Physics-informed Neural Networks

Physics-Informed Spatiotemporal Surrogate Modeling and Robust Operational Optimization for CO₂ Applications in Subsurface Flow under Permeability Uncertainty

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B9 R2325

This talk presents a physics-informed spatiotemporal surrogate that predicts coupled CO₂ storage and geothermal responses under geological uncertainty and enables rapid, risk-aware optimization of staged well controls.

Zhao Beichen

Beichen Zhao is a Ph.D. candidate at China University of Petroleum–Beijing and a visiting student in the Applied Mathematics and Computational Science program at KAUST. His research focuses on physics-informed neural networks and surrogate modeling for subsurface flow, with applications in CO₂ enhanced oil recovery, geological carbon storage, and geothermal reservoir simulation.

A Combination of Physics-informed Neural Networks with the Fixed-stress Splitting Iteration for Solving Biot’s Model

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KAUST

Abstract In this study, we aim to solve Biot’s consolidation models by employing physics-informed neural networks. Based on the fixed-stress splitting method, loss functions are designed for the displacement variable and the pressure variables separately. Such a strategy enables us to train two independent and smaller neural networks. The coupling of different variables is realized via the fixed-stress iterative algorithm. Numerical experiments are provided to show that the fixed-stress iterative algorithm can improve the performance of neural network approximations of the solution of Biot’s

Physics-informed Neural Networks for Learning the Homogenized Coefficients of Multiscale Elliptic Equations

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KAUST

Abstract Multiscale elliptic equations with scale separation are often approximated by the corresponding homogenized equations with slowly varying homogenized coefficients (the G-limit). The traditional homogenization techniques typically rely on the periodicity of the multiscale coefficients, thus finding the G-limits often requires sophisticated techniques in more general settings even when multiscale coefficient is known, if possible. Alternatively, we propose a simple approach to estimate the G-limits from (noisy-free or noisy) multiscale solution data, either from the existing forward

Mohammed Sayyari

Mohammed is a Mathematician with a solid background in scientific programming. Mohammed's mathematical interests are in the analysis of partial differential equations and the discretization thereof.