Monotonic neural networks reveal building water pipes are drastically oversized

Every time a residential tower is designed, engineers must answer a deceptively simple question: how much water can the building demand at its absolute busiest instant? The answer, known as the simultaneous peak water flow, dictates the diameter of pipes, the capacity of booster pumps, and the sizing of heating systems throughout the structure. Get it too low and residents face weak showers and slow-filling kettles; get it too high and the building pays for oversized infrastructure, wasted energy, and avoidable embodied carbon for decades. A new study published in Neural Computing and Applications argues that the industry has been getting this number badly wrong for more than eighty years, and it deploys an unusual machine learning tool to prove the point.

The research, led by Sheena Fernandez of Heriot-Watt University together with Lynne Jack and Sarat Dass, targets a design convention that has gone essentially unchallenged since 1940. That year, Roy Hunter of the US National Bureau of Standards introduced his fixture unit method, the probabilistic foundation of virtually every modern plumbing design code, including the UK’s Chartered Institute of Plumbing and Heating Engineering Design Guide, BS EN 806, and BS 8558. Hunter anchored his method to the 99th percentile of estimated demand, a confidence level chosen, remarkably, on the basis of the number of wake-up phone calls placed by hotel guests during the busiest part of the night. Since then, successive models have inherited that 99th percentile without ever rigorously testing whether it represents an efficient balance between reliability and resource use.

The consequences of that inherited assumption are substantial. Overestimation of peak demand has been a persistent problem in the plumbing literature, inflating pipe sizes and pump capacities, which in turn raises energy consumption and carbon emissions associated with water delivery. Earlier work by one of the research groups had already shown that a data-driven approach could cut overestimation in non-residential buildings, but that method, like its predecessors, evaluated demand only at the 99th percentile. The new study asks a question that sounds almost heretical in building services engineering: is 99 percent actually the right confidence level, or have designers been paying for reliability they do not need?

To answer it, the team turned to monotonic neural networks, a constrained form of machine learning that has rarely, if ever, been applied to water demand estimation. In a conventional neural network, the relationship between inputs and outputs is learned purely by minimizing error, which means the model can produce physically nonsensical behavior, such as predicting a higher peak flow at the 95th percentile than at the 99th. The researchers encountered exactly this problem in preliminary work with standard networks trained separately at each percentile. Monotonicity constraints solve it by forcing the model output to rise whenever a relevant input rises. Since peak water demand must logically increase with both fixture use probability and the chosen confidence level, encoding that expectation directly into the architecture makes the model more robust and far easier for engineers to interpret and trust.

Technically, the team implemented the monotonic network using TensorFlow Lattice, which enforces the constraints through lattice regression, an interpolated look-up table mapped onto the input space. Their architecture combined dense layers that learn the relationship between fixture use probabilities, confidence levels, and peak flow, with a final lattice layer that guarantees increasing outputs across the five quantiles evaluated: 0.95, 0.96, 0.97, 0.98, and 0.99. Hyperparameters, including neuron counts, activation functions, and lattice size, were tuned with the Optuna optimization framework, and model quality was assessed using root mean squared error and the coefficient of determination across five independent runs. Two underlying estimation models were approximated: Wistort’s closed-form method from 1994, which uses a normal approximation to the binomial distribution, and the 2022 Water Demand Estimation Model, which relies on Monte Carlo simulation with hundreds of thousands of runs.

The framework then optimized fixture use probabilities, the fundamental inputs to probabilistic demand models, using the differential evolution algorithm against real measured flow data. The empirical measurements came from two multi-residential buildings in the United Kingdom, recorded over eight days with an ultrasonic flowmeter sampling every ten seconds. Block A, built in 1966, contains 125 two-bedroom flats occupied entirely by residents aged 55 and over, whose water use proved remarkably regular, peaking in the morning. Block B, dating from 1961 but since refurbished, holds 90 flats of mixed size with more diverse occupancy patterns and correspondingly less synchronized demand. Measured data were resampled at hourly, 20-minute, 10-minute, and 5-minute resolutions to test how temporal granularity affects the optimization.

The results were striking on two fronts. First, the monotonic networks achieved coefficients of determination close to one for both underlying models, and a Welch’s t-test found no statistically significant difference in their performance. An explainable AI analysis using SHAP values confirmed that the models had learned physically sensible relationships: baths, washing machines, and kitchen sinks, the fixtures with the highest individual flow rates, dominated the predictions, while the quantile inputs served mainly as scaling factors. Second, and most consequentially, the optimized fixture use probabilities came out dramatically lower than the reference values in the CIPHE Design Guide, and the resulting peak flow estimates showed that the case study buildings could be adequately served at the 98th percentile rather than the 99th.

The scale of the potential savings is the headline finding. For Block A, the new models reduced overestimation to between 53 and 98 percent above measured flows, compared with 315 percent for BS EN 806, 763 percent for the CIPHE Design Guide, and a staggering 1,461 percent for BS 8558. Block B fared even worse under the old standards, with BS 8558 overestimating actual demand by up to 2,036 percent, while the new models stayed within roughly 62 to 71 percent. Selecting the 98th-percentile design flow cut the calculated demand for Block A by up to 17.36 liters per second, an 87.26 percent reduction relative to the code-based design flow, a figure the authors say translates directly into smaller pipes, pumps, and pressure valves, with attendant cost, energy, and carbon savings.

The researchers are careful about the limits of their work. Data-driven methods live or die by the quantity and representativeness of their underlying data, and the trained models are specific to the building types and sizes from which they were built, requiring recalibration for new contexts. High dimensionality also poses scaling challenges: as fixture types multiply, training time and memory demands grow, forcing compromises in dataset size and optimization iterations. The team notes that fixture use probabilities should perhaps be reported as context-dependent ranges rather than fixed values, since a building with many similar fixtures naturally exhibits lower per-fixture usage. Future work will extend the method to a wider range of residential and non-residential buildings and optimize it for large-scale configurations.

Even with those caveats, the study lands at a moment of genuine consequence. Building codes worldwide still trace their sizing logic to a percentile chosen from hotel phone logs in 1940, and the evidence that a modest relaxation to the 98th percentile can slash design flows by nearly 90 percent in real residential blocks will be hard for the industry to ignore. By wrapping the estimation in a monotonic neural network, the researchers have also addressed the trust problem that often accompanies machine learning in safety-relevant engineering: the model cannot, by construction, violate the physical logic that demand rises with confidence level. If longer measurement campaigns confirm that the extreme overestimation seen in these two buildings is typical, the humble water pipe may become an unexpected poster child for how artificial intelligence, applied with physical constraints, can strip decades of hidden waste out of the built environment.

Subject of Research: Estimating simultaneous peak water flow in buildings using monotonic neural networks to re-evaluate the 99th percentile design confidence level

Article Title: Increased interpretability of simultaneous peak water flow estimation using monotonic neural networks

Article References: Fernandez, S., Jack, L., & Dass, S. (2026). Increased interpretability of simultaneous peak water flow estimation using monotonic neural networks. Neural Computing and Applications, 38(19), Article 773. https://doi.org/10.1007/s00521-026-12496-z

Image Credits: AI Generated

DOI: 10.1007/s00521-026-12496-z

Keywords: monotonic neural networks, simultaneous peak water flow, building water supply, fixture use probability, differential evolution, TensorFlow Lattice, plumbing design codes, Hunter's method, water conservation, SHAP interpretability, machine learning, building services engineering