Search Results - "Karniadakis, George Em"

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, Ameya D. Jagtap, George Em Karniadakis, George Em Karniadakis

“…Here we propose a generalized space-time domain decomposition approach for the physics-informed neural networks (PINNs) to solve nonlinear partial differential…”
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On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs by Yeonjong Shin, Yeonjong Shin, Jérôme Darbon, Jérôme Darbon, George Em Karniadakis, George Em Karniadakis

“…Physics informed neural networks (PINNs) are deep learning based techniques for solving partial differential equations (PDEs) encountered in computational…”
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Physics-informed neural networks for high-speed flows by Mao, Zhiping, Jagtap, Ameya D., Karniadakis, George Em

“…In this work we investigate the possibility of using physics-informed neural networks (PINNs) to approximate the Euler equations that model high-speed…”
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Dying ReLU and Initialization: Theory and Numerical Examples by Lu Lu, Lu Lu, Yeonjong Shin, Yeonjong Shin, Yanhui Su, Yanhui Su, George Em Karniadakis, George Em Karniadakis

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Physics-informed neural networks (PINNs) for fluid mechanics: a review by Cai, Shengze, Mao, Zhiping, Wang, Zhicheng, Yin, Minglang, Karniadakis, George Em

“…Despite the significant progress over the last 50 years in simulating flow problems using numerical discretization of the Navier–Stokes equations (NSE), we…”
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Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators by Lu, Lu, Jin, Pengzhan, Pang, Guofei, Zhang, Zhongqiang, Karniadakis, George Em

“…It is widely known that neural networks (NNs) are universal approximators of continuous functions. However, a less known but powerful result is that a NN with…”
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Incorporation of memory effects in coarse-grained modeling via the Mori-Zwanzig formalism by Li, Zhen, Bian, Xin, Li, Xiantao, Karniadakis, George Em

“…The Mori-Zwanzig formalism for coarse-graining a complex dynamical system typically introduces memory effects. The Markovian assumption of delta-correlated…”
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A Petrov–Galerkin spectral element method for fractional elliptic problems by Kharazmi, Ehsan, Zayernouri, Mohsen, Karniadakis, George Em

“…We develop a new C0-continuous Petrov–Galerkin spectral element method for one-dimensional fractional elliptic problems of the form 0Dxαu(x)−λu(x)=f(x),…”
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One-dimensional modeling of fractional flow reserve in coronary artery disease: Uncertainty quantification and Bayesian optimization by Yin, Minglang, Yazdani, Alireza, Karniadakis, George Em

“…Non-invasive estimation of fractional flow reserve (FFR) values, the key index in the diagnosis of obstructive coronary artery disease, is a promising…”
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Learning nonlinear operators in latent spaces for real-time predictions of complex dynamics in physical systems by Kontolati, Katiana, Goswami, Somdatta, Em Karniadakis, George, Shields, Michael D.

“…Predicting complex dynamics in physical applications governed by partial differential equations in real-time is nearly impossible with traditional numerical…”
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Fractional Buffer Layers: Absorbing Boundary Conditions for Wave Propagation by Min Cai, Min Cai, Ehsan Kharazmi, Ehsan Kharazmi, Changpin Li, Changpin Li, George Em Karniadakis, George Em Karniadakis

“…Not provided…”
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Bi-Orthogonal fPINN: A Physics-Informed Neural Network Method for Solving Time-Dependent Stochastic Fractional PDEs by Lei Ma, Lei Ma, Rongxin Li, Rongxin Li, Fanhai Zeng, Fanhai Zeng, Ling Guo, Ling Guo, George Em Karniadakis, George Em Karniadakis

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How the spleen reshapes and retains young and old red blood cells: A computational investigation by Li, He, Liu, Zixiang Leonardo, Lu, Lu, Buffet, Pierre, Karniadakis, George Em

“…The spleen, the largest secondary lymphoid organ in humans, not only fulfils a broad range of immune functions, but also plays an important role in red blood…”
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Computational Biomechanics of Human Red Blood Cells in Hematological Disorders by Li, Xuejin, Li, He, Chang, Hung-Yu, Lykotrafitis, George, Em Karniadakis, George

“…We review recent advances in multiscale modeling of the biomechanical characteristics of red blood cells (RBCs) in hematological diseases, and their relevance…”
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Potassium Buffering in the Neurovascular Unit: Models and Sensitivity Analysis by Witthoft, Alexandra, Filosa, Jessica A., Karniadakis, George Em

“…Astrocytes are critical regulators of neural and neurovascular network communication. Potassium transport is a central mechanism behind their many functions…”
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Multiscale parareal algorithm for long-time mesoscopic simulations of microvascular blood flow in zebrafish by Blumers, Ansel L., Yin, Minglang, Nakajima, Hiroyuki, Hasegawa, Yosuke, Li, Zhen, Karniadakis, George Em

“…Various biological processes such as transport of oxygen and nutrients, thrombus formation, vascular angiogenesis and remodeling are related to…”
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G2Φnet: Relating genotype and biomechanical phenotype of tissues with deep learning by Zhang, Enrui, Spronck, Bart, Humphrey, Jay D, Karniadakis, George Em

“…Many genetic mutations adversely affect the structure and function of load-bearing soft tissues, with clinical sequelae often responsible for disability or…”
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Effect of Chain Chirality on the Self-Assembly of Sickle Hemoglobin by Li, Xuejin, Caswell, Bruce, Karniadakis, George Em

“…We present simulation results on the self-assembly behavior of sickle hemoglobin (HbS). A coarse-grained HbS model, which contains hydrophilic and hydrophobic…”
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Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations by Raissi, Maziar, Yazdani, Alireza, Karniadakis, George Em

“…For centuries, flow visualization has been the art of making fluid motion visible in physical and biological systems. Although such flow patterns can be, in…”
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Deep transfer learning and data augmentation improve glucose levels prediction in type 2 diabetes patients by Deng, Yixiang, Lu, Lu, Aponte, Laura, Angelidi, Angeliki M., Novak, Vera, Karniadakis, George Em, Mantzoros, Christos S.

“…Accurate prediction of blood glucose variations in type 2 diabetes (T2D) will facilitate better glycemic control and decrease the occurrence of hypoglycemic…”
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