Neural Networks with Local Converging Inputs (NNLCI) for Solving Conservation Laws, Part II: 2D Problems

by Haoxiang Huang, Vigor Yang & Yingjie Liu, CiCP 34 (2023), pp. 907-933.

Benchmark Computations of the Phase Field Crystal and Functionalized Cahn-Hilliard Equations via Fully Implicit, Nesterov Accelerated Schemes

by Jea-Hyun Park, Abner J. Salgado & Steven M. Wise, CiCP 33 (2023), pp. 367-398.

Bjorken Flow Revisited: Analytic and Numerical Solutions in Flat Space-Time Coordinates

by Daniele Simeoni, Alessandro Gabbana & Sauro Succi, CiCP 33 (2023), pp. 174-188.

Random Batch Particle Methods for the Homogeneous Landau Equation

by José Antonio Carrillo, Shi Jin & Yijia Tang, CiCP 31 (2022), pp. 997-1019.

Unified Gas-Kinetic Wave-Particle Methods VI: Disperse Dilute Gas-Particle Multiphase Flow

by Xiaojian Yang, Chang Liu, Xing Ji, Wei Shyy & Kun Xu, CiCP 31 (2022), pp. 669-706.

Approximating the Gaussian as a Sum of Exponentials and Its Applications to the Fast Gauss Transform

by Shidong Jiang & Leslie Greengard, CiCP 31 (2022), pp. 1-26.

Ensemble Gradient for Learning Turbulence Models from Indirect Observations

by Carlos A. Michelén Ströfer, Xin-Lei Zhang & Heng Xiao, CiCP 30 (2021), pp. 1269-1289.

Distributed and Adaptive Fast Multipole Method in Three Dimensions

by Jonathan Bull & Stefan Engblom, CiCP 30 (2021), pp. 959-984.

A Linear Scaling in Accuracy Numerical Method for Computing the Electrostatic Forces in the $N$-Body Dielectric Spheres Problem

by Muhammad Hassan & Benjamin Stamm, CiCP 29 (2021), pp. 319-356.

Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations

by Ameya D. Jagtap & George Em Karniadakis, CiCP 28 (2020), pp. 2002-2041.

Machine Learning and Computational Mathematics

by Weinan E, CiCP 28 (2020), pp. 1639-1670.

Parametric POD-Galerkin Model Order Reduction for Unsteady-State Heat Transfer Problems

by Sokratia Georgaka, Giovanni Stabile, Gianluigi Rozza & Michael J. Bluck, CiCP 27 (2020), pp. 1-32.

High Accuracy Benchmark Problems for Allen-Cahn and Cahn-Hilliard Dynamics

by Jon Matteo Church, Zhenlin Guo, Peter K. Jimack, Anotida Madzvamuse, Keith Promislow, Brian Wetton, Steven M. Wise & Fengwei Yang, CiCP 26 (2019), pp. 947-972.

Data-Driven, Physics-Based Feature Extraction from Fluid Flow Fields Using Convolutional Neural Networks

by Carlos Michelén Ströfer, Jin-Long Wu, Heng Xiao & Eric Paterson, CiCP 25 (2019), pp. 625-650.

Fast Evaluation of the Caputo Fractional Derivative and Its Applications to Fractional Diffusion Equations

by Shidong Jiang, Jiwei Zhang, Qian Zhang & Zhimin Zhang, CiCP 21 (2017), pp. 650-678.

Deep Potential: A General Representation of a Many-Body Potential Energy Surface

by Jiequn Han, Linfeng Zhang, Roberto Car & Weinan E, CiCP 23 (2018), pp. 629-639.

A Unified Gas Kinetic Scheme for Continuum and Rarefied Flows V: Multiscale and Multi-Component Plasma Transport

by Chang Liu & Kun Xu, CiCP 22 (2017), pp. 1175-1223.