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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.
Kushwaha et al. (Thu,) studied this question.