Pith. sign in

REVIEW 3 major objections 5 minor 49 references

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

T0 review · 3 major / 5 minor · reviewed 2026-08-01 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A physics-informed neural operator matches a validated heat solver to within 0.2 K on peak wall temperature, reproduces the material ranking exactly, and halves the data needed when physics is enforced.

desk verdict Solid applied study with a verified ranking and regime boundary; the data-efficiency claim needs more seeds and a fair training budget before it can stand. read the letter →

arxiv 2607.25668 v1 pith:Q6GOSL6I submitted 2026-07-28 cs.LG cs.NAmath.NAphysics.comp-ph

Muhammad Akbar Khan , Fahim Raees , Ubaida Fatima This is my paper · ORCID
classification cs.LGcs.NAmath.NAphysics.comp-ph
keywords physics-informedneuraloperatorFourierthermalrankingbuildingenvelopetransientheattransferindigenouswallmaterialshot-dryclimatecost-performanceindex
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper sets out to prove that a physics-informed neural operator can serve as a fast, near-exact surrogate for one-dimensional transient heat conduction through walls, and that its predictions are accurate enough to rank building materials exactly as a validated finite-difference solver would. It demonstrates this on five low-cost indigenous materials for hot-dry rural Sindh housing, reporting a relative field error of 5.14e-4 and a mean absolute error of 0.201 K on the peak inner-surface temperature. The paper also establishes that the physics term in the loss is most valuable when data are scarce: a physics-informed model trained on 150 solver samples matches a data-only model trained on 300, halving the simulation budget. The practical payoff is a concrete material recommendation — clay-straw adobe as the best cost-performance choice among widely available materials — and a climate sweep that reveals a regime boundary where conductive fired clay brick becomes optimal under sub-ambient outdoor conditions.

What carries the argument

The load-bearing mechanism is the physics-informed neural operator (PINO): a Fourier Neural Operator backbone that maps the nine-dimensional parameter vector (conductivity, density, specific heat, moisture coefficient, wall thickness, moisture content, outdoor max temperature, indoor temperature, solar peak) to the full space-time temperature field, trained with a loss combining data fidelity and a finite-difference PDE residual. The physics residual acts as a regulariser concentrated where the quantity of interest lives — the inner surface — and as a data substitute when samples are scarce. The periodic-day extraction protocol (five-day spin-up, final day as periodic quasi-steady state) tur

What would settle it

Thermocouple measurements on full-scale specimens of clay-straw adobe and lime-stabilised bamboo panel under a representative Sindh summer day would settle the ranking: if bamboo's peak inner-surface temperature is not lower than adobe's by the predicted margin, the ranking claim fails. Separately, training the same PINO on 150 FDM samples and a data-only FNO on 300 on a shared test set would decide the data-efficiency claim; if PINO does not match FNO's accuracy, the 'halves the data' conclusion is wrong.

Watch

Extended reading notes

Core claim

Central claim: the map μ→T(x,t) for 1D transient wall heat conduction is learnable by a physics-informed neural operator so accurately that it reproduces the temperature field to a relative L2 error of 5.14e-4 and peak inner-surface temperature to 0.201 K MAE, preserving the FDM material ranking exactly. The physics loss is most valuable at the inner surface (15.5% RMSE cut) and in the data-scarce regime (19–28% QoI error cut at 150–300 samples), letting a PINO trained on 150 samples match a data-only FNO trained on 300. The periodic-day formulation yields ISO 13786 time lag and decrement factor within 0.99 h and 0.010 MAE. The ranking is stable across heating-dominated climates but inverts

Load-bearing premise

The thermal properties and costs of the five materials are literature-derived or author-assigned rather than measured on physical Sindh specimens, and the top-two ranking gap (0.7 K) is comparable to the surrogate's own error on the bamboo panel.

