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arxiv: 2604.03233 · v1 · submitted 2026-01-27 · 💻 cs.LG · cs.NA· math.NA

Integrating Artificial Intelligence, Physics, and Internet of Things: A Framework for Cultural Heritage Conservation

Carmine Valentino , Federico Pichi , Francesco Colace , Dajana Conte , Gianluigi Rozza This is my paper

Pith reviewed 2026-05-16 11:04 UTC · model grok-4.3

classification 💻 cs.LG cs.NAmath.NA
keywords cultural heritage conservationphysics-informed neural networksPINNsreduced order modelsInternet of Things3D modelingdegradation simulationscientific machine learning
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The pith

A framework integrates PINNs with reduced-order models to simulate degradation in 3D cultural heritage models from IoT data and physics laws.

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

The paper presents a four-layer framework that processes 3D digital replicas of cultural assets and runs simulations blending sensor data with physical laws of material degradation. Physics-Informed Neural Networks form the core by embedding governing equations into neural models to combine data-driven learning with known physics. These are paired with Proper Orthogonal Decomposition reduced-order models to make computations feasible on complex geometries while remaining compatible with traditional finite-element methods. The approach supports both forward prediction of future damage under environmental conditions and inverse inference of parameters from observations. Tests on simulated scenarios using real-life geometries demonstrate the separate components for monitoring and predictive conservation.

Core claim

The framework structures analysis into four functional layers that permit examination of 3D models of cultural assets and elaborate simulations based on data and physics knowledge. Scientific Machine Learning through Physics-Informed Neural Networks incorporates physical laws into deep learning models. Integration with Reduced Order Methods via Proper Orthogonal Decomposition improves efficiency for modeling degradation processes driven by environmental and material parameters, while supporting both direct and inverse problems on complex geometries.

What carries the argument

Physics-Informed Neural Networks (PINNs) integrated with Proper Orthogonal Decomposition reduced-order models (ROMs) applied to automatically processed 3D digital replicas for simulating degradation influenced by environmental and material parameters.

If this is right

  • Provides a methodology for processing 3D models of cultural assets for reliable simulation.
  • Applies PINNs to combine data-driven and physics-based approaches in cultural heritage conservation.
  • Integrates PINNs with ROMs to efficiently model degradation processes influenced by environmental and material parameters.
  • Handles both direct and inverse problems on simulated scenarios using real-life geometries.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Real-time IoT sensor streams could continuously update the models for ongoing predictive maintenance of heritage sites.
  • The same PINN-ROM structure might transfer to other domains involving physics-constrained degradation such as building infrastructure or engineered materials.
  • Automated inverse modeling could infer material properties or hidden damage states from surface observations without physical sampling.

Load-bearing premise

The physical laws chosen for the PINNs accurately capture the dominant degradation mechanisms across the varied materials and environmental conditions found in real cultural heritage objects.

What would settle it

Direct comparison of the framework's predicted degradation rates against measured physical changes on actual artifacts under controlled variations in humidity, temperature, or pollutants would falsify the claim if errors exceed acceptable thresholds for conservation use.

Figures

Figures reproduced from arXiv: 2604.03233 by Carmine Valentino, Dajana Conte, Federico Pichi, Francesco Colace, Gianluigi Rozza.

