Physics-Informed Spatiotemporal Deep Learning for Emulating Coupled Dynamical Systems

Accurately predicting the propagation of fractures, or cracks, in brittle materials is an important problem in evaluating the reliability of objects such as airplane wings and concrete structures. Efficient crack propagation emulators that can run in a fraction of the time of high-fidelity physics simulations are needed. A primary challenge of modeling fracture networks and the stress propagation in materials is that the cracks themselves introduce discontinuities, making existing partial differential equation (PDE) discovery models unusable. Furthermore, existing physics-informed neural networks are limited to learning PDEs with either constant initial conditions or changes that do not depend on the PDE outputs at the previous time. In fracture propagation, at each timestep, there is a damage field and a stress field; where the stress causes further damage in the material. The stress field at the next time step is affected by the discontinuities introduced by the propagated damage. Thus, both stress and damage fields are heavily dependent on each other; which makes modeling the system difficult. Spatiotemporal LSTMs have shown promise in the area of real-world video prediction. Building on this success, we approach this physics emulation problem as a video generation problem: training the model on simulation data to learn the underlying dynamic behavior. Our novel deep learning model is a Physics-Informed Spatiotemporal LSTM, that uses modified loss functions and partial derivatives from the stress field to build a data-driven coupled dynamics emulator. Our approach outperforms other neural net architectures at predicting subsequent frames of a simulation, enabling fast and accurate emulation of fracture propagation. Introduction and Motivation Brittle materials fail suddenly with little warning due to the growth of micro-fractures that quickly propagate and coalesce. Prediction of fracture propagation in brittle materials is a multi-scale modeling problem whose time dynamics are well understood at the micro-scale but do not scale well to the macro-scale necessary for practical evaluation of materials under strain (White 2006; Hyman et al. 2016; Kim et al. 2014). Fracture formation in brittle materials Copyright c © 2020 for this paper by its authors. Use permitted under Creative Commons License Attribution International (CC BY 4.0). Continu um mod el Micro cracks and loading in one cell Constitutive model for summary statistics Emulate dynamics Damage evolution accounts for crack interactions