Editorial extensions

If this is right

  • If the PINO is as accurate as reported, building-material screening can move from thousands of transient simulations to millisecond queries, making exhaustive parametric design-space exploration practical for hot-dry housing.
  • The data-efficiency result implies that for other physics problems where each training sample comes from an expensive solver or experiment, the PDE residual can halve the required data budget at a fixed accuracy level.
  • If the climate sweep is correct, the heat-exclusion/heat-rejection regime boundary is a design rule: in heating-dominated conditions choose low-diffusivity, high-mass walls; under sub-ambient conditions choose the most conductive wall to reject indoor heat.
  • The cost-performance index, if the cost data hold, gives an actionable recommendation: clay-straw adobe is the best cooling-per-rupee choice among widely available materials for rural Sindh reconstruction.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The regime boundary likely generalises beyond Sindh: any wall in a climate where the mean sol-air temperature crosses the indoor set-point will have a crossover from insulating to conductive optima, so the same operator could map adaptive-envelope strategies (e.g., seasonal shading or vented cavities) in other hot-dry regions.
  • The Sobol' result that indoor temperature dominates the absolute peak temperature suggests that for unconditioned housing, ventilation and shading may move comfort more than wall material choice — a hypothesis the paper's own sensitivity analysis supports but does not pursue.
  • A testable extension is to apply the same PINO loss to the moisture-coupled heat–moisture PDE the paper flags as future work; if the data-efficiency gain carries over, full hygrothermal material ranking with dynamic moisture transport becomes feasible with a modest training set.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper develops and validates a two-stage computational framework for ranking five low-cost indigenous wall materials for rural Sindh. Stage 1 is a Crank–Nicolson finite-difference solver for the 1D transient heat equation with Robin boundary conditions and diurnal solar/air-temperature forcing; it is validated by manufactured solutions, a Robin zero-drift test, space–time convergence, and periodicity checks, and is used to generate 1500 Latin-hypercube periodic-day solutions over a nine-dimensional parameter space. Stage 2 is a physics-informed neural operator (PINO) with an FNO backbone that maps the parameter vector to the space–time temperature field. The paper reports high surrogate accuracy (relative L2 field error 5.14e-4, 0.201 K MAE on peak inner-surface temperature), exact reproduction of the FDM material ranking, dynamic thermal metrics in line with ISO 13786, a data-efficiency study claiming that PINO trained on 150 samples matches a data-only FNO trained on 300, a climate sweep revealing a heat-exclusion/heat-rejection regime boundary, a Sobol sensitivity analysis, and a cost–performance index leading to clay–straw adobe as the recommended widely available material.

Significance. The study is potentially valuable as a transferable workflow: a carefully verified inexpensive 1D solver paired with a neural operator can turn wide design-space exploration into near-instantaneous evaluation, and the authors explicitly provide the solver, training code, dataset, and climate verification package on Zenodo. The FDM validation is thorough and the reported surrogate errors are very small. The material-selection application is relevant to post-flood reconstruction in hot-dry climates. However, the two most novel claims — that the physics loss halves the FDM data budget and that the material recommendation is robust to property uncertainty — are not yet established at the level of certainty implied by the abstract and conclusions. The central derivation is sound, but these load-bearing empirical claims need additional robustness checks.

major comments (3)
  1. [§6.3, Table 6, Figure 9] The headline data-efficiency claim — PINO@150 matches FNO@300, halving the FDM data budget — rests on a single training run per configuration at Ntrain=150 and 300. The paper's own three-seed analysis at Ntrain=600 gives FNO 0.246±0.026 K versus PINO 0.234±0.008 K on the QoI MAE, i.e. the two are statistically indistinguishable. Since the across-seed standard deviation of FNO at 600 is about three times that of PINO, the 18.8% and 27.5% advantages at 150 and 300 could plausibly lie within seed noise. Moreover, at these sizes the PINO runs reached the 200-epoch cap while the FNO runs early-stopped, so the comparison conflates the physics regularizer with additional optimization budget. Please run multi-seed experiments at Ntrain=150 and 300, report per-run epochs and early-stopping behaviour, and either confirm the advantage or revise the abstract and conclusions.
  2. [§6.5, Table 7; §6.2, Figure 8] The claim that the trained PINO 'preserves the FDM material ranking exactly' is true for the five reported test cases, but the margin of reliability is thin: the largest PINO error on the ranking task, 0.708 K for lime-stabilised bamboo, equals the bamboo–adobe gap of 0.70 K, and the worst-case test error is 1.76 K. As written, the reader cannot tell whether the surrogate would preserve the ranking for nearby material properties or slight perturbations of the nominal climate. Since the paper explicitly retains FDM values for the downstream ranking table, the surrogate's 'exact ranking' claim should be qualified, e.g. by reporting the distribution of predicted margins over the test set and the fraction of test pairs whose predicted ranking differs from FDM.
  3. [§7 versus §6.7, Tables 2 and 9] The statement in Section 7 that 'any residual uncertainty in these values is immaterial to the ranking QoI' is not supported by the cited Sobol analysis. Table 9 shows total-order indices dominated by Tin and Tout,max because the analysis averages over the full nine-dimensional design space; it does not measure sensitivity of the pairwise material ranking to simultaneous perturbations of the nominal properties in Table 2 at fixed climate and geometry. Given that the top-two gap is only 0.70 K and no experimental validation of the material properties was performed, the robustness of the recommendation should be quantified by a local perturbation study around the Table 2 values (and the Table 10 costs), not by a global variance decomposition. Without such a check, the cost–performance recommendation is overstated.
minor comments (5)
  1. [§6.3] The sentence 'The comparison is, if anything, conservative towards PINO' is confusing. If PINO hit the 200-epoch cap while still improving, it was trained for more epochs than FNO; please state explicitly how many epochs each run used and whether both models were subject to the same early-stopping rule.
  2. [§6.8, Table 10] The cost figures are described as authors' market estimates; this is appropriately flagged, but the CPI values in Table 10 should be accompanied by a sensitivity note showing how the rank changes if C_mat varies by, say, ±25%. This would strengthen the cost–performance recommendation without requiring new simulations.
  3. [Abstract and §8] The abstract and conclusions state the data-efficiency result as established fact. Until the multi-seed check requested in the first major comment is provided, these statements should be qualified as single-seed results under a 200-epoch cap.
  4. [§6.7, Table 9] The claim that the total-order indices of the four material properties 'sum to ≈0.05' is used loosely; the text correctly notes that total-order indices are not strictly additive, but the reader may still infer additivity. Please cite the individual S_T values explicitly and avoid the additive interpretation.
  5. [General] Minor typographical and formatting issues: some in-text citations appear without page numbers, and the caption of Figure 8 says 'Worst-case test sample' without stating that it is the worst among PINO test predictions. These are cosmetic and do not affect the results.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular reasoning found; the PINO is an independently benchmarked surrogate against FDM ground truth.

