Ready-to-use deep-learning surrogate models for problems with spatially variable inputs and outputs

Abstract

Data-driven intelligent surrogate models gain popularity recently. Particularly in Monte-Carlo-style stochastic analysis, the influencing factors are considered as inputs, the quantities of interest are considered as outputs, and cheaper-to-evaluate surrogates models are built from a small amount of sample data and are used for the full Monte-Carlo analysis. This paper presents a framework with three innovations: (1) we build surrogate models for a particular problem that covers any possible material properties or boundary conditions commonly encountered in practice, so the models are ready to use, and do not require new data or training anymore. (2) The inputs and outputs to the problem are both spatially variable. Even after discretization, the input and output sizes are in the order of tens of thousands, which is challenging for traditional machine-learning algorithms. We take the footing failure mechanism as an example. Two types of neural networks are examined, fully connected networks and deep neural networks with complicated non-sequential structures (a modified U-Net). (3) This study is also the first attempt to use U-Nets as surrogate models for geotechnical problems. Results show that fully connected networks can fit well simple problems with a small input and output size, but fail for complex problems. Deep neural networks that account for the data structure give better results.