Planar 3D models of hydraulic fracturing provide a practical balance between models with restrictive geometric assumptions and fully 3D simulators, capturing fractures with arbitrary planar footprints at moderate computational cost. Nevertheless, applications such as treatment design optimization and mini-frac test interpretation require large ensembles of simulations, for which the cost of planar 3D models remains a significant bottleneck. This work presents acceleration strategies for the planar 3D Implicit Level Set Algorithm (ILSA) to reduce simulation runtime while preserving numerical accuracy. A unified planar 3D ILSA scheme that consolidates the nested loops of the elastohydrodynamic solver and the front tracking algorithm into a single iterative process is introduced. A matrix splitting approach is applied to the linearized elastohydrodynamic system, moving the dense part of the elasticity operator to the right-hand side and yielding a sparse system matrix that can be solved more efficiently. Anderson acceleration is incorporated into the solution of the elastohydrodynamic system to improve convergence under varying fracture geometry. Additionally, a predictor--corrector scheme is examined with the proposed methods to assess their combined effect. Each technique is evaluated individually and in combination on both the reference and unified planar 3D ILSA schemes across five benchmark cases. Numerical experiments demonstrate that the unified scheme alone delivers an average 2.5x speedup, reaching 5.7x for the sandglass geometry. The combined application of all techniques achieves an average 4x speedup and up to 11x for the sandglass case, with the relative discrepancy in fracture aperture below 5% compared with the reference scheme.

Soil microorganisms control organic matter cycling and largely determine how soil systems can cope with and mitigate climate change and environmental threats. Representing microbial dynamics in process-based soil models is therefore critical to predict carbon cycling in soils, albeit highly challenging to inform from data. One promising approach to improve their parametrisation is the integration of genomic data, yet modelling the complex and unknown relationship between genomes and the processes the microbes are driving is an unsolved problem. In this work, we present the first hybrid modeling framework for deriving biokinetic parameter values of a process-based soil organic matter turnover model from metagenome-inferred functional traits based on DNA sequencing data. Our model predicts biokinetic parameters of the process-based model from genomic trait data with a neural network and integrates constraints from ecological theory and literature to ensure realistic behavior, even of non-observed state variables. We evaluate our method on synthetic genomic trait datasets of varying complexity and on real data, showing that our approach improves performance over multiple baselines and learns the dynamics of unmeasurable components of the process-based model effectively, even for small training datasets.

The geochemical evolution of long-lived magma oceans is strongly regulated by volatile exchange between the molten mantle and the atmosphere. For planets inside the runaway-greenhouse limit, this coupled evolution can persist for billions of years. However, most existing studies assume Earth-like (oxidized) conditions and neglect the influence of redox state on melt thermodynamics and volatile release. We quantified how experimentally derived, oxygen-fugacity-dependent melting curves implemented within the coupled interior-atmosphere framework PROTEUS propagate into the thermal structure, melt fraction, and rheological evolution of rocky exoplanet interiors, applying this to the short-period super-Earth GJ 1132 b. We found strongly non-linear thermal responses to variations in melting curves. In volatile-poor systems, reduced melting curves promote earlier deep-mantle crystallisation relative to oxidised and Earth-like cases, favouring late-stage surface magma oceans sustained by greenhouse warming, while oxidized melting curves maintain higher melt fractions and a vertically extended magma ocean. Reduced mantles produce massive H$_2$-CO-rich atmospheres; oxidized mantles favour thinner H$_2$O-CO$_2$ envelopes. In volatile-rich systems, the interior reaches radiative equilibrium at high melt fractions, sustaining a steady-state global magma ocean in which melting curve variations do not significantly influence solidification timing. This indicates a hierarchical control: volatile inventory and surface oxygen fugacity act as the primary regulators of thermal state, while oxygen-fugacity-dependent melting relations provide a secondary modulation. These contrasting regimes produce distinct atmospheric compositions and formation timescales, offering testable spectral predictions for close-in rocky exoplanets evaluable with forthcoming JWST observations.