full rationale

The paper's derivation chain is self-contained and non-circular. The FDM solver is validated independently via the method of manufactured solutions, a Robin zero-drift test, a space-time convergence study, and periodicity/initial-condition checks (Section 6.1). The 1500-sample dataset is generated by LHS and split into train/validation/test before training (Section 5.2). The reported errors (relative L2 = 5.14e-4, MAE on J = 0.201 K) are measured on the held-out test set, so they are genuine predictions rather than refitted inputs. The material ranking in Table 7 uses FDM values as ground truth, with PINO errors reported and acknowledged; the PINO ranking is checked against FDM and is not used to define the target. The climate sweep is confirmed by 45 FDM spot checks (Table 8), an independent confirmation. The cost-performance indices (24)-(25) are definitions computed from simulation outputs and cost estimates, not fitted parameters renamed as predictions. The global sensitivity analysis uses the validated PINO as a surrogate for FDM, which is a standard computational expedient and does not introduce circularity: the surrogate was benchmarked on held-out FDM data. The only self-citation, Ref. [40], appears in a non-load-bearing consistency remark ('This physics-enforcement strategy is consistent with the authors' prior work...') and is not used to justify any result. The skeptical concern about single-seed comparisons at Ntrain=150/300 is a statistical robustness issue, not a circularity issue; the paper itself reports multi-seed results at Ntrain=600. No derivation step reduces by construction to its own inputs.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The paper's central results depend on the numerical model, the surrogate training, and a set of author-assigned or literature-derived inputs (material properties, costs, moisture-conductivity coefficients). The model assumptions are stated and partly justified by timescale arguments, but none of the material properties or costs are experimentally measured in this study.

free parameters (4)
  • alpha (moisture-conductivity coefficient) for the five materials = 0.003–0.005 W m2 kg−1 K−1 (Table 2)
    Author-assigned, not measured for these materials; based on order-of-magnitude from a cementitious material [15]; swept over [0.001, 0.010].
  • Nominal kdry of lime-mud composite = 0.55 W m−1 K−1
    Material not in international literature; assigned from bounds of stabilised earth blocks [10,12,35].
  • Nominal cp of lime-stabilised bamboo panel = 1800 J kg−1 K−1
    No measured value for this composite; chosen within DSC range for bamboo scrimber [36].
  • Material cost estimates C_mat (PKR/m3) = 3500, 4500, 8000, 20000, 10500
    Authors' indicative 2025-2026 market estimates for rural Sindh; drive the cost-performance index and final recommendation.
assumptions (5)
  • domain assumption Effective thermal conductivity varies linearly with moisture content: keff = kdry + alpha w0 (Eq. 2).
    Adopted from building-physics literature [15,26]; argued adequate for small moisture contents.
  • domain assumption Moisture content is spatially uniform and constant during the 120-h simulation.
    Justified by moisture diffusion timescale tau_m ~26 days >> 120 h (Eq. 12).
  • domain assumption Diurnal forcing is idealized: half-sine solar profile (Eq. 3), sinusoidal air temperature with fixed 12 K swing and 3-h phase shift (Eq. 6), constant indoor air temperature.
    Periodic-day idealization; acknowledged in Section 7 limitations.
  • domain assumption Robin boundary coefficients h_out=25 and h_in=7.69 W m−2 K−1 are taken from ISO 6946 surface resistances.
    Standard building physics values; not varied in the study.
  • domain assumption The nominal material properties in Table 2 are representative of materials available in rural Sindh.
    Derived from literature for comparable earthen and bio-based materials, not measured on local specimens; this is the weakest premise for the material ranking.

