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Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations
Maziar Raissi, Paris Perdikaris, George Em Karniadakis
We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general…
Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations
Maziar Raissi, Paris Perdikaris, George Em Karniadakis
We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general…
Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations
Maziar Raissi, George Em Karniadakis
While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial…
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…
Machine Learning of Linear Differential Equations using Gaussian Processes
Maziar Raissi, George Em. Karniadakis
This work leverages recent advances in probabilistic machine learning to discover conservation laws expressed by parametric linear equations. Such equations involve, but are not li…