Figure 1
Figure 1. Figure 1: The architecture associated with the proposed framework consisting of four functional layers: the [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Acquisition of the 3D model related to the rock represented in Figure. The 3D Model (a) is acquired [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Acquisition of the 3D model related to the column. [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Acquisition of the 3D model related to the temple. [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Steps of the model elaboration performed by the 3D Model Module. [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Highlighted are the active modules of the architecture to perform the numerical approximation of [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Normal random sampling for µ ∈ [0, 1]3 and M = 100. 0 5 10 15 20 25 k 10 10 10 8 10 6 10 4 10 2 10 0 (a) Singular Values Decay 0 5 10 15 20 25 k 10 5 10 3 10 1 10 1 10 3 Mean absolute error Max absolute error Mean relative error Max relative error (b) Error Analysis [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Decay of the singular values and error analysis, respectively left and right, obtained from the ROM [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Convergence of λ, α, β during training to the real values λreal, αreal, βreal. Finally, the Online Module load the reduction method through the ROM Loading Submodule for the iden￾tified parameter value and solve the analyzed problem by exploiting the Online Solver Submodule. The msh2xdmf Module allows the construction of the xdmf file supported by a h5 file, enabling the visu￾alization and inspection of th… view at source ↗
Figure 10
Figure 10. Figure 10: Reduced approximation, full order solution, and relative error (left, middle, and right respectively) [PITH_FULL_IMAGE:figures/full_fig_p018_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Decay of the singular values and error analysis, respectively left and right, obtained from the ROM [PITH_FULL_IMAGE:figures/full_fig_p020_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Convergence of λ, α, β during training to the real values λreal, αreal, βreal. Finally, [PITH_FULL_IMAGE:figures/full_fig_p021_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Reduced approximation, full order solution, and relative error (left, middle, and right respectively) [PITH_FULL_IMAGE:figures/full_fig_p022_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Architecture’s active modules to obtain direct problem solutions via PINNs with known parameters. [PITH_FULL_IMAGE:figures/full_fig_p023_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Simulated boundary temperature data for the rock domain during 24 hours for Test Problem 3. [PITH_FULL_IMAGE:figures/full_fig_p024_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Reduced approximation, full order solution, and relative error (left, middle, and right respectively) [PITH_FULL_IMAGE:figures/full_fig_p026_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Values of boundary data with respect the two components [PITH_FULL_IMAGE:figures/full_fig_p027_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Comparison between the PINN and the full order FEM solutions, left and middle respectively, and [PITH_FULL_IMAGE:figures/full_fig_p028_18.png] view at source ↗
read the original abstract

The conservation of cultural heritage increasingly relies on integrating technological innovation with domain expertise to ensure effective monitoring and predictive maintenance. This paper presents a novel framework to support the preservation of cultural assets, combining Internet of Things (IoT) and Artificial Intelligence (AI) technologies, enhanced with the physical knowledge of phenomena. The framework is structured into four functional layers that permit the analysis of 3D models of cultural assets and elaborate simulations based on the knowledge acquired from data and physics. A central component of the proposed framework consists of Scientific Machine Learning, particularly Physics-Informed Neural Networks (PINNs), which incorporate physical laws into deep learning models. To enhance computational efficiency, the framework also integrates Reduced Order Methods (ROMs), specifically Proper Orthogonal Decomposition (POD), and is also compatible with classical Finite Element (FE) methods. Additionally, it includes tools to automatically manage and process 3D digital replicas, enabling their direct use in simulations. The proposed approach offers three main contributions: a methodology for processing 3D models of cultural assets for reliable simulation; the application of PINNs to combine data-driven and physics-based approaches in cultural heritage conservation; and the integration of PINNs with ROMs to efficiently model degradation processes influenced by environmental and material parameters. The reproducible and open-access experimental phase exploits simulated scenarios on complex and real-life geometries to test the efficacy of the proposed framework in each of its key components, allowing the possibility of dealing with both direct and inverse problems. Code availability: https://github.com/valc89/PhysicsInformedCulturalHeritage

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes a four-layer framework integrating IoT sensors, AI (via Physics-Informed Neural Networks), and physics-based modeling for cultural heritage conservation. It claims three contributions: a methodology for processing 3D digital replicas of assets for simulation; the use of PINNs to combine data-driven and physics-based approaches for degradation modeling; and the integration of PINNs with Reduced Order Methods (specifically POD) to efficiently handle environmental and material parameters. The framework is stated to support both direct and inverse problems and is validated only on simulated scenarios using real-life geometries, with open code provided.

