arXiv subjects

Sarah Perez

Publications and source records attributed to Sarah Perez.

7 recordsLinked to original sources

arXiv2026

Probabilistic Upscaling of Hydrodynamics in Geological Fractures Under Uncertainty

Flow and transport in fractured geological media are strongly controlled by aperture heterogeneity and uncertainty in subsurface characterisation, yet most upscaling approaches rely on deterministic representations of fracture permeability. This study presents a scalable probabilistic workflow that bridges image-based fracture geometry and uncertainty-aware hydraulic predictions across scales. The approach integrates Bayesian correction of aperture-permeability model misspecification, a deep learning surrogate for predicting spatially distributed permeability statistics, and Darcy-scale flow upscaling to propagate uncertainty to effective transmissivity. The workflow is applied to natural shear fractures from core material in the Little Grand Wash Fault damage zone (Utah) and to simplified geometries derived from the same datasets. The Bayesian component quantifies uncertainty due to measurement errors and imperfect constitutive relations, while a Residual U-Net learns the effects of local heterogeneity and spatial correlation on predicted permeability uncertainty. Together, these components generate ensembles of permeability fields that are subsequently upscaled to probabilistic macroscopic flow responses. Results show that common empirical aperture-permeability relations are systematically biased for natural fractures, whereas the proposed probabilistic workflow yields uncertainty-aware permeability estimates consistent with physics-based behaviour. The method captures the impact of channelisation, connectivity, and complex 3D void geometries on transmissivity while quantifying the resulting uncertainty bounds. Computational efficiency arises from the proposed hybrid strategy for probabilistic upscaling, which combines physics-informed and data-driven approaches, preserves Stokes-flow consistency and supports uncertainty propagation without repeated high-fidelity simulations.

physics.comp-ph↗

arXiv2026

Physics-Informed Neural Networks for Methane Sorption: Cross-Gas Transfer Learning, Ensemble Collapse Under Physics Constraints, and Monte Carlo Dropout Uncertainty Quantification

Accurate methane sorption prediction across heterogeneous coal ranks requires models that combine thermodynamic consistency, efficient knowledge transfer across data-scarce geological systems, and calibrated uncertainty estimates, capabilities that are rarely addressed together in existing frameworks. We present a physics-informed transfer learning framework that adapts a hydrogen sorption PINN to methane sorption prediction via Elastic Weight Consolidation, coal-specific feature engineering, and a three-phase curriculum that progressively balances transfer preservation with thermodynamic fine-tuning. Trained on 993 equilibrium measurements from 114 independent coal experiments spanning lignite to anthracite, the framework achieves R2 = 0.932 on held-out coal samples, a 227% improvement over pressure-only classical isotherms, while hydrogen pre-training delivers 18.9% lower RMSE and 19.4% faster convergence than random initialization. Five Bayesian uncertainty quantification approaches reveal a systematic divergence in performance across physics-constrained architectures. Monte Carlo Dropout achieves well-calibrated uncertainty at minimal overhead, while deep ensembles, regardless of architectural diversity or initialization strategy, exhibit performance degradation because shared physics constraints narrow the admissible solution manifold. SHAP and ALE analyses confirm that learned representations remain physically interpretable and aligned with established coal sorption mechanisms: moisture-volatile interactions are most influential, pressure-temperature coupling captures thermodynamic co-dependence, and features exhibit non-monotonic effects. These results identify Monte Carlo Dropout as the best-performing UQ method in this physics-constrained transfer learning framework, and demonstrate cross-gas transfer learning as a data-efficient strategy for geological material modeling.

cs.LG↗

arXiv2025

When Cubic Law and Darcy Fail: Bayesian Correction of Model Misspecification in Fracture Conductivities

Structural uncertainties and unresolved features in fault zones hinder the assessment of leakage risks in subsurface CO2 storage. Understanding multi-scale uncertainties in fracture network conductivity is crucial for mitigating risks and reliably modelling upscaled fault leakage rates. Conventional models, such as the Cubic Law, which is based on mechanical aperture measurements, often neglect fracture roughness, leading to model misspecifications and inaccurate conductivity estimates. Here, we develop a physics-informed, AI-driven correction of these model misspecifications by automatically integrating roughness effects and small-scale structural uncertainties. Using Bayesian inference combined with data-driven and geometric corrections, we reconstruct local hydraulic aperture fields that reliably estimate fracture conductivities. By leveraging interactions across scales, we improve upon traditional empirical corrections and provide a framework for propagating uncertainties from individual fractures to network scales. Our approach thereby supports robust calibration of conductivity ranges for fault leakage sensitivity analyses, offering a scalable solution for subsurface risk assessment.

