A Physics-Informed Neural Network for Pressurized Cavities of Arbitrary Shape in Heterogeneous Rock

Pressurized cavity problems underlie a wide range of rock engineering applications, including tunneling, drilling, and in situ testing, but accurate field prediction remains challenging in heterogeneous rock masses where discontinuities are pervasive. This work proposes a Physics-Informed Neural Network to solve forward problems of pressurized cavities with arbitrary smooth shapes embedded in heterogeneous elastic media. The novelty of the approach is that a single shared network is augmented with signed-distance and level-set embeddings, and domain-conditioned activation functions allow the representation of piecewise-smooth fields across discontinuities. The physics-informed loss enforces equilibrium, constitutive relationships, traction boundary conditions, interface continuity, and sparse observation data. Ground-truth data are generated using Finite-Element simulations. The model achieves displacement mean absolute errors of O(10⁻⁵)\,m in both homogeneous and heterogeneous rock masses. In homogeneous benchmarks, the relative L₂ -norm errors for the normal stress components remain below 3.1× 10⁻³ on average. In heterogeneous cases with intersecting discontinuities, the mean relative L₂ -norm errors for σ ₓₓ and σ yy remain below 6.6× 10⁻³ , with discrepancies localized near interfaces. Compared with XPINN, the proposed PINN framework delivers comparable stress accuracy with smaller displacement errors near discontinuities while keeping the number of parameters nearly constant across subdomains, yielding a ~ 5× training speedup. Furthermore, the number of training epochs for related heterogeneous cases can be reduced by half through transfer learning.