no code implementations • 20 Mar 2024 • Minglei Lu, Chensen Lin, Martian Maxey, George Karniadakis, Zhen Li
In order to bridge the gap between microscale stochastic fluid models and continuum-based fluid models for bubble dynamics, we develop a composite neural operator model to unify the analysis of nonlinear bubble dynamics across microscale and macroscale regimes by integrating a many-body dissipative particle dynamics (mDPD) model with a continuum-based Rayleigh-Plesset (RP) model through a novel neural network architecture, which consists of a deep operator network for learning the mean behavior of bubble growth subject to pressure variations and a long short-term memory network for learning the statistical features of correlated fluctuations in microscale bubble dynamics.
2 code implementations • 7 Jun 2023 • Ehsan Haghighat, Umair bin Waheed, George Karniadakis
The Eikonal equation plays a central role in seismic wave propagation and hypocenter localization, a crucial aspect of efficient earthquake early warning systems.
no code implementations • 29 May 2023 • Chayan Banerjee, Kien Nguyen, Clinton Fookes, George Karniadakis
The incorporation of physical information in machine learning frameworks is opening and transforming many application domains.
no code implementations • 26 Apr 2023 • Simin Shekarpaz, Fanhai Zeng, George Karniadakis
We introduce a new approach for solving forward systems of differential equations using a combination of splitting methods and physics-informed neural networks (PINNs).
no code implementations • 16 Aug 2021 • Somdatta Goswami, Minglang Yin, Yue Yu, George Karniadakis
We propose a physics-informed variational formulation of DeepONet (V-DeepONet) for brittle fracture analysis.
no code implementations • 23 Dec 2019 • José del Águila Ferrandis, Michael Triantafyllou, Chryssostomos Chryssostomidis, George Karniadakis
Here, we put forward a new simulation paradigm by training recurrent type neural networks (RNNs) that take as input the stochastic wave elevation at a certain sea state and output the main vessel motions, e. g., pitch, heave and roll.
no code implementations • 29 Oct 2019 • Liu Yang, Sean Treichler, Thorsten Kurth, Keno Fischer, David Barajas-Solano, Josh Romero, Valentin Churavy, Alexandre Tartakovsky, Michael Houston, Prabhat, George Karniadakis
Uncertainty quantification for forward and inverse problems is a central challenge across physical and biomedical disciplines.
no code implementations • 2 Aug 2018 • Mamikon Gulian, Maziar Raissi, Paris Perdikaris, George Karniadakis
We extend this framework to linear space-fractional differential equations.
1 code implementation • 26 Apr 2016 • Maziar Raissi, George Karniadakis
We develop a novel multi-fidelity framework that goes far beyond the classical AR(1) Co-kriging scheme of Kennedy and O'Hagan (2000).