  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.