how reviews work

0 comments
Cite this review

Pith. "Pith review of A Physics-Informed Neural Operator for Thermal Ranking of Low-Cost Wall Materials in Hot-Dry Climates." pith.science (2026). https://pith.science/paper/Q6GOSL6I

@misc{pith2026260725668,
  author       = {Pith},
  title        = {Pith review of: A Physics-Informed Neural Operator for Thermal Ranking of Low-Cost Wall Materials in Hot-Dry Climates},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Q6GOSL6I}},
  note         = {Machine review of arXiv:2607.25668}
}
read the original abstract

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.

Figures

Figures reproduced from arXiv: 2607.25668 by the authors.

Figure 1
Figure 1. Schematic of the one-dimensional transient heat conduction problem. The outer [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Diurnal forcing model over one day at nominal Sindh conditions ( [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Temperature field T(ξ, t) over the final periodic day for the median-PINO￾error test sample (Dtest, sample index 28): FDM ground truth (left), FNO prediction (middle), and PINO prediction (right). All three panels share a common colour scale and no clipping is applied to the predictions; the time axis shows clock time from sunrise (06:00) to sunrise. 06:00 12:00 18:00 00:00 06:00 Clock time 40.75 41.00 41.25 41.50 4… view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: Inner surface temperature T(L, t) over the final periodic day, the time series J(t; µ) (15) underlying the scalar QoI J(µ) (16), for the same median-error test sample as [PITH_FULL_IMAGE:figures/full_fig_p020_4.png]
Figure 5
Figure 5. Figure 5: Parity plots of the predicted peak inner surface temperature [PITH_FULL_IMAGE:figures/full_fig_p021_5.png]
Figure 6
Figure 6. Figure 6: Training and validation loss curves for the data-only FNO baseline (left) and [PITH_FULL_IMAGE:figures/full_fig_p021_6.png]
Figure 7
Figure 7. Figure 7: Test-set RMSE (over samples and time) as a function of normalised position [PITH_FULL_IMAGE:figures/full_fig_p022_7.png]
Figure 8
Figure 8. Figure 8: Worst-case test sample for PINO (index 128, QoI error 1 [PITH_FULL_IMAGE:figures/full_fig_p022_8.png]
Figure 9
Figure 9. Figure 9: Data efficiency of the physics loss: test-set relative [PITH_FULL_IMAGE:figures/full_fig_p023_9.png]
Figure 10
Figure 10. Figure 10: Parity of the dynamic thermal metrics across the test set: time lag ( [PITH_FULL_IMAGE:figures/full_fig_p024_10.png]
Figure 11
Figure 11. Figure 11: Winning material (lowest J(µ)) as a function of daily-maximum outdoor temperature Tout,max and peak solar irradiance Gs,peak, evaluated via the trained PINO Gθ across a 20 × 20 grid spanning the full ranges of [PITH_FULL_IMAGE:figures/full_fig_p027_11.png]
Figure 12
Figure 12. Figure 12: Recommendation robustness: margin (K) between the best and runner-up [PITH_FULL_IMAGE:figures/full_fig_p028_12.png]
Figure 13
Figure 13. Figure 13: First-order (S1) and total-order (ST ) Sobol’ sensitivity indices for the nine parameters of µ, ranked by influence on the peak inner surface temperature J(µ). 29 [PITH_FULL_IMAGE:figures/full_fig_p029_13.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

49 extracted references · 22 canonical work pages

  1. [1]

    NASA Prediction of Worldwide Energy Resources (POWER), Hourly and Daily Data, MERRA-2 and CERES SYN1deg,

    NASA Langley Research Center, “NASA Prediction of Worldwide Energy Resources (POWER), Hourly and Daily Data, MERRA-2 and CERES SYN1deg,” NASA POWER Project, 2025. Accessed: Jul. 20, 2026. https://power.larc.nasa.gov

    2025

  2. [2]

    A comparative simulation study of the thermal performances of the building envelope wall materials in the tropics,

