Solving crustal heat transfer for thermochronology using physics-informed neural networks
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Bibliographic record
Abstract
Abstract. We present a deep-learning approach based on the physics-informed neural networks (PINNs) for estimating thermal evolution of the crust during tectonic uplift with a changing landscape. The approach approximates the temperature field of the crust with a deep neural network, which is trained by optimizing the heat advection–diffusion equation, assuming initial and boundary temperature conditions that follow a prescribed topographic history. From the trained neural network of temperature field and the prescribed velocity field, one can predict the temperature history of a given rock particle that can be used to compute the cooling ages of thermochronology. For the inverse problem, the forward model can be combined with a global optimization algorithm that minimizes the misfit between predicted and observed thermochronological data, in order to constrain unknown parameters in the rock uplift history or boundary conditions. We demonstrate the approach with solutions of one- and three-dimensional forward and inverse models of the crustal thermal evolution, which are consistent with results of the finite-element method. As an example, the three-dimensional model simulates the exhumation and post-orogenic topographic decay of the Dabie Shan, eastern China, whose post-orogenic evolution has been constrained by previous thermochronological data and models. This approach takes advantage of the computational power of machine learning algorithms, offering a valuable alternative to existing analytical and numerical methods, with great adaptability to diverse boundary conditions and easy integration with various optimization schemes.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it