What question did this study set out to answer?

Develop a physics-guided Bayesian neural network framework incorporating conductive heat-transfer constraints to accurately reconstruct 3D subsurface geothermal temperatures from sparse, depth-imbalanced borehole data.

August 16, 2026GeothermicsOpen Access

Learning with constraints: A physics-guided Bayesian framework for reliable geothermal temperature mapping in northeastern Italy

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Authors

DDDanial Sheini DashtgoliUniversity of Trieste MGMichela GiustinianiNational Institute of Oceanography and Applied Geophysics MBMartina BusettiNational Institute of Oceanography and Applied Geophysics

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Implication

Computational study demonstrates robust 3D geothermal temperature mapping using physics-guided Bayesian networks, indicating improved subsurface extrapolation in sparse data domains.

Key Points

Develop a physics-guided Bayesian neural network framework incorporating conductive heat-transfer constraints to accurately reconstruct 3D subsurface geothermal temperatures from sparse, depth-imbalanced borehole data.
Trained a Bayesian neural network using Monte Carlo dropout and heteroscedastic learning on N=849 irregularly distributed temperature measurements from the Lower Friulian Plain (NE Italy).
Integrated physical domain constraints, including vertical monotonicity and gradient-band bounds representing plausible conductive heat-transfer ranges.
Assessed extrapolation capability by withholding deep borehole observations (1000–1200 m) during training and validating against the Grado-1 well across 100–1200 m.
In the data-supported domain (<1000 m), models attained R² ≈ 0.95–0.96 and RMSE ≈ 2.6–2.8 °C.
Under deep extrapolation (1000–1200 m), the monotonic model achieved R² = 0.877 and RMSE = 1.33 °C, with models delivering 97–99% prediction-interval coverage and eliminating nonphysical deep-zone oscillations.
Independent validation against the Grado-1 well profile demonstrated temperature estimation agreement within ±1 °C across the entire 100–1200 m depth range.

Cite This Study

Dashtgoli et al. (2026) studied this question.

synapsesocial.com/papers/6a8178fcf2fb91fc834ac20e https://doi.org/10.1016/j.geothermics.2026.103816

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Implication

Computational study demonstrates robust 3D geothermal temperature mapping using physics-guided Bayesian networks, indicating improved subsurface extrapolation in sparse data domains.

Learning with constraints: A physics-guided Bayesian framework for reliable geothermal temperature mapping in northeastern Italy

Discussion

Member takes

Implication

Key Points

Cite This Study

Learning with constraints: A physics-guided Bayesian framework for reliable geothermal temperature mapping in northeastern Italy

Discussion

Member takes

Implication

Key Points

Cite This Study

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