88 citations · 382 across the 20 of their papers we have counts for
10 papers · 1 filter
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…
Bijective Mapping Analysis to Extend the Theory of Functional Connections to Non-rectangular 2-dimensional Domains
Daniele Mortari, David Anas
This work presents an initial analysis of using bijective mappings to extend the Theory of Functional Connections to non-rectangular two-dimensional domains. Specifically, this man…
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…
Nonlinear Function Inversion using k-vector
David Arnas, Daniele Mortari
This work introduces a general numerical technique to invert one dimensional analytic or tabulated nonlinear functions in assigned ranges of interest. The proposed approach is base…
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…
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…