    N. Jannat, A. Hussien, B. Abdullah, and A. Cotgrave, “A comparative simulation study of the thermal performances of the building envelope wall materials in the tropics,”Sustainability, vol. 12, no. 12, p. 4892, 2020. doi: 10.3390/su12124892

    work page doi:10.3390/su12124892 2020

  3. [3]

    Resilient cooling pathway for extremely hot climates in southern Asia,

    S. Mehmood, J. Lizana, M. N´ u˜ nez-Peir´ o, S. A. Maximov, and D. Friedrich, “Resilient cooling pathway for extremely hot climates in southern Asia,”Appl. Energy, vol. 325, p. 119811, 2022. doi: 10.1016/j.apenergy.2022.119811

    arXiv 2022

  4. [4]

    Indoor heat measurement data from low-income households in rural and urban South Asia,

    P. Tasgaonkar, D. Zade, S. Ehsan, G. Gorti, N. Mamnun, C. Siderius, and T. Singh, “Indoor heat measurement data from low-income households in rural and urban South Asia,”Sci. Data, vol. 9, p. 285, 2022. doi: 10.1038/s41597-022-01314-5 36

    doi:10.1038/s41597-022-01314-5 2022

  5. [5]

    Bamboo houses mitigate the effects of climate change in Pakistan,

    Z. T. Ebrahim, “Bamboo houses mitigate the effects of climate change in Pakistan,” The UNESCO Courier, vol. 2024, no. 1, pp. 11–13, Jan.–Mar. 2024. available online

    2024

  6. [6]

    Investigating traditional construc- tion techniques and local knowledge in response to flood vulnerabilities in Sindh, Pakistan,

    A. Iqbal, H. Nazir, and M. A. Awan, “Investigating traditional construc- tion techniques and local knowledge in response to flood vulnerabilities in Sindh, Pakistan,”Int. Plan. Stud., vol. 30, no. 1–2, pp. 191–212, 2025. doi: 10.1080/13563475.2025.2460701

    arXiv 2025

  7. [7]

    Thermal comfort and passive survivabil- ity in earthen buildings,

    L. Ben-Alon and A. R. Rempel, “Thermal comfort and passive survivabil- ity in earthen buildings,”Build. Environ., vol. 238, p. 110339, 2023. doi: 10.1016/j.buildenv.2023.110339

    arXiv 2023

  8. [8]

    Is sustainable development a paradox? Bamboo housing and sustainable development: stories from Pakistan,

    S. Abbasi, “Is sustainable development a paradox? Bamboo housing and sustainable development: stories from Pakistan,”Discov. Sustain., vol. 6, p. 1074, 2025. doi: 10.1007/s43621-025-01247-0

    work page doi:10.1007/s43621-025-01247-0 2025

Show all 49 references
  1. [9]

    Sustainable earthen construction: A meta-analytical review of environmental, mechanical, and thermal performance,

    V. Mora-Ruiz, J. Soto-Paz, S. Attia, and C. Mej ´ ıa-Parada, “Sustainable earthen construction: A meta-analytical review of environmental, mechanical, and thermal performance,”Buildings, vol. 15, no. 6, p. 918, 2025. doi: 10.3390/buildings15060918

    2025 doi

  2. [10]

    Design thermal values for unfired clay bricks,

    J. E. Oti, J. M. Kinuthia, and J. Bai, “Design thermal values for unfired clay bricks,” Mater. Des., vol. 31, no. 1, pp. 104–112, 2010. doi: 10.1016/j.matdes.2009.07.011

    2010 doi

  3. [11]

    Thermal perfor- mance of unfired clay bricks used in construction in the north of France: Case study,

    F. El Fgaier, Z. Lafhaj, F. Brachelet, E. Antczak, and C. Chapiseau, “Thermal perfor- mance of unfired clay bricks used in construction in the north of France: Case study,” Case Stud. Constr. Mater., vol. 3, pp. 102–111, 2015. doi: 10.1016/j.cscm.2015.09.001

    2015 doi

  4. [12]

    A comprehensive review of the improvement of the thermal and mechanical properties of unfired clay bricks by incorporating waste materials,

    M. Lachheb, N. Youssef, and Z. Younsi, “A comprehensive review of the improvement of the thermal and mechanical properties of unfired clay bricks by incorporating waste materials,”Buildings, vol. 13, no. 9, p. 2314, 2023. doi: 10.3390/buildings13092314

    2023 doi

  5. [13]

    Measurement of thermal properties of brick materials based on clay mixtures,

    N. Laaroussi, G. Lauriat, M. Garoum, A. Cherki, and Y. Jannot, “Measurement of thermal properties of brick materials based on clay mixtures,”Constr. Build. Mater., vol. 70, pp. 351–361, 2014. doi: 10.1016/j.conbuildmat.2014.07.104

