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.

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