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…
Random Sampling using k-vector
David Arnas, Carl Leake, Daniele Mortari
This work introduces two new techniques for random number generation with any prescribed nonlinear distribution based on the k-vector methodology. The first approach is based on in…
The n-dimensional k-vector and its application to orthogonal range searching
David Arnas, Carl Leake, Daniele Mortari
This work focuses on the definition and study of the n-dimensional k-vector, an algorithm devised to perform orthogonal range searching in static databases with multiple dimensions…
Non-dimensional Star-Identification
Carl Leake, David Arnas, Daniele Mortari
This study introduces a new "Non-Dimensional" star identification algorithm to reliably identify the stars observed by a wide field-of-view star tracker when the focal length and o…
Recursive Star-Identification Algorithm using an Adaptive SVD-based Angular Velocity Estimator
Hunter Johnston, Carl Leake, Marcelino M. de Almeida +1
This paper describes an algorithm obtained by merging a recursive star identification algorithm with a recently developed adaptive SVD-based estimator of the angular velocity vecto…
Least-squares Solutions of Eighth-order Boundary Value Problems using the Theory of Functional Connections
Hunter Johnston, Carl Leake, Daniele Mortari
This paper shows how to obtain highly accurate solutions of eighth-order boundary-value problems of linear and nonlinear ordinary differential equations. The presented method is ba…
The Tensor Theory of Connections
Daniele Mortari, Carl Leake
This paper extends the univariate Theory of Connections, introduced in (Mortari,2017), to the multivariate case on rectangular domains with detailed attention to the bivariate case…
Deep Theory of Functional Connections: A New Method for Estimating the Solutions of PDEs
Carl Leake
This article presents a new methodology called deep Theory of Functional Connections (TFC) that estimates the solutions of partial differential equations (PDEs) by combining neural…
Analytically Embedding Differential Equation Constraints into Least Squares Support Vector Machines using the Theory of Functional Connections
Carl Leake, Hunter Johnston, Lidia Smith +1
Differential equations (DEs) are used as numerical models to describe physical phenomena throughout the field of engineering and science, including heat and fluid flow, structural…