Extreme theory of functional connections: A fast physics-informed neural network method for solving ordinary and partial differential equations
We present a novel, accurate, fast, and robust physics-informed neural network method for
solving problems involving differential equations (DEs), called Extreme Theory of Functional …
solving problems involving differential equations (DEs), called Extreme Theory of Functional …
A novel numerical approach for time-varying impulsive fractional differential equations using theory of functional connections and neural network
SM Sivalingam, V Govindaraj - Expert Systems with Applications, 2024 - Elsevier
In this paper, we propose a physics-informed neural network-based scheme to solve time-
varying impulsive fractional differential equations without any labeled data. At first, the …
varying impulsive fractional differential equations without any labeled data. At first, the …
Image-based deep reinforcement meta-learning for autonomous lunar landing
Future exploration and human missions on large planetary bodies (eg, moon, Mars) will
require advanced guidance navigation and control algorithms for the powered descent …
require advanced guidance navigation and control algorithms for the powered descent …
Physics-informed neural networks for the point kinetics equations for nuclear reactor dynamics
The paper presents a novel approach based on Physics-Informed Neural Networks (PINNs)
for the solution of Point Kinetics Equations (PKEs) with temperature feedback. The approach …
for the solution of Point Kinetics Equations (PKEs) with temperature feedback. The approach …
Physics-informed neural networks for rarefied-gas dynamics: Thermal creep flow in the Bhatnagar–Gross–Krook approximation
This work aims at accurately solve a thermal creep flow in a plane channel problem, as a
class of rarefied-gas dynamics problems, using Physics-Informed Neural Networks (PINNs) …
class of rarefied-gas dynamics problems, using Physics-Informed Neural Networks (PINNs) …
Physics-informed neural networks and functional interpolation for data-driven parameters discovery of epidemiological compartmental models
In this work, we apply a novel and accurate Physics-Informed Neural Network Theory of
Functional Connections (PINN-TFC) based framework, called Extreme Theory of Functional …
Functional Connections (PINN-TFC) based framework, called Extreme Theory of Functional …
Physics-informed neural networks for optimal planar orbit transfers
This paper presents a novel framework, combining the indirect method and Physics-
Informed Neural Networks (PINNs), to learn optimal control actions for a series of optimal …
Informed Neural Networks (PINNs), to learn optimal control actions for a series of optimal …
The multivariate theory of functional connections: Theory, proofs, and application in partial differential equations
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 …
methodology for functional interpolation that can embed a set of user-specified linear …
A novel method to approximate fractional differential equations based on the theory of functional connections
In this paper, we propose a new method of using the theory of functional connections (TFC)
to approximate the solution of fractional differential equations. For functions with one …
to approximate the solution of fractional differential equations. For functions with one …
Energy-optimal trajectory problems in relative motion solved via Theory of Functional Connections
In this paper, we present a new approach for solving a broad class of energy-optimal
trajectory problems in relative motion using the recently developed Theory of Functional …
trajectory problems in relative motion using the recently developed Theory of Functional …