    2014 doi

  6. [14]

    Energy efficiency and thermal properties of the composite material clay–straw,

    K. El Azhary, Y. Chihab, M. Mansour, N. Laaroussi, and M. Garoum, “Energy efficiency and thermal properties of the composite material clay–straw,”Energy Pro- cedia, vol. 141, pp. 160–164, 2017. doi: 10.1016/j.egypro.2017.11.030

    2017 doi

  7. [15]

    Numerical simulation of heat and moisture trans- fer of wall with insulation,

    M. Wei, B. Wang, and S. Liu, “Numerical simulation of heat and moisture trans- fer of wall with insulation,”J. Phys.: Conf. Ser., vol. 1300, p. 012029, 2019. doi: 10.1088/1742-6596/1300/1/012029 37

    2019 doi

  8. [16]

    Hygrothermal properties of raw earth materials: A literature review,

    G. Giuffrida, R. Caponetto, and F. Nocera, “Hygrothermal properties of raw earth materials: A literature review,”Sustainability, vol. 11, no. 19, p. 5342, 2019. doi: 10.3390/su11195342

    2019 doi

  9. [17]

    Neural operators for accelerating scientific simulations and design,

    K. Azizzadenesheli, N. Kovachki, Z. Li, M. Liu-Schiaffini, J. Kossaifi, and A. Anand- kumar, “Neural operators for accelerating scientific simulations and design,”Nat. Rev. Phys., vol. 6, pp. 320–328, 2024. doi: 10.1038/s42254-024-00712-5

    2024 doi

  10. [18]

    Fourier neural operator for parametric partial differential equations,

    Z. Li, N. Kovachki, K. Azizzadenesheli, B. Liu, K. Bhattacharya, A. Stuart, and A. Anandkumar, “Fourier neural operator for parametric partial differential equations,” Int. Conf. Learning Representations (ICLR), 2021. arXiv:2010.08895

    2021 arXiv

  11. [19]

    Physics-informed neural operator for learning partial differen- tial equations,

    Z. Li, H. Zheng, N. Kovachki, D. Jin, H. Chen, B. Liu, K. Azizzadenesheli, and A. Anandkumar, “Physics-informed neural operator for learning partial differen- tial equations,”ACM/IMS J. Data Sci., vol. 1, no. 3, Art. 9, pp. 1–27, 2024. doi: 10.1145/3648506. arXiv:2111.03794

    2024 arXiv

  12. [20]

    Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving non- linear partial differential equations,

    M. Raissi, P. Perdikaris, and G. E. Karniadakis, “Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving non- linear partial differential equations,”J. Comput. Phys., vol. 378, pp. 686–707, 2019. doi: 10.1016/j.jcp.2018.10.045

    2019 doi

  13. [21]

    Physics-informed neural networks for heat transfer problems,

    S. Cai, Z. Wang, S. Wang, P. Perdikaris, and G. E. Karniadakis, “Physics-informed neural networks for heat transfer problems,”J. Heat Transfer, vol. 143, no. 6, p. 060801, 2021. doi: 10.1115/1.4050542

    2021 doi

  14. [22]

    Physics-informed neural networks for studying heat transfer in porous media,

    J. Xu, H. Wei, and H. Bao, “Physics-informed neural networks for studying heat transfer in porous media,”Int. J. Heat Mass Transf., vol. 217, p. 124671, 2023. doi: 10.1016/j.ijheatmasstransfer.2023.124671

    2023

  15. [23]

    Data-driven and physics-informed deep learning operators for solution of heat conduction equation with parametric heat source,

    S. Koric and D. W. Abueidda, “Data-driven and physics-informed deep learning operators for solution of heat conduction equation with parametric heat source,”Int. J. Heat Mass Transf., vol. 203, p. 123809, 2023. doi: 10.1016/j.ijheatmasstransfer.2022.123809

    2023

  16. [24]

    Physics-informed neural networks in heat transfer-dominated multiphysics systems: A comprehensive review,

    Z. Zhao, Y. Wang, W. Zhang, Z. Ba, and L. Sun, “Physics-informed neural networks in heat transfer-dominated multiphysics systems: A comprehensive review,”Eng. Appl. Artif. Intell., vol. 157, p. 111098, 2025. doi: 10.1016/j.engappai.2025.111098

    2025

  17. [25]

    Multi-objective optimization of insulation materials for building energy and comfort improvements in hot and arid regions,

