Sequential deep operator neural networks for plastic and thermo-viscoplastic transient material behavior

Deep Operator Networks (DeepONet) are among the most advanced artificial neural network architectures, which approximate linear and nonlinear solution operators by taking parametric functions (infinite-dimensional objects) as inputs and mapping them to full partial differential equation (PDE) solution fields on a computational grid without training or transfer learning. Building on this idea, the Sequential Deep Operator (S-DeepONet) and the newly introduced Sequential Neural Operator Transformer (S-NOT) are particularly effective for path-dependent plasticity and temperature, path and rate-dependent thermo-viscoplasticity driven by variable transient loadings. In this novel work, we present and compare recent variants of these architectures that predict full histories of stress, temperature, and plastic-strain fields for real-world problems—from highly nonlinear thermo-viscoplastic multiphysics in steel solidification within continuous-casting molds to plastic deformation in complex 2D and 3D domains. Once properly trained, the models can accurately predict entire histories of multiple solution fields up to four orders of magnitude faster than conventional non-linear finite-element analyses. As surrogate models, they can enable rapid modeling, design iterations, optimization, inverse and sensitivity studies, uncertainty quantification, and online control with data assimilation for many processes involving plastic and viscoplastic phenomena that were previously impractical.