AI Insight
This paper systematically benchmarks four Scientific Machine Learning (SciML) approaches — MLPs, PINNs, DeepONet, and GNS — against conventional numerical solvers (finite-difference and particle-based methods) across standard geotechnical engineering problems. The results reveal significant limitations: PINNs fail to extrapolate outside their training domain, are up to 96,000 times slower than finite-difference methods, and produce less accurate results; DeepONet's training cost is equivalent to approximately 1.8 million finite-difference solves; and simple MLPs produce large prediction errors outside validated data ranges. By contrast, automatic differentiation through a conventional finite-difference solver recovers material profiles in seconds with roughly 1% error, outperforming neural network-based inversion.
Why it matters
The findings caution geotechnical engineers and researchers against uncritical adoption of SciML methods as drop-in replacements for established numerical solvers, particularly for extrapolation or inverse problems where reliable physics-based solvers already exist. The study provides concrete computational benchmarks that can guide more informed decisions about when and whether neural network approaches offer genuine practical advantages.
arXiv:2512.24365v2 Announce Type: replace
Abstract: Scientific machine learning (SciML) offers neural-network alternatives to numerical workflows in geotechnical engineering. This paper benchmarks multi-layer perceptrons (MLPs), physics-informed neural networks (PINNs), deep operator networks (DeepONet), and graph network simulators (GNS) against finite-difference and particle-based references on geotechnical benchmarks, and compares PINN inversion with automatic differentiation (AD) through a conventional solver. We evaluate each method for extrapolation, training, and inference cost, transfer across problem instances, and physics accuracy. An MLP trained on two years of Terzaghi consolidation fits the data, but at year ten predicts ~290 mm with ReLU and ~60 mm with tanh or sigmoid, against a reference of 99.3 mm. A PINN on a damped oscillator with a time domain inside [0,1] matches the closed form within that interval but fails outside, since the residual constrains the fit only where it is sampled. For the 1D wave equation, PINN training is ~96,000 times slower than finite-difference methods and less accurate. DeepONet avoids PINN retraining, yet for the beam on elastic foundation, its training cost equals ~1.8 million finite-difference solves, and inference is slower per query than the direct solver. GNS improves geometric transfer through local particle interactions, though formulations still need trajectories, large training sets, and substantial memory. In the inverse wave benchmark, AD through the finite-difference solver recovers the material profile in seconds with ~1% error. The results support a cautious role for SciML. Neural networks suit interpolation and pattern recognition inside validated domains, while inverse analysis should first try differentiable physics-based solvers when a reliable forward solver exists.
Source: A Critical Assessment of PINNs and Operator Learning for Geotechnical Engineering