Efficient Modelling of Magmatic Systems: A Pseudo-Component Approach to Phase Equilibria in Coupled Simulations

Deciphering magmatic system dynamics is inherently challenging due to the lack of direct observations of subsurface processes. Numerical modelling serves as a key tool to interpret indirect evidence from petrological and geochemical analyses of igneous rocks. At the heart of magma dynamics lies the interplay between complex multiphase fluid mechanics and multicomponent thermochemistry. Accurate modelling of these systems requires determining stable phase assemblages, which involves computationally demanding Gibbs free energy minimisation across high-dimensional compositional spaces with dozens of end-members. Current algorithms often lack the robustness and efficiency required for real-time integration into coupled thermos-chemical-mechanical models.

Traditional approaches to coupled modelling have frequently employed highly simplified phase relationships, such as single-phase loops, or relied on precomputed lookup tables to avoid the computational cost of real-time phase equilibrium calculations. These methods, however, impose significant limitations. This work introduces an alternative—a petrological model that generates multi-dimensional pseudo-phase diagrams in P-T-X space using pseudo-component end-members. Inspired by ideal solution thermodynamics, this approach eliminates the need for computationally expensive energy minimisation, overly simplistic phase representations, or cumbersome lookup tables. Instead, it employs a computationally efficient Newton method to solve a constrained nonlinear system.

Calibration of the model using standard machine learning techniques allows it to closely approximate key petrological trends, such as fractional crystallisation, observed in experimental data and full thermodynamic calculations. Once calibrated, the model efficiently tracks the dynamic evolution of major mineral and melt phases, including their compositions, across extensive P-T-X ranges. The calibration process further identifies the principal axes of variability, typically reducing the system to 5-6 dominant pseudo-components associated with major liquidus phases. This dimensional reduction significantly simplifies the system’s complexity compared to full thermodynamic models while retaining essential petrological insights.