Bridging Geomechanics and Machine Learning with Physics-Informed Neural Surrogates for Triaxial Soil Testing

Modeling the time-dependent responses of geotechnical materials under triaxial loading poses a dual challenge: capturing strongly nonlinear constitutive behavior while mitigating the influence of experimental noise. We present a two-model learning benchmark that jointly predicts \emph{Displacement}, \emph{Load}, and \emph{Deviator Strain} from elapsed time, compare a transparent LinearRegressor baseline with a \emph{Physics-Informed Neural Network} (PINN). The PINN encodes two physically grounded priors, (i) monotonic displacement progression and (ii) non-negative incremental work as differentiable penalty terms embedded directly in the training objective. This design ensures physically admissible trajectories without constraining the network's capacity to model nonlinear temporal patterns. The pipeline incorporates precise preprocessing time normalization, feature alignment, z-score standardization and a fixed train–test split for reproducible benchmarking. Across all target channels, the PINN achieves substantial gains in mean absolute error and $R^2$, with \emph{Deviator Strain} showing the largest improvement due to its inherently nonlinear dynamics. All evaluations are reported in denormalized physical units to preserve engineering interpretability. Results confirm that integrating minimal, interpretable physics priors into neural predictors significantly improves fidelity in time-series modeling of laboratory geomechanics, offering a scalable, domain-adaptable framework for triaxial testing and related applications.