45 citations · 187 across the 9 of their papers we have counts for
9 papers
The Theory of Functional Connections: A journey from theory to application
Hunter Johnston
The Theory of Functional Connections (TFC) is a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The functionals derived…
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…
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…
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…
Fuel-Efficient Powered Descent Guidance on Large Planetary Bodies via Theory of Functional Connections
Hunter Johnston, Enrico Schiassi, Roberto Furfaro +1
In this paper we present a new approach to solve the fuel-efficient powered descent guidance problem on large planetary bodies with no atmosphere (e.g. the Moon or Mars) using the…
Least-squares solutions of boundary-value problems in hybrid systems
Hunter Johnston, Daniele Mortari
This paper looks to apply the mathematical framework of the Theory of Functional Connections to the solution of boundary-value problems arising from hybrid systems. The Theory of F…
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…