physics.geo-ph↗

arXiv2024

A semi-Lagrangian method for the direct numerical simulation of crystallization and precipitation at the pore scale

This article introduces a new efficient particle method for the numerical simulation of crystallization and precipitation at the pore scale of real rock geometries extracted by X-Ray tomography. It is based on the coupling between superficial velocity models of porous media, Lagrangian description of chemistry using Transition-State-Theory, involving underlying grids. Its ability to successfully compute dissolution process has been established in the past and is presently generalized to precipitation and crystallization by means of adsorption modeling. Numerical simulations of mineral CO2 trapping are provided, showing evidence of clogging/non-clogging regimes, and one of the main results is the introduction of a new non-dimensional number needed for this characterization.

cs.CE↗

arXiv2023

Auto-weighted Bayesian Physics-Informed Neural Networks and robust estimations for multitask inverse problems in pore-scale imaging of dissolution

In this article, we present a novel data assimilation strategy in pore-scale imaging and demonstrate that this makes it possible to robustly address reactive inverse problems incorporating Uncertainty Quantification (UQ). Pore-scale modeling of reactive flow offers a valuable opportunity to investigate the evolution of macro-scale properties subject to dynamic processes. Yet, they suffer from imaging limitations arising from the associated X-ray microtomography (X-ray microCT) process, which induces discrepancies in the properties estimates. Assessment of the kinetic parameters also raises challenges, as reactive coefficients are critical parameters that can cover a wide range of values. We account for these two issues and ensure reliable calibration of pore-scale modeling, based on dynamical microCT images, by integrating uncertainty quantification in the workflow. The present method is based on a multitasking formulation of reactive inverse problems combining data-driven and physics-informed techniques in calcite dissolution. This allows quantifying morphological uncertainties on the porosity field and estimating reactive parameter ranges through prescribed PDE models with a latent concentration field and dynamical microCT. The data assimilation strategy relies on sequential reinforcement incorporating successively additional PDE constraints. We guarantee robust and unbiased uncertainty quantification by straightforward adaptive weighting of Bayesian Physics-Informed Neural Networks (BPINNs), ensuring reliable micro-porosity changes during geochemical transformations. We demonstrate successful Bayesian Inference in 1D+Time and 2D+Time calcite dissolution based on synthetic microCT images with meaningful posterior distribution on the reactive parameters and dimensionless numbers.

cs.LG↗

arXiv2023

Adaptive weighting of Bayesian physics informed neural networks for multitask and multiscale forward and inverse problems

In this paper, we present a novel methodology for automatic adaptive weighting of Bayesian Physics-Informed Neural Networks (BPINNs), and we demonstrate that this makes it possible to robustly address multi-objective and multi-scale problems. BPINNs are a popular framework for data assimilation, combining the constraints of Uncertainty Quantification (UQ) and Partial Differential Equation (PDE). The relative weights of the BPINN target distribution terms are directly related to the inherent uncertainty in the respective learning tasks. Yet, they are usually manually set a-priori, that can lead to pathological behavior, stability concerns, and to conflicts between tasks which are obstacles that have deterred the use of BPINNs for inverse problems with multi-scale dynamics. The present weighting strategy automatically tunes the weights by considering the multi-task nature of target posterior distribution. We show that this remedies the failure modes of BPINNs and provides efficient exploration of the optimal Pareto front. This leads to better convergence and stability of BPINN training while reducing sampling bias. The determined weights moreover carry information about task uncertainties, reflecting noise levels in the data and adequacy of the PDE model. We demonstrate this in numerical experiments in Sobolev training, and compare them to analytically $ε$-optimal baseline, and in a multi-scale Lokta-Volterra inverse problem. We eventually apply this framework to an inpainting task and an inverse problem, involving latent field recovery for incompressible flow in complex geometries.

physics.comp-ph↗

arXiv2016

Active learning in pre-class assignments: Exploring the use of interactive simulations to enhance reading assignments

Pre-class reading assignments help prepare students for active classes by providing a first exposure to the terms and concepts to be used during class. We investigate if the use of inquiry-oriented PhET-based activities in conjunction with pre-class reading assignments can improve both the preparation of students for in-class learning and student attitudes towards and engagement with pre-class assignments. Over three course modules covering different topics, students were assigned randomly to complete either a textbook-only pre-class assignment or both a textbook pre-class assignment and a PhET-based activity. The assignments helped prepare students for class, as measured by performance on the pre-class quiz relative to a beginning-of-semester pre-test, but no evidence for increased learning due the PhET activity was observed. Students rated the assignments which included PhET as more enjoyable and, for the topic latest in the semester, reported engaging more with the assignments when PhET was included.

physics.ed-ph↗