Significance. If the central claims hold after quantitative validation, the work could provide a practical, reproducible tool for predictive maintenance of cultural assets by reducing computational cost through PINN-ROM coupling while incorporating physical constraints. The open-source code and focus on real-life 3D geometries are positive elements that support reproducibility and potential adoption in the field.

major comments (2)
  1. [Abstract and experimental phase] Abstract and experimental phase description: the manuscript asserts that the framework's efficacy is tested on simulated scenarios for direct and inverse problems, yet supplies no quantitative results, error metrics, convergence rates, or comparisons against baselines (e.g., pure FEM or data-only networks), rendering the central efficacy claims unverifiable.
  2. [PINNs component and degradation modeling] PINNs and degradation modeling sections: the framework embeds specific physical laws (PDEs) into the loss function to model degradation influenced by environmental and material parameters, but provides no evidence or sensitivity analysis showing that these laws remain dominant for heterogeneous real-world materials (stone, wood, frescoes) whose processes include unmodeled couplings such as moisture-driven chemistry or biological activity; the simulated scenarios use prescribed laws by construction and therefore do not test this load-bearing assumption.
minor comments (2)
  1. [Framework description] Clarify the precise form of the physics-data loss weighting coefficient (listed as a free parameter) and its selection procedure, as this affects reproducibility of the PINN training.
  2. [Introduction and methods] Add explicit citations to the foundational PINN and POD papers when first introducing the methods, rather than relying on the general terms.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed report. We address each major comment below and indicate the planned revisions to improve the manuscript.

read point-by-point responses

  1. Referee: [Abstract and experimental phase] Abstract and experimental phase description: the manuscript asserts that the framework's efficacy is tested on simulated scenarios for direct and inverse problems, yet supplies no quantitative results, error metrics, convergence rates, or comparisons against baselines (e.g., pure FEM or data-only networks), rendering the central efficacy claims unverifiable.

    Authors: We agree that the current manuscript would be strengthened by including explicit quantitative results directly in the text. While the open-source code repository enables full reproduction of the experiments on the real-life geometries, the main body focuses on framework description without tabulated metrics. In the revised manuscript we will add a new subsection (or expand the experimental phase) that reports relative L2 errors for both direct and inverse problems, convergence rates with respect to network depth/width and training iterations, and side-by-side comparisons against classical FEM and purely data-driven networks. These additions will make the efficacy claims verifiable from the paper itself. revision: yes

  2. Referee: [PINNs component and degradation modeling] PINNs and degradation modeling sections: the framework embeds specific physical laws (PDEs) into the loss function to model degradation influenced by environmental and material parameters, but provides no evidence or sensitivity analysis showing that these laws remain dominant for heterogeneous real-world materials (stone, wood, frescoes) whose processes include unmodeled couplings such as moisture-driven chemistry or biological activity; the simulated scenarios use prescribed laws by construction and therefore do not test this load-bearing assumption.

    Authors: The referee correctly notes that the present validation uses prescribed PDEs on simulated data and therefore cannot demonstrate dominance of those laws over unmodeled real-world couplings. Our contribution is methodological: we show how PINNs can be coupled with POD to solve the chosen physics on complex 3-D geometries while remaining computationally tractable. We will revise the manuscript to (i) explicitly state that the current experiments are controlled simulations intended to verify numerical correctness and efficiency, (ii) discuss the modular nature of the framework that permits additional physics terms, and (iii) outline the need for future field-data validation to assess sensitivity to moisture-driven chemistry or biological activity. A full sensitivity study on heterogeneous heritage materials lies beyond the scope of this paper but can be enabled by the released code. revision: partial

Circularity Check

0 steps flagged

Framework relies on externally defined standard methods (PINNs, POD) with no self-referential reductions in equations or claims

full rationale

The paper describes a four-layer framework for cultural heritage conservation that combines IoT data with PINNs (to embed physical laws) and ROMs (POD) for efficient simulation of degradation on 3D models. All core components—PINNs, POD, and FE methods—are cited as established external techniques rather than derived inside the paper. The three listed contributions are methodological (processing 3D models, applying PINNs, integrating PINNs with ROMs) and are tested only on simulated scenarios with prescribed physics; no equations, fitted parameters, or self-citations are shown that would make any claimed output equivalent to an input by construction. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The framework rests on the assumption that known physical laws for degradation can be directly embedded in neural networks and that reduced-order approximations preserve sufficient accuracy for the target geometries.

free parameters (1)
  • Physics-data loss weighting coefficient
    Standard hyperparameter in PINNs that balances the data-fitting term against the physics residual term; its specific value is not stated in the abstract.
axioms (1)
  • domain assumption Physical laws governing material degradation under environmental loads are known and can be expressed as differential equations suitable for PINN enforcement.
    Invoked when the abstract states that PINNs incorporate physical laws into the models.

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