Symbolic genetic algorithm for discovering open-form partial differential equations (SGA-PDE) [PDF]
Physical Review Research, 2022 Partial differential equations (PDEs) are concise and understandable representations of domain knowledge, which are essential for deepening our understanding of physical processes and predicting future responses.
Yuntian Chen +4 more
doaj +2 more sources
DLGA-PDE: Discovery of PDEs with incomplete candidate library via combination of deep learning and genetic algorithm [PDF]
Journal of Computational Physics, 2020 Data-driven methods have recently been developed to discover underlying partial differential equations (PDEs) of physical problems. However, for these methods, a complete candidate library of potential terms in a PDE are usually required.
Dongxiao Zhang, Hao Xu
exaly +2 more sources
PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers [PDF]
Neural Information Processing Systems, 2023 Time-dependent partial differential equations (PDEs) are ubiquitous in science and engineering. Recently, mostly due to the high computational cost of traditional solution techniques, deep neural network based surrogates have gained increased interest ...
Phillip Lippe +4 more
semanticscholar +1 more source
Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems [PDF]
Computer Methods in Applied Mechanics and Engineering, 2021 Deep learning has been shown to be an effective tool in solving partial differential equations (PDEs) through physics-informed neural networks (PINNs). PINNs embed the PDE residual into the loss function of the neural network, and have been successfully ...
J. Yu, Lu Lu, Xuhui Meng, G. Karniadakis
semanticscholar +1 more source
Towards Multi-spatiotemporal-scale Generalized PDE Modeling [PDF]
Trans. Mach. Learn. Res., 2022 Partial differential equations (PDEs) are central to describing complex physical system simulations. Their expensive solution techniques have led to an increased interest in deep neural network based surrogates. However, the practical utility of training
Jayesh K. Gupta, Johannes Brandstetter
semanticscholar +1 more source
Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems [PDF]
Computer Methods in Applied Mechanics and Engineering, 2021 Despite the great promise of the physics-informed neural networks (PINNs) in solving forward and inverse problems, several technical challenges are present as roadblocks for more complex and realistic applications. First, most existing PINNs are based on
Han Gao, M. Zahr, Jian-Xun Wang
semanticscholar +1 more source
Vinpocetine’s immunomodulating, anti-oxidant, anti-inflammatory, ant-ifibrotic, and PDE inhibiting potencies ameliorate bleomycin-induced pulmonary fibrosis [PDF]
Iranian Journal of Basic Medical Sciences, 2023 Objective(s): Pulmonary fibrosis (PF) is a global health problem with a high economic burden. Intratracheal administration of bleomycin is the best model that resembles the pathogenesis of PF in humans.
Mohamed Balaha +3 more
doaj +1 more source
Scalable Transformer for PDE Surrogate Modeling [PDF]
Neural Information Processing Systems, 2023 Transformer has shown state-of-the-art performance on various applications and has recently emerged as a promising tool for surrogate modeling of partial differential equations (PDEs).
Zijie Li, Dule Shu, A. Farimani
semanticscholar +1 more source
Neural Inverse Operators for Solving PDE Inverse Problems [PDF]
International Conference on Machine Learning, 2023 A large class of inverse problems for PDEs are only well-defined as mappings from operators to functions. Existing operator learning frameworks map functions to functions and need to be modified to learn inverse maps from data.
R. Molinaro +3 more
semanticscholar +1 more source
Partial differential equations for oceanic artificial intelligence [PDF]
ESAIM: Proceedings and Surveys, 2021 The Sea Surface Temperature (SST) plays a significant role in analyzing and assessing the dynamics of weather and also biological systems. It has various applications such as weather forecasting or planning of coastal activities.
Guillot Jules +5 more
doaj +1 more source