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oa Application of Physics Informed Neural Networks to Solving Problems of the Non-Homogeneous Elasticity in Geological Environment
- Publisher: European Association of Geoscientists & Engineers
- Source: Conference Proceedings, 18th International Conference Monitoring of Geological Processes and Ecological Condition of the Environment, Apr 2025, Volume 2025, p.1 - 5
Abstract
A general approach for simulating the behavior of geological systems by calculating the stress-strain state of non-homogeneous regions subjected to gravitational forces has been developed. This approach reduces boundary value problems in solid mechanics to unconstrained optimization problems. Using Physics-Informed Neural Networks (PINNs) within this framework simplifies the solution to constructing substitution functions that depend on the boundary and initial conditions and the neural network solution of the corresponding optimization problem.
The problem of non-homogeneous plane elasticity was analyzed within this approach. For Neumann conditions set on the top and right sides, and Dirichlet conditions on the left and bottom sides of a trapezoid-shaped region with inhomogeneous mechanical properties, the ansatz functions for displacements for the unconstrained optimisation problem were obtained. To verify the proposed methodology, the stress-strain state was calculated for the two-dimensional problem of a non-homogeneous heavy half-plane. Additionally, for a trapezoid-shaped region with non-homogeneous properties subjected solely to gravitational forces, with zero stresses set on one pair of adjacent sides and zero displacements on another pair, numerical simulations were carried out using the proposed methodology. The proposed methodology can be extended to problems in the theory of thermal elasticity, including piecewise-homogeneous and thermosensitive media.
