Machine learning in mechanics

Artificial intelligence (AI), understood as "a system’s ability to interpret external data correctly, to learn from such data, and to use those learnings to achieve specific goals and tasks through flexible adaptation," is increasingly becoming an integral part of our daily lives. Many breakthroughs have recently been made in language processing and voice/image recognition, signal processing, and information retrieval. These were possible thanks to advances in machine learning (ML) algorithms, that help acquire knowledge "without being explicitly programmed" by processing of vast amounts of data in parallel graphic processing units (GPUs). The application of ML to engineering mechanics is still in its infancy, with most works focusing in data-driven computing using regression and principal component analysis. In topology optimization (TO), ML algorithms have been scarcely explored just to enhance one aspect of TO’s computational efficiency.

This research explores the use of machine learning for solving boundary value problems and for obtaining optimized structures via topology optimization. For the former, we look at the use of physics-informed neural networks (PINNs), whereby the boundary value problem is defined in the loss function via the addition of multiple "physics terms." For the latter, we use neural networks to obtain optimized structures almost instantly. This is done by dividing the topology optimization process into offline and online stages. The offline stage, where the networks are trained, then allows for obtaining excellent topological configurations to an arbitrary set of boundary conditions.

Machine learning of optimized topologies
The image shows the training of a neural network (left) and the predicted results compared to standard TO (right). The error is also quantified as a funtion of the number of configurations used during training. We show machine learning is able to obtain topologies that are very close to those obtained by standard TO.

Related publications

  • P. Nigro, P. Esfahani, and A. M. Aragón. "A deep learning approach to obtaining instant optimized configurations in topology optimization." Structural and Multidisciplinary Optimization (2021), In Preparation.