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arxiv: 2605.22111 · v1 · pith:FDULVF2Jnew · submitted 2026-05-21 · 💻 cs.LG · cs.CE· stat.ML

Aerodynamic force reconstruction using physics-informed Gaussian processes

Gledson Rodrigo Tondo , Igor Kavrakov , Guido Morgenthal This is my paper

Pith reviewed 2026-05-22 08:10 UTC · model grok-4.3

classification 💻 cs.LG cs.CEstat.ML
keywords physics-informed Gaussian processesaerodynamic force reconstructionstructural dynamicsnoisy databridge aerodynamicsprobabilistic machine learningload identification
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The pith

A physics-informed Gaussian process reconstructs aerodynamic loads from noisy structural response measurements.

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

The paper presents a probabilistic physics-informed machine learning method to recover aerodynamic forces acting on structures from noisy measurements of their dynamic responses. This Gaussian process approach incorporates physical knowledge to avoid overfitting without requiring regularization techniques and supports data of varying types and fidelities. Demonstrated on simulations of the Great Belt East Bridge, it achieves close matches to true loads in terms of errors, magnitudes, phases, and peaks. Such reconstruction could aid in validating aerodynamic models, estimating future loads, and assessing structural health in civil engineering applications.

Core claim

The probabilistic physics-informed machine learning approach reconstructs the underlying aerodynamic loads from noisy measurements of structural dynamic responses. The model avoids overfitting, eliminates the need for regularization schemes, and allows for the use of heterogeneous and multi-fidelity data. Efficacy is shown through reconstruction on the Great Belt East Bridge simulated under a linear unsteady assumption, with strong agreement in root mean squared errors, magnitude, phase angle, and peak values.

What carries the argument

Physics-informed Gaussian process that embeds aerodynamic physics constraints into probabilistic reconstruction from structural dynamics data.

If this is right

  • Supports validation of simplified aerodynamic models using real-world noisy data.
  • Facilitates future load estimation on structures like bridges.
  • Contributes to structural damage prognosis through accurate load reconstruction.
  • Broadly applicable to modeling complex structural systems under aerodynamic forces.

Where Pith is reading between the lines

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

  • This approach could potentially be adapted for nonlinear aerodynamic regimes by modifying the embedded physics model.
  • Integration with sensor networks on existing bridges might enable ongoing load monitoring without direct force measurements.
  • Similar methods might apply to other inverse problems in structural engineering, such as reconstructing wind loads from building responses.

Load-bearing premise

The demonstration assumes that the aerodynamic behavior can be adequately modeled with linear unsteady assumptions; if actual conditions involve significant nonlinear effects, the agreement between predicted and true loads may not hold.

What would settle it

Apply the method to experimental data from a wind tunnel test on a bridge section model where direct force measurements are available alongside response data, and check if the reconstructed loads match the measured forces within low error bounds across different wind speeds.

Figures

Figures reproduced from arXiv: 2605.22111 by Gledson Rodrigo Tondo, Guido Morgenthal, Igor Kavrakov.

Figure 1
Figure 1. Figure 1: Framework for the physics-informed Gaussian process. Models for different data types are created and jointly [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The Great Belt East Bridge in Denmark. Top: elevation sketch (left) and deck coordinate system (right), with [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Top: turbulence spectrum in the vertical direction [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Modal responses for the first bending mode shape ( [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: True modal force signal F(t) for the first structural mode, along with mean and 95% confidence interval of predictions in time (top) and the correspondent power spectral density (bottom). The force predictions in the mean sense are in very good agreement with the true values calculated by the LU model. The physics-informed GP outputs are a smoothed version of the original force. In regions where high-frequ… view at source ↗
Figure 6
Figure 6. Figure 6: Comparison metric values between the original forces from the linear unsteady model and the mean values [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Left: the numerical model’s third mode shape ( [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Global responses at midspan in drag direction (p [PITH_FULL_IMAGE:figures/full_fig_p006_8.png] view at source ↗
read the original abstract

Accurate modeling of aerodynamic loads is essential for understanding and predicting the responses of complex structural systems. However, these models often rely on simplifications of the true physical forces, introducing assumptions that can limit their accuracy. Validating such models becomes particularly challenging in the presence of noisy or incomplete data. To address this, we introduce a probabilistic physics-informed machine learning approach designed to reconstruct the underlying aerodynamic loads from noisy measurements of structural dynamic responses. The model avoids overfitting, eliminates the need for regularization schemes, and allows for the use of heterogeneous and multi-fidelity data during the training process. The efficacy of the approach is demonstrated through the reconstruction of aerodynamic loads on the Great Belt East Bridge, simulated under a linear unsteady assumption. Results show a strong agreement between true and predicted loads, particularly related to root mean squared errors, magnitude, phase angle and peak values of the signals. The method for load reconstructing holds broad applicability, such as modeling validation, future load estimation, and structural damage prognosis.

