Artificial intelligence for partial differential equations in computational mechanics: A review

Y Wang, J Bai, Z Lin, Q Wang, C Anitescu, J Sun… - arXiv preprint arXiv …, 2024 - arxiv.org
In recent years, Artificial intelligence (AI) has become ubiquitous, empowering various fields,
especially integrating artificial intelligence and traditional science (AI for Science: Artificial …

Physics-informed graph convolutional neural network for modeling fluid flow and heat convection

JZ Peng, Y Hua, YB Li, ZH Chen, WT Wu, N Aubry - Physics of Fluids, 2023 - pubs.aip.org
This paper introduces a novel surrogate model for two-dimensional adaptive steady-state
thermal convection fields based on deep learning technology. The proposed model aims to …

Entropy-dissipation informed neural network for mckean-vlasov type pdes

Z Shen, Z Wang - Advances in Neural Information …, 2023 - proceedings.neurips.cc
Abstract The McKean-Vlasov equation (MVE) describes the collective behavior of particles
subject to drift, diffusion, and mean-field interaction. In physical systems, the interaction term …

Deciphering and integrating invariants for neural operator learning with various physical mechanisms

R Zhang, Q Meng, ZM Ma - National Science Review, 2024 - academic.oup.com
Neural operators have been explored as surrogate models for simulating physical systems
to overcome the limitations of traditional partial differential equation (PDE) solvers. However …

A physics-guided machine learning framework for real-time dynamic wake prediction of wind turbines

B Li, M Ge, X Li, Y Liu - Physics of Fluids, 2024 - pubs.aip.org
Efficient and accurate prediction of the wind turbine dynamic wake is crucial for active wake
control and load assessment in wind farms. This paper proposes a real-time dynamic wake …

Immersed boundary method-incorporated physics-informed neural network for simulation of incompressible flows around immersed objects

Y Xiao, LM Yang, C Shu, X Shen, YJ Du, YX Song - Ocean Engineering, 2025 - Elsevier
In this work, an immersed boundary method-incorporated physics informed neural network
(IBM-PINN) is proposed to simulate steady incompressible flows around immersed objects …

An improved physical information network for forecasting the motion response of ice floes under waves

X Peng, C Wang, G Xia, F Han, Z Liu, W Zhao… - Physics of …, 2024 - pubs.aip.org
Physics-informed neural networks (PINNs) have increasingly become a key intelligent
technology for solving partial differential equations. Nevertheless, for simulating the dynamic …

The Decoupling Concept Bottleneck Model

R Zhang, X Du, J Yan, S Zhang - IEEE Transactions on Pattern …, 2024 - ieeexplore.ieee.org
The Concept Bottleneck Model (CBM) is an interpretable neural network that leverages high-
level concepts to explain model decisions and conduct human-machine interaction …

Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation

R Zhang, Q Meng, R Zhu, Y Wang, W Shi… - arXiv preprint arXiv …, 2023 - arxiv.org
In scenarios with limited available or high-quality data, training the function-to-function
neural PDE solver in an unsupervised manner is essential. However, the efficiency and …

Monte Carlo Neural PDE Solver

R Zhang, Q Meng, R Zhu, Y Wang, W Shi, S Zhang… - openreview.net
Training neural PDE solver in an unsupervised manner is essential in scenarios with limited
available or high-quality data. However, the performance and efficiency of existing methods …