… In this two part treatise, we present our developments in the context of solving two main …
first part of our two-part treatise, we focus on computing datadriven solutions to partial differential …

… of problems: data-driven solution and data-driven discovery of partial differential equations.
… In fact, if u denotes the real part of h and v is the imaginary part, we are placing a multi-out …

… functions, DeepONet approximates linear and nonlinear PDE solution operators … PDE
solution function output spaces. We devise, apply, and compare data-driven and physics-informed …

… a deep learning approach for discovering nonlinear partial … Specifically, we consider nonlinear
partial differential equations … Let u denote the real part of ψ and v the imaginary part. Then…

… partial differential equation (PDE) using its solution data. Instead of identifying the terms
in the underlying PDE, we seek to approximate the evolution operator of the underlying PDE …

… and was part of the Annus Mirabilis papers, which lay the foundations of modern physics. We
… This integration of nonlinear dynamics and machine learning opens the door for principled …

… unknown physics and … learning PDE under noisy data and limited discrete data. To overcome
these challenges, in this work, a deep-learning based data-driven method, called DL-PDE, …

… solutions attain state-of-the-art performance when trained with large amounts of data. However,
purely data driven approaches for machine learning … part of h and v is the imaginary part. …

… gain insights into the underlying physics of the system based on the terms in the identified
… To keep the size of the machine learning problem tractable, we subsample 1000 random …

… In this paper we use machine learning, and deep learning in particular, to discover PDEs …
by an ordinary differential equation which is automatically discovered by our deep learning …