Visualizing energy landscape in phase-field fracture using deep learning

The energy landscape governs the dynamics of how a solution (energy minimum) is reached. Visualizing the energy landscape helps develop intuition about its critical features and low-dimensional structure. Additionally, it can guide the selection and design of solution algorithms. However, the solution field, even in a discrete setting, is high-dimensional. By applying linear and nonlinear order reduction techniques, we reduce the dimensionality to two, allowing for visualization of the solution approach. The plots on the left illustrate the differences between the features of the AT1 and AT2 model landscapes, and the solution trajectories at the loading stage where the phase field localizes in a 1D bar.

[1] Manav, M., & De Lorenzis, L. Visualization and characterization of energy landscape in phase-field fracture. In preparation.