Abstract Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode
model equations, like Partial Differential Equations (PDE), as a component of the neural …

Physics-informed neural networks (PINNs) are demonstrating remarkable promise in
integrating physical models with gappy and noisy observational data, but they still struggle …

The solution of a partial differential equation can be obtained by computing the inverse
operator map between the input and the solution space. Towards this end, we introduce a …

Physics-informed neural networks (PINNs) as a means of solving partial differential
equations (PDE) have garnered much attention in the Computational Science and …

We introduce physics-informed neural networks–neural networks that are trained to solve
supervised learning tasks while respecting any given laws of physics described by general …

In this work, we demonstrate how physical principles—such as symmetries, invariances and
conservation laws—can be integrated into the dynamic mode decomposition (DMD). DMD is …

This paper is an introductory tutorial for numerical trajectory optimization with a focus on
direct collocation methods. These methods are relatively simple to understand and …

We introduce a new algorithm for approximation by rational functions on a real or complex
set of points, implementable in 40 lines of MATLAB and requiring no user input parameters …

The survey is devoted to numerical solution of the equation A α u= f, 0< α< 1, where A is a
symmetric positive definite operator corresponding to a second order elliptic boundary value …

INTRODUCTION Financial markets may collapse, rainforest can shift to savanna, a person
can become trapped in a depression, and the Gulf Stream can come to a standstill. Such …