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Parallel Physics-Informed Neural Networks via Domain Decomposition [article]

Khemraj Shukla, Ameya D. Jagtap, George Em Karniadakis
2021 arXiv   pre-print
We develop a distributed framework for the physics-informed neural networks (PINNs) based on two recent extensions, namely conservative PINNs (cPINNs) and extended PINNs (XPINNs), which employ domain decomposition  ...  Our results indicate that for space domain decomposition, cPINNs are more efficient in terms of communication cost but XPINNs provide greater flexibility as they can also handle time-domain decomposition  ...  Karniadakis, Extended physics-informed neural networks (xpinns): A generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations, Communications  ... 
arXiv:2104.10013v3 fatcat:s2u74mcsnnduhhf2yes2ekniga

Scalable algorithms for physics-informed neural and graph networks [article]

Khemraj Shukla, Mengjia Xu, Nathaniel Trask, George Em Karniadakis
2022 arXiv   pre-print
Instead, we can train such networks from additional information obtained by employing the physical laws and evaluating them at random points in the space-time domain.  ...  Here, we review some of the prevailing trends in embedding physics into machine learning, using physics-informed neural networks (PINNs) based primarily on feed-forward neural networks and automatic differentiation  ...  Physics-informed neural networks (PINNs) (Raissi et al., 2019) can solve a partial differential equation (PDE) by directly incorporating the PDE into the loss function of the neural network (NN) and  ... 
arXiv:2205.08332v1 fatcat:3bq25a266vhyfhoommuj2uqtp4

Physics-informed neural networks for inverse problems in supersonic flows [article]

Ameya D. Jagtap, Zhiping Mao, Nikolaus Adams, George Em Karniadakis
2022 arXiv   pre-print
To this end, we 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  ...  We compare solutions obtained by PINNs and XPINNs and invoke some theoretical results that can be used to decide on the generalization errors of the two methods.  ...  Mao was conducted while he was a postdoc at Brown University and also during his one month-visit to the Technical University of Munich working with Prof. N. Adams.  ... 
arXiv:2202.11821v1 fatcat:zzwk5dpiujh5rbyennrzm3kx2y

SSNO: Spatio-spectral Neural Operator for Functional Space Learning of Partial Differential Equations

Muhammad Rafiq, Ghazala Rafiq, Ho-Youl Jung, Gyu Sang Choi
2022 IEEE Access  
Recent research to solve the parametric partial differential equations shifted the focus of conventional neural networks from finite-dimensional Euclidean space to generalized functional spaces.  ...  We formulate a novel neural network architecture to produce a state-of-the-art reproduction accuracy and a much reduced relative error over partial differential equations solutions.  ...  (Jagtap and Karniadakis, 2021) [16] proposed a generalized space-time domain decomposition framework for the extended physics informed neural network (XPINN).  ... 
doi:10.1109/access.2022.3148401 fatcat:maxl6opdnvgnhmsu5ow2m4vlpi

Three Ways to Solve Partial Differential Equations with Neural Networks – A Review [article]

Jan Blechschmidt, Oliver G. Ernst
2021 arXiv   pre-print
Neural networks are increasingly used to construct numerical solution methods for partial differential equations.  ...  In this expository review, we introduce and contrast three important recent approaches attractive in their simplicity and their suitability for high-dimensional problems: physics-informed neural networks  ...  Physics-informed neural networks (PINNs) are a scientific machine learning technique for solving partial differential equation (PDE) problems in the small data setting, meaning only the PDE problem data  ... 
arXiv:2102.11802v2 fatcat:xc647il5q5f4baixs74arorbbm

Hybrid FEM-NN models: Combining artificial neural networks with the finite element method [article]

Sebastian K. Mitusch, Simon W. Funke, Miroslav Kuchta
2021 arXiv   pre-print
We present a methodology combining neural networks with physical principle constraints in the form of partial differential equations (PDEs).  ...  Finally, we demonstrate the method on a complex cardiac cell model problem using deep neural networks.  ...  Karniadakis, Extended Physics-Informed Neural Networks (XPINNs): A Gener- alized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Dif-  ... 
arXiv:2101.00962v1 fatcat:vvarnz6wavhwxfdcmgtgilzncq

Mosaic Flows: A Transferable Deep Learning Framework for Solving PDEs on Unseen Domains [article]

