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.

翻译：不同于经典人工神经网络需要针对每组新参数输入重新训练，深度算子网络（DeepONet）作为一种近期提出的深度学习框架，通过将参数函数（无穷维对象）作为输入并映射至完整解场，来近似线性和非线性解算子。本文首次训练了两种新设计的DeepONet结构，分别采用序列学习和残差U-Net（ResUNet）架构，以同步预测变载荷、载荷历史、工艺参数乃至变几何条件下的完整热学和力学解场。本文演示了两个实际应用案例：1）采用多种粘塑性本构模型的钢连铸热-力耦合分析；2）增材制造中顺序耦合的直接能量沉积过程。尽管目标应力分布具有高度挑战性的空间变异性，DeepONet仍能推断出相当精确的全场温度与应力解，其求解速度比传统且高度优化的有限元分析（FEA）快数个数量级，即便FEA模拟在最新高性能计算平台上运行。所提出的DeepONet模型能够近乎即时地为未见输入参数提供场预测，这为未来这些关键工业过程的初步评估与设计优化打开了大门。