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

1 major / 2 minor

Summary. The paper presents a probabilistic physics-informed Gaussian process approach to reconstruct aerodynamic loads from noisy structural dynamic response measurements. It claims advantages in avoiding overfitting and regularization, supporting heterogeneous and multi-fidelity data, and shows strong agreement with true loads in a simulation of the Great Belt East Bridge under linear unsteady aerodynamics using metrics such as RMSE, magnitude, phase angle, and peak values.

Significance. Should the approach prove robust to deviations from the linear unsteady assumption, it would offer a useful probabilistic framework for aerodynamic load reconstruction in structural engineering applications, with potential for model validation and damage prognosis. The integration of physics constraints in a GP setting is a positive aspect, though the current validation does not yet establish this robustness.

major comments (1)
  1. [Abstract] The efficacy demonstration relies on data simulated under the linear unsteady assumption, which matches the physics model likely incorporated in the GP. This results in testing internal consistency rather than the ability to reconstruct loads when the true aerodynamics include unmodeled effects such as nonlinearities or vortex shedding, undermining the general applicability claim.
minor comments (2)
  1. The manuscript would benefit from additional details on the exact formulation of the physics-informed kernel or constraints used in the Gaussian process.
  2. Include comparisons to standard regularization-based reconstruction methods to highlight the claimed advantages.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the thoughtful review and for identifying a key limitation in the scope of our validation. We address the major comment below and have made revisions to the manuscript to clarify the demonstration's assumptions and to moderate claims of general applicability.

read point-by-point responses

  1. Referee: [Abstract] The efficacy demonstration relies on data simulated under the linear unsteady assumption, which matches the physics model likely incorporated in the GP. This results in testing internal consistency rather than the ability to reconstruct loads when the true aerodynamics include unmodeled effects such as nonlinearities or vortex shedding, undermining the general applicability claim.

    Authors: We agree that the numerical experiments use data generated from the identical linear unsteady aerodynamic model embedded in the physics-informed GP. This choice verifies the framework's capacity to recover loads from noisy structural responses when the physics model is correct, including its handling of heterogeneous data and avoidance of explicit regularization. However, we acknowledge that this does not constitute a test of robustness against model mismatch, such as nonlinear aerodynamic effects or vortex shedding. To address the concern, we have revised the abstract to state explicitly that the demonstration is performed under the linear unsteady assumption and to qualify the applicability claim. We have also added a dedicated paragraph in the discussion section that notes this limitation and identifies validation against nonlinear and unsteady phenomena as an important direction for future work. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation remains self-contained

full rationale

The paper introduces a physics-informed Gaussian process that embeds the linear unsteady aerodynamic governing equations as constraints within the probabilistic model to reconstruct loads from noisy structural response measurements. This setup uses external physical relations (the linear unsteady assumption) to regularize the inference rather than defining the target loads in terms of the fitted outputs. Validation occurs on synthetic data generated under the same model, which tests consistency with the embedded physics but does not reduce the reconstruction to a tautological fit by construction, as the noisy observations supply independent information and the method explicitly supports multi-fidelity and heterogeneous data without forcing equivalence to inputs. No load-bearing self-citations, ansatzes smuggled via prior work, or uniqueness theorems from the same authors are indicated in the abstract or description that would collapse the central claim.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review is limited to the abstract, so the ledger reflects only explicitly mentioned elements. The approach rests on embedding physical laws into the GP model and on the linear unsteady assumption for the demonstration case.

axioms (1)
  • domain assumption Linear unsteady assumption governs the simulated aerodynamic forces on the Great Belt East Bridge
    Explicitly stated as the basis for the simulation used to demonstrate the method.

pith-pipeline@v0.9.0 · 5703 in / 1305 out tokens · 60019 ms · 2026-05-22T08:10:47.941055+00:00 · methodology

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Reference graph

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18 extracted references · 18 canonical work pages

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