    I. Ali, C. Peng, H. Ullah, J. Deng, A. Bibi, and W. A. Mahar, “Multi-objective optimization of insulation materials for building energy and comfort improvements in hot and arid regions,”Build. Res. Inf., vol. 53, no. 6, pp. 797–816, 2025. doi: 10.1080/09613218.2025.2506052 38

    2025

  18. [26]

    Nonlinear effect of moisture content on effective thermal conductivity of building materials with different pore size distri- butions,

    Y. Liu, C. Ma, D. Wang, Y. Wang, and J. Liu, “Nonlinear effect of moisture content on effective thermal conductivity of building materials with different pore size distri- butions,”Int. J. Thermophys., vol. 37, p. 56, 2016. doi: 10.1007/s10765-016-2062-0

    2016 doi

  19. [27]

    Determination of the mois- ture diffusivity of rammed earth from transient capillary absorption mois- ture content profiles,

    M. L. Indekeu, H. Janssen, and M. Woloszyn, “Determination of the mois- ture diffusivity of rammed earth from transient capillary absorption mois- ture content profiles,”Constr. Build. Mater., vol. 318, art. 125978, 2022. doi:10.1016/j.conbuildmat.2021.125978

    2022

  20. [28]

    Heat and moisture transport and storage parameters of bricks affected by the environment,

    V. Koˇ c ´ ı, M.ˇC´ achov´ a, D. Koˇ n´ akov´ a, E. Vejmelkov´ a, M. Jerman, M. Keppert, J. Madˇ era, and R. ˇCern´ y, “Heat and moisture transport and storage parameters of bricks affected by the environment,”Int. J. Thermophys., vol. 39, art. 63, 2018. doi:10.1007/s10765-018-2383-2

    2018 doi

  21. [29]

    Comprehensive correc- tion of thermal conductivity of moist porous building materials with static mois- ture distribution and moisture transfer,

    Y. Wang, Z. Zhao, Y. Liu, D. Wang, C. Ma, and J. Liu, “Comprehensive correc- tion of thermal conductivity of moist porous building materials with static mois- ture distribution and moisture transfer,”Energy, vol. 176, pp. 103–118, 2019. doi: 10.1016/j.energy.2019.03.178

    2019 doi

  22. [30]

    EnergyPlus™Input Output Reference,

    U.S. Department of Energy, “EnergyPlus™Input Output Reference,” Version 26.1.0,

  23. [31]

    Building components and building elements—Thermal resistance and thermal transmittance—Calculation methods,

    ISO, “Building components and building elements—Thermal resistance and thermal transmittance—Calculation methods,”ISO 6946:2017, International Organization for Standardization, Geneva, Switzerland, 2017

    2017

  24. [32]

    Thermal performance of building components—Dynamic thermal characteristics—Calculation methods,

    ISO, “Thermal performance of building components—Dynamic thermal characteristics—Calculation methods,”ISO 13786:2017, International Organi- zation for Standardization, Geneva, Switzerland, 2017

    2017

  25. [33]

    Thermal conductivity of engineered bamboo composites,

    D. U. Shah, M. C. D. Bock, H. Mulligan, and M. H. Ramage, “Thermal conductivity of engineered bamboo composites,”J. Mater. Sci., vol. 51, pp. 2991–3002, 2016. doi: 10.1007/s10853-015-9610-z

    2016 doi

  26. [34]

    Effect of moisture content on thermal properties of porous building ma- terials,

    V. Koˇ c ´ ı, E. Vejmelkov´ a, M.ˇC´ achov´ a, D. Koˇ n´ akov´ a, M. Keppert, J. Madˇ era, and R. ˇCern´ y, “Effect of moisture content on thermal properties of porous building ma- terials,”Int. J. Thermophys., vol. 38, p. 28, 2017. doi: 10.1007/s10765-016-2164-8

    2017 doi

  27. [35]

    Thermophysical properties of stabilised soil building blocks,

    E.A. Adam and P.J. Jones, “Thermophysical properties of stabilised soil building blocks,”Build. Environ., vol. 30, no. 2, pp. 245–253, 1995. doi: 10.1016/0360- 1323(94)00041-P 39

    1995 doi

  28. [36]

    Experimental study on thermal performance of bamboo scrimber at elevated temperatures,

    Z. Cui, M. Xu, Z. Chen, and J. Xiang, “Experimental study on thermal performance of bamboo scrimber at elevated temperatures,”Constr. Build. Mater., vol. 182, pp. 178–187, 2018. doi: 10.1016/j.conbuildmat.2018.06.124

    2018 doi

  29. [37]

    Thermal insulation performance of bamboo- and wood-based shear walls in light-frame buildings,

