Can ChatGPT implement finite element models for geotechnical engineering applications?

This study assesses the capability of ChatGPT to generate finite element code for geotechnical engineering applications from a set of prompts. We tested three different initial boundary value problems using a hydro-mechanically coupled formulation for unsaturated soils, including the dissipation of excess pore water pressure through fluid mass diffusion in one-dimensional space, time-dependent differential settlement of a strip footing, and gravity-driven seepage. For each case, initial prompting involved providing ChatGPT with necessary information for finite element implementation, such as balance and constitutive equations, problem geometry, initial and boundary conditions, material properties, and spatiotemporal discretization and solution strategies. Any errors and unexpected results were further addressed through prompt augmentation processes until the ChatGPT-generated finite element code passed the verification/validation test. Our results demonstrate that ChatGPT required minimal code revisions when using the FEniCS finite element library, owing to its high-level interfaces that enable efficient programming. In contrast, the MATLAB code generated by ChatGPT necessitated extensive prompt augmentations and/or direct human intervention, as it involves a significant amount of low-level programming required for finite element analysis, such as constructing shape functions or assembling global matrices. Given that prompt engineering for this task requires an understanding of the mathematical formulation and numerical techniques, this study suggests that while a large language model may not yet replace human programmers, it can greatly assist in the implementation of numerical models.

Discovering interpretable elastoplasticity models via the neural polynomial method enabled symbolic regressions

Conventional neural network elastoplasticity models are often perceived as lacking interpretability. This paper introduces a two-step machine-learning approach that returns mathematical models interpretable by human experts. In particular, we introduce a surrogate model where yield surfaces are expressed in terms of a set of single-variable feature mappings obtained from supervised learning. A postprocessing step is then used to re-interpret the set of single-variable neural network mapping functions into mathematical form through symbolic regression. This divide-and-conquer approach provides several important advantages. First, it enables us to overcome the scaling issue of symbolic regression algorithms. From a practical perspective, it enhances the portability of learned models for partial differential equation solvers written in different programming languages. Finally, it enables us to have a concrete understanding of the attributes of the materials, such as convexity and symmetries of models, through automated derivations and reasoning. Numerical examples have been provided, along with an open-source code to enable third-party validation.