Mixing Data‐Driven and Physics‐Based Constitutive Models Using Uncertainty‐Driven Phase Fields

There is a high interest in accelerating multiscale models using data‐driven surrogate modeling techniques. Creating a large training dataset encompassing all relevant load scenarios is essential for a good surrogate, yet the computational cost of producing this data quickly becomes a limiting factor. Commonly, a pre‐trained surrogate is used throughout the computational domain. We introduce an alternative adaptive mixture approach that uses a fast probabilistic surrogate model as a constitutive model when possible, but resorts to the true high‐fidelity model when necessary. The surrogate is thus not required to be accurate for every possible load condition, enabling a significant reduction in the data collection time. We achieve this by creating phases in the computational domain corresponding to the different models. These phases evolve using a phase‐field model driven by the surrogate uncertainty. When the surrogate uncertainty becomes large, the phase‐field model causes a local transition from the surrogate to the high‐fidelity model, maintaining a highly accurate simulation. We discuss requirements for accuracy and numerical stability and compare the phase‐field model to a local approach that does not enforce spatial smoothness in phase mixing. Using a Gaussian Process surrogate for an elasto‐plastic material, we demonstrate the potential of this mixture of models to accelerate multiscale simulations.