    J. S. Wang, C. Demartino, Y. Xiao, and Y. Y. Li, “Thermal insulation performance of bamboo- and wood-based shear walls in light-frame buildings,”Energy Build., vol. 168, pp. 167–179, 2018. doi: 10.1016/j.enbuild.2018.03.017

    2018 doi

  30. [38]

    K. W. Morton and D. F. Mayers,Numerical Solution of Partial Differential Equa- tions: An Introduction, Cambridge University Press, Cambridge, UK, 1994

    1994

  31. [39]

    A comparison of three methods for selecting values of input variables in the analysis of output from a computer code,

    M. D. McKay, R. J. Beckman, and W. J. Conover, “A comparison of three methods for selecting values of input variables in the analysis of output from a computer code,”Technometrics, vol. 21, no. 2, pp. 239–245, 1979. doi: 10.1080/00401706.1979.10489755

    1979

  32. [40]

    A systematic study of physics-informed neural networks for the level-set interface advection,

    M. A. Khan and F. Raees, “A systematic study of physics-informed neural networks for the level-set interface advection,”Mach. Learn.: Sci. Technol., in press, 2026. doi: 10.1088/2632-2153/ae8b74

    2026 doi

  33. [41]

    Code verification by the method of manufactured solutions,

    P. J. Roache, “Code verification by the method of manufactured solutions,”J. Fluids Eng., vol. 124, no. 1, pp. 4–10, 2002. doi: 10.1115/1.1436090

    2002 doi

  34. [42]

    Code verification by the method of manufactured solu- tions,

    K. Salari and P. Knupp, “Code verification by the method of manufactured solu- tions,” Sandia National Laboratories Report SAND2000-1444, Albuquerque, NM, 2000

    2000

  35. [43]

    Vari- ance based sensitivity analysis of model output: Design and estimator for the total sensitivity index,

    A. Saltelli, P. Annoni, I. Azzini, F. Campolongo, M. Ratto, and S. Tarantola, “Vari- ance based sensitivity analysis of model output: Design and estimator for the total sensitivity index,”Comput. Phys. Commun., vol. 181, no. 2, pp. 259–270, 2010. doi: 10.1016/j.cpc.2009.09.018

    2010 doi

  36. [44]

    A comparative analysis of thermal performance, annual energy use, and life cycle costs of low-cost houses made with mud bricks and earthbag wall systems in Sub-Saharan Africa,

    R. Wesonga, H. Kasedde, N. Kibwami, and M. Manga, “A comparative analysis of thermal performance, annual energy use, and life cycle costs of low-cost houses made with mud bricks and earthbag wall systems in Sub-Saharan Africa,”Energy Built Environ., vol. 4, pp. 13–24, 2023. do...

    2023 doi

  37. [45]

    Phase and microstructure of brick-clay soil and fired clay-bricks from some areas in Peshawar Pakistan,

    S. Ahmad, Y. Iqbal, and F. Ghani, “Phase and microstructure of brick-clay soil and fired clay-bricks from some areas in Peshawar Pakistan,”J. Pak. Mater. Soc., vol. 2, no. 1, pp. 33–39, 2008

    2008

  38. [46]

    Multi-criteria evaluation model for the selection of sustainable materials for building projects,

    P. O. Akadiri, P. O. Olomolaiye, and E. A. Chinyio, “Multi-criteria evaluation model for the selection of sustainable materials for building projects,”Autom. Constr., vol. 30, pp. 113–125, 2013. doi: 10.1016/j.autcon.2012.10.004 40

    2013 doi

  39. [47]

    Effect of sintering temperature on mechanical and thermophysical properties of biowaste-added fired clay bricks,

    F. Anjum, A. Ghaffar, Y. Jamil, and M. I. Majeed, “Effect of sintering temperature on mechanical and thermophysical properties of biowaste-added fired clay bricks,”J. Mater. Cycles Waste Manag., vol. 21, pp. 503–524, 2019. doi: 10.1007/s10163-018- 0810-x

    2019 doi

  40. [48]

    Replication package for: A Physics-Informed Neural Operator for Thermal Ranking of Low-Cost Wall Materials in Hot-Dry Climates,

    M. A. Khan and F. Raees, “Replication package for: A Physics-Informed Neural Operator for Thermal Ranking of Low-Cost Wall Materials in Hot-Dry Climates,” Zenodo, version 1.1.0, 2026. doi: 10.5281/zenodo.21311299 41

    2026 doi

  41. [2026]

    https://energyplus.net/documentation

Pith tools

Reviewed August 1, 2026 · model on record in the stance chip above.