Hengjie Wang, Robert Planas, Aparna Chandramowlishwaran, Ramin Bostanabad
2021 arXiv   pre-print
Physics-informed neural networks (PINNs) are increasingly employed to replace/augment traditional numerical methods in solving partial differential equations (PDEs).  ...  We introduce a transferable framework for solving boundary value problems (BVPs) via deep neural networks which can be trained once and used forever for various unseen domains and BCs.  ...  ) can result in a transferable deep learning framework for operator learning.  ... 
arXiv:2104.10873v2 fatcat:yvvxu7mh5fgwlnxkcl5be2u6mi

Physics and data informed neural networks for two-dimensional turbulence [article]

Vijay Kag, Kannabiran Seshasayanan, Venkatesh Gopinath
2022 arXiv   pre-print
In this work, we present physics-informed neural network (PINN) based methods to predict flow quantities and features of two-dimensional turbulence with the help of sparse data in a rectangular domain  ...  It relies on the training of the low and high wavenumber behaviour separately leading to a better estimate for the full turbulent flow.  ...  Karniadakis, "Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations," Journal of Computational Physics  ... 
arXiv:2203.02555v1 fatcat:xo5qxplg7ncbrbrkh6w2sdcp7a

Multifidelity Modeling for Physics-Informed Neural Networks (PINNs) [article]

Michael Penwarden, Shandian Zhe, Akil Narayan, Robert M. Kirby
2021 arXiv   pre-print
Physics-informed Neural Networks (PINNs) are candidates for these types of approaches due to the significant difference in training times required when different fidelities (expressed in terms of architecture  ...  In this paper, we propose a particular multifidelity approach applied to PINNs that exploits low-rank structure.  ...  Review of Physics-Informed Neural Networks Physics-Informed Neural Networks (PINNs) were originally proposed by Karniadakis and co-workers [12, 13, 14] as a neural network based alternative to traditional  ... 
arXiv:2106.13361v1 fatcat:gadm3ixoxbdh7eheh5wsrwddnq

Physics-informed neural networks (PINNs) for fluid mechanics: A review [article]

Shengze Cai, Zhiping Mao, Zhicheng Wang, Minglang Yin, George Em Karniadakis
2021 arXiv   pre-print
Here, we review flow physics-informed learning, integrating seamlessly data and mathematical models, and implementing them using physics-informed neural networks (PINNs).  ...  into existing algorithms, mesh-generation is complex, and we cannot tackle high-dimensional problems governed by parametrized NSE.  ...  Here, we consider a Physics-informed neural networks (PINNs) for fluid mechanics: A review 3 Fig. 1 : Schematic of a physics-informed neural network (PINN).  ... 
arXiv:2105.09506v1 fatcat:ww4kzexf6zgc3exiiqnatgpz54

Physics informed neural networks for continuum micromechanics [article]

Alexander Henkes, Henning Wessels, Rolf Mahnken
2021 arXiv   pre-print
The principle idea is to use a neural network as a global ansatz function to partial differential equations.  ...  Recently, physics informed neural networks have successfully been applied to a broad variety of problems in applied mathematics and engineering.  ...  Acknowledgement We thank Ameya Jagtap for the fruitful discussion and insights into cPINNs and the Kunststofftechnik Paderborn (KTP) for providing the WPC µCT-scans.  ... 
arXiv:2110.07374v1 fatcat:mbqrelv3jzc67luqxacvcsy54u

Deep learning of inverse water waves problems using multi-fidelity data: Application to Serre-Green-Naghdi equations [article]

Ameya D. Jagtap, Dimitrios Mitsotakis, George Em Karniadakis
To this end, we employ physics-informed neural networks (PINNs) to generate solutions to such ill-posed problems using only data of the free surface elevation and depth of the water.  ...  The applicability of the PINN methodology for the estimation of the impact of water waves onto solid obstacles is demonstrated after deriving the corresponding equations.  ...  [10] , and further by more general space-time domain decomposition based extended PINN (XPINN) methodology, see Jagtap & Karniadakis [11] , and for the theory of XPINN see [12] .  ... 
doi:10.48550/arxiv.2202.02899 fatcat:sizg4cwij5aaziggapwfqaohfe

State-of-the-Art Review of Design of Experiments for Physics-Informed Deep Learning [article]

Sourav Das, Solomon Tesfamariam
PINN uses physical information in the form of differential equations to enhance the performance of the neural networks.  ...  In particular, this study demonstrates the necessity of the design of experiment schemes for the Physics-Informed Neural Network (PINN), which belongs to the supervised learning class.  ...  Physics-Informed Neural Network A physics-informed neural network (PINN) is a special class of feed-forward neural network where physical conditions are imposed on the neural network as a loss function  ... 
doi:10.48550/arxiv.2202.06416 fatcat:dvf4i2amjrautj5imsh4cvamb4