1.1k citations · 2.3k across the 19 of their papers we have counts for
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Conditional deep surrogate models for stochastic, high-dimensional, and multi-fidelity systems
Yibo Yang, Paris Perdikaris
We present a probabilistic deep learning methodology that enables the construction of predictive data-driven surrogates for stochastic systems. Leveraging recent advances in variat…
Physics-informed deep generative models
Yibo Yang, Paris Perdikaris
We consider the application of deep generative models in propagating uncertainty through complex physical systems. Specifically, we put forth an implicit variational inference form…
Adversarial Uncertainty Quantification in Physics-Informed Neural Networks
Yibo Yang, Paris Perdikaris
We present a deep learning framework for quantifying and propagating uncertainty in systems governed by non-linear differential equations using physics-informed neural networks. Sp…
Numerical Gaussian Processes for Time-dependent and Non-linear Partial Differential Equations
Maziar Raissi, Paris Perdikaris, George Em Karniadakis
We introduce the concept of numerical Gaussian processes, which we define as Gaussian processes with covariance functions resulting from temporal discretization of time-dependent p…