A surrogate model for predicting ground surface deformation gradient induced by pressurized fractures

Article Engineering, Multidisciplinary

Multi-fidelity Bayesian optimization to solve the inverse Stefan problem

J. M. Winter et al.

Summary: In this work, the authors propose an efficient solution to the inverse Stefan problem using multi-fidelity Bayesian optimization. They construct a multi-fidelity Gaussian process surrogate model by combining low-fidelity estimates with high-fidelity measurements. The proposed method improves the stability of the optimization procedure by reformulating the target function as a composite function. It demonstrates superior convergence properties compared to an approach based solely on high-fidelity measurements.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2023)

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Article Engineering, Multidisciplinary

Physics-informed deep learning for simultaneous surrogate modeling and PDE-constrained optimization of an airfoil geometry

Yubiao Sun et al.

Summary: We use a physics-informed neural network (PINN) to model and optimize the flow around an airfoil for maximizing lift to drag ratio. The PINN takes airfoil shape parameters as inputs and approximates the Navier-Stokes equations using collocation points. The gradients of the lift-to-drag ratio with respect to the shape parameters are calculated using the differentiability of the PINN.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2023)

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Article Mathematics, Applied

Deep convolutional Ritz method: parametric PDE surrogates without labeled data

J. N. Fuhg et al.

Summary: This study presents a parametric PDE solver called Deep Convolutional Ritz Method (DCRM), which reduces the order of differential operators by minimizing energy functionals compared to residual-based methods. Based on studies involving the Poisson equation with spatially parameterized source term and boundary conditions, CNNs trained on labeled data outperform DCPINNs in convergence speed and generalization abilities. However, the surrogates generated from DCRM converge significantly faster than their DCPINN counterparts and prove to generalize faster and better than the surrogates obtained from both CNNs trained on labeled data and DCPINNs, suggesting the possibility of training PDE solution surrogates without labeled data using DCRM.

APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION (2023)

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Article Green & Sustainable Science & Technology

Deep learning-accelerated 3D carbon storage reservoir pressure forecasting based on data assimilation using surface displacement from InSAR

Hewei Tang et al.

Summary: This study presents a fast forecasting method for the reservoir pressure distribution in geologic carbon storage (GCS) using low-cost InSAR data and a deep learning-accelerated workflow. By assimilating surface displacement maps and predicting dynamic reservoir pressure, the method is able to complete data assimilation and pressure forecasting in half an hour.

INTERNATIONAL JOURNAL OF GREENHOUSE GAS CONTROL (2022)

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Article Mathematics, Applied

WHEN DO EXTENDED PHYSICS-INFORMED NEURAL NETWORKS (XPINNS) IMPROVE GENERALIZATION?

Zheyuan Hu et al.

Summary: Physics-informed neural networks (PINNs) have become a popular choice for solving high-dimensional partial differential equations (PDEs) due to their excellent approximation power and generalization ability. Recently, extended PINNs (XPINNs) based on domain decomposition methods have attracted considerable attention due to their effectiveness in modeling multiscale and multiphysics problems and their parallelization. However, theoretical understanding of their convergence and generalization properties remains unexplored. This study takes an initial step towards understanding how and when XPINNs outperform PINNs.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2022)

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Article Engineering, Geological

Verification of Coupled Hydraulic Fracturing Simulators Using Laboratory-Scale Experiments

Paromita Deb et al.

Summary: This study aims to verify the numerical predictions of hydraulic stimulation experiments by comparing controlled laboratory experiments in granite samples to simulations using CSMP and GEOS. The results show that both simulators accurately reproduced the experimental pressure behavior, emphasizing the impact of fluid-loss and unsaturated flow on fracture pressure.

ROCK MECHANICS AND ROCK ENGINEERING (2021)

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Article Computer Science, Interdisciplinary Applications

A framework for data-driven solution and parameter estimation of PDEs using conditional generative adversarial networks

Teeratorn Kadeethum et al.

Summary: The study utilizes cGAN for image-to-image translation to learn forward and inverse solution operators of PDEs. By parameterizing spatially heterogeneous coefficients, steady-state solutions of coupled hydromechanical processes are achieved. The framework provides significant speed-up compared to finite-element solvers, with lower errors in both forward and inverse modeling.

NATURE COMPUTATIONAL SCIENCE (2021)

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Article Computer Science, Hardware & Architecture