Physics-informed machine learning of multi-source monitoring data sparsely measured within a 2D vertical cross-section

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Conventional machine learning (ML) methods suffer from several limitations, e.g., overreliance on large training datasets and poor performance in extrapolating beyond observations. Geotechnical monitoring data at specific sites are multi-sourced (e.g., settlement and horizontal displacement data). Moreover, each source of monitoring data may vary temporally and be sparsely measured, e.g., within a two-dimensional (2D) geological cross-section. Thus, effectively learning multi-source and limited monitoring data is difficult using existing ML methods. To address this challenge, this study proposes a physics-informed ML method combining geotechnical numerical models (e.g., the finite element model (FEM)) with sparse dictionary learning (SDL) methods. It uses a range of probable numerical model results corresponding to multiple, temporally varying responses in a 2D spatial range to construct a “dictionary” in SDL and employs multi-source and limited monitoring data to identify a few “atoms” from the constructed dictionary to improve model predictions. An engineering project for embankment construction is used to illustrate the proposed approach. Our results indicate that the proposed approach effectively integrates FEM results with multi-source and sparsely measured monitoring data and improves the predictions of multiple spatio-temporally varying geotechnical responses significantly, particularly those at subsequent time steps and unmonitored spatial locations within a 2D vertical cross-section.