Physics-encoded recurrent graph neural network for long-term consolidation

Abstract

Although physics-informed neural networks (PINNs) have become a leading paradigm for solving both forward and inverse partial differential equations (PDEs) in a unified framework, their efficacy is often hindered by long-term prediction instability in black-box time marching, training imbalances stemming from multiple physical loss functions, and the inherent difficulty of representing complex geometries within neural architectures. This study develops the first-ever physics-encoded recurrent graph neural network (PeRGNN), a novel graph-based architecture that inherently handles irregular geometries to solve the consolidation problem that is challenging in geomechanics. Continuous PINN incorporates residuals of PDEs, boundary conditions, initial conditions, and data discrepancies, without respecting causal evolution between time snapshots. In comparison, PeRGNN hard-encodes the temporal evolution laws, initial and boundary conditions into a recurrent unit. By treating spatial operators as learnable graph-based message-passing functions while strictly enforcing the time-marching structure, the framework establishes a strong inductive bias that ensures physical consistency. The efficacy of PeRGNN is validated through six geomechanical case studies involving different tunnel geometries, anisotropic material behaviours, forward and inverse analysis. PeRGNN achieves (1) zero-shot prediction for extended time spans, generalizing across initial conditions and consolidation parameters, (2) remarkable data efficiency while maintaining high accuracy on decimated meshes with node counts nearly two orders of magnitude lower than that traditionally required for multi-dimensional consolidation analysis, and (3) robust inverse modelling with sparse and noisy data. The proposed PeRGNN, thus, proves to be a promising method for real-world geotechnical analysis and deserves further development. Graphical abstract: [Figure not available: see fulltext.]