# A Physics-Informed Neural Operator for Thermal Ranking of Low-Cost Wall Materials in Hot-Dry Climates

arXiv: https://arxiv.org/abs/2607.25668 · HTML: https://mlsanity.com/paper/2607.25668/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 47 references that are in the map.
- First posted on arXiv 28 Jul 2026.

## Builds on (most cited first, 3 of 3)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Neural Operators for Accelerating Scientific Simulations and Design](https://mlsanity.com/paper/2309.15325/) (2023)

## Abstract (arXiv)

Identifying cost-effective indigenous building materials that minimise heat penetration through walls is critical for indoor thermal comfort in low-income rural housing in hot-dry climates, where summer temperatures routinely exceed 45 C. We present a two-stage computational framework for thermal ranking of five low-cost indigenous wall materials: mud brick, clay-straw adobe, lime-stabilised bamboo panel, fired clay brick, and lime-mud composite. First, a validated Crank-Nicolson finite difference method (FDM) solves the one-dimensional transient heat equation with Robin boundary conditions under diurnal solar and outdoor air-temperature forcing, generating 1500 periodic-day solutions across a nine-dimensional parameter space by Latin Hypercube sampling. Second, a Physics-Informed Neural Operator (PINO) with a Fourier Neural Operator (FNO) backbone learns the parameter-to-solution operator mu -> T(x,t), enforcing both data fidelity and PDE consistency. The trained PINO attains a relative L2 field error of 5.14e-4 and a 0.201 K mean absolute error on the peak inner surface temperature, preserving the FDM material ranking exactly; PINO trained on 150 FDM samples matches a data-only FNO trained on twice as many, so the physics loss is most valuable when data are scarce. The periodic-day formulation also yields the ISO 13786 time lag and decrement factor, reproduced to within 0.99 h and 0.010. At nominal hot-dry summer conditions, clay-straw adobe achieves the best cost-performance index among widely available materials. A climate sweep, confirmed by FDM spot checks, reveals a regime boundary: under sub-ambient outdoor conditions the ranking inverts to conductive fired clay brick, delineating heat-exclusion and heat-rejection regimes. The framework supports evidence-based material selection for post-flood reconstruction in hot-dry regions.