3.4k citations · 27.2k across the 213 of their papers we have counts for
3 papers · 2 filters
Linking Gaussian Process regression with data-driven manifold embeddings for nonlinear data fusion
Seungjoon Lee, Felix Dietrich, George E. Karniadakis +1
In statistical modeling with Gaussian Process regression, it has been shown that combining (few) high-fidelity data with (many) low-fidelity data can enhance prediction accuracy, c…
Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations
Liu Yang, Dongkun Zhang, George Em Karniadakis
We developed a new class of physics-informed generative adversarial networks (PI-GANs) to solve in a unified manner forward, inverse and mixed stochastic problems based on a limite…
Collapse of Deep and Narrow Neural Nets
Lu Lu, Yanhui Su, George Em Karniadakis
Recent theoretical work has demonstrated that deep neural networks have superior performance over shallow networks, but their training is more difficult, e.g., they suffer from the…