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Forward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equations
Maziar Raissi
Classical numerical methods for solving partial differential equations suffer from the curse dimensionality mainly due to their reliance on meticulously generated spatio-temporal g…
Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations
Maziar Raissi
A long-standing problem at the interface of artificial intelligence and applied mathematics is to devise an algorithm capable of achieving human level or even superhuman proficienc…
Parametric Gaussian Process Regression for Big Data
Maziar Raissi
This work introduces the concept of parametric Gaussian processes (PGPs), which is built upon the seemingly self-contradictory idea of making Gaussian processes parametric. Paramet…
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…