MOD-Net: A Machine Learning Approach via Model-Operator-Data Network for Solving PDEs
Lulu Zhang, Tao Luo, Yaoyu Zhang, Weinan E, Zhi-Qin John Xu & Zheng Ma

Frame Invariance and Scalability of Neural Operators for Partial Differential Equations
Muhammad I. Zafar, Jiequn Han, Xu-Hui Zhou & Heng Xiao

Moment-Based Multi-Resolution HWENO Scheme for Hyperbolic Conservation Laws
Jiayin Li, Chi-Wang Shu & Jianxian Qiu

Solving Time Dependent Fokker-Planck Equations via Temporal Normalizing Flow
Xiaodong Feng, Li Zeng & Tao Zhou

An Improved Peridynamic Model with Energy-Based Micromodulus Correction Method for Fracture in Particle Reinforced Composites
Zihao Yang, Shaoqi Zheng, Fei Han, Shangkun Shen & Xiaofei Guan

A Quantitative Comparison of Physical Accuracy and Numerical Stability of Lattice Boltzmann Color Gradient and Pseudopotential Multicomponent Models for Microfluidic Applications
Karun P. N. Datadien, Gianluca Di Staso, Herman M. A. Wijshoff & Federico Toschi

A NURBS-Enhanced Finite Volume Method for Steady Euler Equations with Goal-Oriented $h$-Adaptivity
Xucheng Meng & Guanghui Hu

A Holomorphic Operator Function Approach for the Transmission Eigenvalue Problem of Elastic Waves
Yingxia Xi & Xia Ji

A RKDG Method for 2D Lagrangian Ideal Magnetohydrodynamics Equations with Exactly Divergence-Free Magnetic Field
Shijun Zou, Xiaolong Zhao, Xijun Yu & Zihuan Dai

Modeling of Bound Electron Effects in Particle-in-Cell Simulation
Xiangyan An, Min Chen, Zheng-Ming Sheng & Jie Zhang