How to train your machine (to understand how the ground behaves)
A neural network meets century-old soil theory — and learns to predict what happens when the ground starts to sink.
Have you heard of the curious case of sinking skyscrapers?
In downtown San Francisco, the Millennium Tower, a luxury high-rise completed in 2009, has sunk more than 18 inches and tilted about 22 inches to one side. It wasn’t a design flaw in the building itself. It was the ground beneath it — soft, compressible and consolidating under the immense weight.
Perhaps the most iconic example is the Leaning Tower of Pisa, which has been slanting at a glacial pace since the 12th century due to its unstable soil.
The lesson, it seems, is that the earth beneath our feet has a mind of its own, and understanding how it works is both an engineering necessity and an ongoing challenge.
Assistant Professor Zhang Pin from the Department of Civil and Environmental Engineering, College of Design and Engineering, National University of Singapore, has taken on the challenge of harnessing the power of machine learning (ML).
In Géotechnique , Asst Prof Zhang introduces a new physics-informed data-driven approach to analyse soil consolidation — the process by which water is squeezed out of saturated soil, causing the ground to settle. It’s foundational to the safety and reliability of buildings, roads and even underground infrastructure.
Why settle for less?
Traditionally, engineers use a century-old model known as Terzaghi’s consolidation theory to describe how soft soil behaves under pressure. However, soil in the real world rarely adheres to equations on paper. Its properties fluctuate from place to place, measurements are noisy or sparse and the equations can be difficult to apply, especially when data is incomplete.
To tackle this, Asst Prof Zhang’s team formulated a system that combines two powerful tools. First, sparse regression strips away unnecessary mathematical clutter to keep only the most relevant bits from the equations in a process known as partial differential equation (PDE) discovery. Then, a physics-informed neural network, learns to solve these equations, guided by the laws of physics. It is this end-to-end pipeline that sets the team’s work apart from many other ML-based approaches.
Interestingly, the team’s method works even when data is messy and incomplete — the sort engineers acquire from fieldwork. For instance, even with just a few pressure readings, the system can detect the intrinsic pattern and churn out reliable predictions. They tested it using lab data from two loading scenarios: surcharge (like the pressure from a building) and vacuum preloading (a technique used to
Together with his team, Assistant Professor Zhang Pin introduced a physics-informed data-driven approach to analyse soil consolidation.
Issue 06 | Aug 2025
firm up soil before construction). In both cases, the model successfully recovered the governing equations and predicted how pressure dissipated through the soil over time.
To make the system even more reliable, the researchers used a version of the equations known as a weak-form PDEs. These are better suited to handling realworld data as they are less sensitive to fluctuations and work by averaging them out over space and time. They also added a feature called Monte Carlo dropout, which is a way for the model to express how confident it is in its predictions. This offers engineers a quantifiable sense of how much they can trust the system.
The result is a ML-driven tool that can simulate the future behaviour of soil and infer key parameters from limited measurements — much like reverse-engineering the bigger picture from a few scattered pieces of evidence.
“It’s a new way of thinking about how we model the ground,” says Asst Prof Zhang. “Instead of imposing theory onto data, this approach allows data to reveal its own underlying structure, guided by the guardrails of physics.”
“Engineers don’t always have complete data at their disposal, and soil is inherently complicated. What we’ve built is a framework that is general, robust and can adapt to what’s available,” he adds.
“What we’ve built is a framework that is general, robust and can adapt to what’s available.”
The system’s flexibility means its usefulness could extend beyond this single application. It can be used to validate patterns discovered manually, or in work that involves large experimental or simulated datasets, in which it pulls out governing equations without needing expert guidance at every step. For instance, it can be applied to tackle problems in areas ranging from solid and fluid mechanics to bioinformatics to neuroscience and even finance.
The team’s future work includes extending the system to more complex scenarios, such as wave-structure interactions or extreme weather-induced geohazards — the kinds of multi-physics, high-dimensional problems that engineers often face when figuring out thorny terrain or modelling underground systems.
I feel the earth move under my feet, goes Carole King.
But with Asst Prof Zhang’s work, we may be learning to read its rhythm