Reliable and Data-Efficient Machine Learning for Tractable Multiscale Material Simulations

Abstract

Advanced materials promise to cut material use and enable structural designs that conventional materials cannot achieve. Composite materials — materials that combine two or more constituents — such as fiber-reinforced polymers, are an example of an advanced material whose properties can exceed those of traditional building materials. However, developing a new material for a specific structure is a costly process that requires vast experimental trial and error. Virtual testing using computational models has the potential to reduce this cost and accelerate material innovation. Computational methods have been developed for these advanced materials that account for phenomena at a very small scale (the microscale) while simulating a large structure (the macroscale). The high fidelity of these multiscale methods imposes a significant computational burden. Running one such multiscale simulation could scale up to take years, and designing and optimizating a structure often requires simulating many variations. To enable virtual testing and optimization of these materials, we thus require acceleration techniques. A popular avenue to accelerate these simulations is using machine learning.

Data-driven machine learning techniques allow for approximating the simulation outcome at a fraction of the computational cost. The microscale material behaviour can be replaced by a data-driven surrogate model that is then integrated in the macroscale simulation. These data-driven surrogate models can make accurate predictions by learning from precomputed microscale simulations. While promising, this approach faces several challenges: rich microscale information is lost, predictions become unreliable, and training an accurate surrogate model requires large quantities of training data. This dissertation develops methods aimed at addressing each of these challenges.

To enable optimization, a model should predict well for a range of different microstructures. However, most surrogates avoid the microscale completely, and directly predict homogenized quantities for one specific microstructure. We develop a surrogate that instead predicts the rich microscale response for varying microstructures, using a graph neural network that maps onto any microscale mesh. Regardless of the surrogate used, when little data is available, it can become unreliable and lead to inaccurate simulations. We therefore introduce a method that adaptively switches between a fast surrogate and the slow ground-truth model, using the surrogate only in the range on which it has been trained. The uncertainty of a probabilistic surrogate informs the switch, and a phase-field at the macroscale smoothens the transition to increase stability. This approach increases the reliability of data-driven multiscale simulations, leading to accurate simulations even for inadequately trained surrogates. Finally, we enrich an existing surrogate, a physically recurrent neural network, with microstructural descriptors. The strong inductive bias in this model enables it to learn with very few training samples. With this model, we demonstrate that data-driven multiscale simulations can capture high-fidelity microscopic effects and are sufficiently tractable to enable multiscale optimization.