complete solution fields. In this paper, two newly devised DeepONet formulations with sequential learning and Residual U-Net (ResUNet) architectures are trained for the first time to simultaneously predict complete thermal and mechanical solution fields under variable loading, loading histories, process parameters, and even variable geometries. Two real-world applications are demonstrated: 1- coupled thermo-mechanical analysis of steel continuous casting with multiple visco-plastic constitutive laws and 2- sequentially coupled direct energy deposition for additive manufacturing. Despite highly challenging spatially variable target stress distributions, DeepONets can infer reasonably accurate full-field temperature and stress solutions several orders of magnitude faster than traditional and highly optimized finite-element analysis (FEA), even when FEA simulations are run on the latest high-performance computing platforms. The proposed DeepONet model's ability to provide field predictions almost instantly for unseen input parameters opens the door for future preliminary evaluation and design optimization of these vital industrial processes.

Figures (19)

• Figure 1: Continuous caster with solidifying slice finite element domain
• Figure 2: Thermal and Mechanical BVPs with Random Input Profiles
• Figure 3: Three typical designs from topology optimization.
• Figure 4: A typical mesh used in thermal-mechanical simulation.
• Figure 5: Architecture of the multi-component S-DeepONet for multiphysics problems. $d$ and $f$ represent the time-dependent input displacement and heat flux used in simulation, and $x$, $y$ are nodal coordinates. $\Hat{G}$, as a solution operator, produces final von Mises stress and temperature for each node in the domain.