Solving crustal heat transfer for thermochronology using physics-informed neural networks

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.