Deep Operator Network (DeepONet), a recently introduced deep learning operator network, approximates linear and nonlinear solution operators by taking parametric functions (infinite-dimensional objects) as inputs and mapping them to solution functions in contrast to classical neural networks (NNs) that need re-training for every new set of parametric inputs. In this work, we have extended the classical formulation of DeepONets by introducing recurrent neural networks (RNNs) in its branch in so-called sequential DeepONets (S-DeepONets) thus allowing accurate solution predictions in the entire domain for parametric and time-dependent loading histories. We have demonstrated this novel formulation's generality and exceptional accuracy with thermal and mechanical random loading histories applied to highly nonlinear thermal solidification and plastic deformation use cases. We show that once S-DeepONet is properly trained, it can accurately predict the final solutions in the entire domain and is several orders of magnitude more computationally efficient than the finite element method for arbitrary loading histories without additional training.

翻译：深度算子网络（DeepONet）是一种近期提出的深度学习算子网络，它通过将参数化函数（无限维对象）作为输入并映射到解函数来逼近线性和非线性解算子，这与传统神经网络（NNs）需针对每组新参数输入重新训练的方式不同。在本研究中，我们通过在其分支中引入循环神经网络（RNNs），扩展了经典DeepONet的表述，形成了所谓的序列式DeepONet（S-DeepONet），从而能够在整个域内对参数化及时变载荷历程进行精确解预测。我们通过将热学与力学随机载荷历程应用于高度非线性的热凝固和塑性变形用例，展示了这一新型表述的通用性和卓越精度。实验表明，一旦S-DeepONet得到充分训练，它便能在整个域内精确预测最终解，且对于任意载荷历程，其计算效率比有限元方法高出数个数量级，且无需额外训练。