88 citations · 233 across the 14 of their papers we have counts for
14 papers
The Theory of Functional Connections on Vector Spaces
Carl Leake
The Theory of Functional Connections (TFC) is most often used for constraints over the field of real numbers. However, previous works have shown that it actually extends to arbitra…
The Multivariate Theory of Functional Connections: An n-Dimensional Constraint Embedding Technique Applied to Partial Differential Equations
Carl Leake
The Theory of Functional Connections (TFC) is a functional interpolation framework founded upon the so-called constrained expression: a functional that expresses the family of all…
Fast 2-impulse non-Keplerian orbit-transfer using the Theory of Functional Connections
Allan K. de Almeida Junior, Hunter Johnston, Carl Leake +1
This study applies a new approach, the Theory of Functional Connections (TFC), to solve the two-point boundary-value problem (TPBVP) in non-Keplerian orbit transfer. The perturbati…
Motivations and Preliminary Design for Mid-Air Deployment of a Science Rotorcraft on Mars
Jeff Delaune, Jacob Izraelevitz, Larry A. Young +18
Mid-Air Deployment (MAD) of a rotorcraft during Entry, Descent and Landing (EDL) on Mars eliminates the need to carry a propulsion or airbag landing system. This reduces the total…
The Multivariate Theory of Functional Connections: Theory, Proofs, and Application in Partial Differential Equations
Carl Leake, Hunter Johnston, Daniele Mortari
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear cons…
Extreme Theory of Functional Connections: A Physics-Informed Neural Network Method for Solving Parametric Differential Equations
Enrico Schiassi, Carl Leake, Mario De Florio +3
In this work we present a novel, accurate, and robust physics-informed method for solving problems involving parametric differential equations (DEs) called the Extreme Theory of Fu…