Showing papers in "Journal of Computational Physics in 2022"

TL;DR: In this paper, a neural tangent kernel (NTK) was derived for physics-informed neural networks (PINNs) and a novel gradient descent algorithm was proposed to adaptively calibrate the convergence rate of the total training error.

TL;DR: In this article , a neural tangent kernel (NTK) was derived for physics-informed neural networks and shown to converge to a deterministic kernel that stays constant during training in the infinite width limit.

TL;DR: In this article , the authors employ the physics-informed neural networks (PINNs) and its extended version, extended PINNs (XPINNs), where domain decomposition allows deploying locally powerful neural networks in each subdomain, which can provide additional expressivity in subdomains, where a complex solution is expected.

TL;DR: In this article , the authors proposed a mathematical and numerical model for cardiac electromechanics, wherein biophysically detailed core models describe the different physical processes concurring to the cardiac function.

TL;DR: The relaxed-SAV (RSAV) method proposed in this paper penalizes the numerical errors of the auxiliary variables by a relaxation technique and improves the accuracy and consistency noticeably.

TL;DR: In this paper , a nonlinear manifold ROM (NM-ROM) was proposed to better approximate high-fidelity model solutions with a smaller latent space dimension than the traditional linear subspace reduced order models.

TL;DR: In this paper , a data-model integration scheme for fire progression forecasting, that combines Reduced-order modelling, recurrent neural networks (LSTM), data assimilation, and error covariance tuning, was developed and tested.

TL;DR: Nonlocal Kernel Network (NKN) as discussed by the authors is a nonlocal neural operator that is resolution independent, characterized by deep neural networks, and capable of handling a variety of tasks such as learning governing equations and classifying images.

TL;DR: In this paper , a precomputation algorithm is proposed that yields immediate guarantees that a complete basis is obtained, and a fast recursive algorithm for efficient evaluation and illustrate its performance in numerical tests.

TL;DR: In this paper, a least square space-time control volume scheme is proposed to handle regularity requirements, imposition of boundary conditions, entropy compatibility, and conservation, substantially reducing requisite hyperparameters in the process.

TL;DR: In this article , a least square space-time control volume scheme is proposed to handle regularity requirements, imposition of boundary conditions, entropy compatibility, and conservation, substantially reducing requisite hyperparameters in the process.

TL;DR: In this paper , a quadratic approximation manifold is presented for performing nonlinear, projection-based, model order reduction (PMOR), which constitutes a departure from the traditional affine subspace approximation that is aimed at mitigating the Kolmogorov barrier for nonlinear PMOR, particularly for convectiondominated transport problems.

TL;DR: In this article , a mixed Deep Energy Method (mDEM) is proposed to resolve fine features of the stress and displacement fields, for example concentration features in solid mechanics applications, by introducing stress measures as an additional output of the NN to the recently introduced pure displacement formulation.

TL;DR: In this paper , the authors show that deep fully convolutional neural networks (CNNs) can accurately predict the SGS forcing terms and the inter-scale transfers in a priori tests, and if trained with enough samples, lead to stable and accurate a posteriori LES-CNN.

TL;DR: In this paper , an auxiliary physics informed neural network (A-PINN) framework was proposed to solve forward and inverse problems of nonlinear IDEs without the need of label data.

TL;DR: In this paper, the authors proposed a fully decoupled structure and second-order time accuracy for highly coupled nonlinear incompressible magnetohydrodynamic (MHD) systems.

TL;DR: In this paper , a fully connected neural network (FCNN) was proposed to solve the inverse scattering problem with limited-aperture radar cross-section (RCS) data collected corresponding to a single incident field.

TL;DR: In this paper, a fully connected neural network (FCNN) was proposed to solve the inverse scattering problem with limited-aperture radar cross-section (RCS) data collected corresponding to a single incident field.

TL;DR: In this article , the authors developed a weakly compressible smoothed particle hydrodynamics (SPH) model for multi-phase flows with large density ratios while allowing large CFL numbers.

TL;DR: In this article , the authors proposed a fully decoupled structure and second-order time accuracy for highly coupled nonlinear incompressible magnetohydrodynamic (MHD) systems.

TL;DR: In this paper , a two-stage PINN method was proposed to simulate abundant localized wave solutions of integrable equations, including the Boussinesq-Burgers equations and coupled equations.

TL;DR: A novel and efficient deep learning framework adopting the Temporal Convolutional Network (TCN) model is proposed to simulate the ultra-long-history-dependent stress-strain constitutive model, which achieves higher prediction accuracy and efficiency compared to the traditional RNN model for constitutive modeling.

TL;DR: Based on the discrete element method (DEM) and the multiphase fluid model in the framework of the lattice Boltzmann method (LBM), a multi-phase fluid-solid two-way coupling algorithm is proposed in this article .

TL;DR: In this paper , a gradient-based deep neural network (GDNN) is used to predict the nonlinear patterns of subsurface responses including the temporal-spatial evolution of the pressure and saturation plumes.

TL;DR: In this article , three adaptive techniques to improve the computational performance of deep neural network (DNN) methods for high-dimensional partial differential equations (PDEs) are presented, which are adaptive choice of the loss function, adaptive activation function, and adaptive sampling, all of which will be applied to the training process of a DNN for PDEs.

TL;DR: In this paper , a physics-informed deep learning framework for solving steady-state incompressible flow on multiple sets of irregular geometries is presented, which uses a point-cloud based neural network to capture geometric features of computational domains, and using the mean squared residuals of the governing partial differential equations, boundary conditions, and sparse observations as the loss function of the network.

TL;DR: In this paper , the second order ETDRK (ETDRK2) scheme unconditionally preserves the energy dissipation law for a family of phase field models, such as the Allen-Cahn equation, the Cahn-Hilliard equation and the molecular beam epitaxy (MBE) model.

TL;DR: A resolved coupling model to simulate interaction between two-phase fluids and irregularly shaped particles by using Computational Fluid Dynamics (CFD) and Discrete Element Method (DEM) is developed, showing great potential to apply this model in coastal engineering.