Search Results for author: George E. Karniadakis

Found 5 papers, 2 papers with code

Multifidelity Deep Operator Networks For Data-Driven and Physics-Informed Problems

no code implementations19 Apr 2022 Amanda A. Howard, Mauro Perego, George E. Karniadakis, Panos Stinis

We demonstrate the new multi-fidelity training in diverse examples, including modeling of the ice-sheet dynamics of the Humboldt glacier, Greenland, using two different fidelity models and also using the same physical model at two different resolutions.

Operator learning

nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications

no code implementations8 Apr 2020 Guofei Pang, Marta D'Elia, Michael Parks, George E. Karniadakis

In this paper, we extend PINNs to parameter and function inference for integral equations such as nonlocal Poisson and nonlocal turbulence models, and we refer to them as nonlocal PINNs (nPINNs).

DeepXDE: A deep learning library for solving differential equations

6 code implementations10 Jul 2019 Lu Lu, Xuhui Meng, Zhiping Mao, George E. Karniadakis

We also present a Python library for PINNs, DeepXDE, which is designed to serve both as an education tool to be used in the classroom as well as a research tool for solving problems in computational science and engineering.

Linking Gaussian Process regression with data-driven manifold embeddings for nonlinear data fusion

no code implementations16 Dec 2018 Seungjoon Lee, Felix Dietrich, George E. Karniadakis, Ioannis G. Kevrekidis

In this paper, we will explore mathematical algorithms for multifidelity information fusion that use such an approach towards improving the representation of the high-fidelity function with only a few training data points.

Gaussian Processes regression

GPU-accelerated Red Blood Cells Simulations with Transport Dissipative Particle Dynamics

2 code implementations18 Nov 2016 Ansel L. Blumers, Yu-Hang Tang, Zhen Li, Xuejin Li, George E. Karniadakis

We observe a speedup of 10. 1 on one GPU over all 16 cores within a single node, and a weak scaling efficiency of 91% across 256 nodes.

Computational Physics Biological Physics

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