Article
Mechanics
Heiko Pleskun, Tobias Bode, Andreas Bruemmer
Summary: The mass flow rate of Couette flow in a long rectangular channel is calculated for various gas rarefaction levels and width-to-height ratios. Analytical solutions are derived for different width-to-height ratios in the hydrodynamic, slip, and free molecular regimes. Simulations using the direct simulation Monte Carlo method are performed in the transitional regime. The results, presented as tabulated data, can be applied to cases with constant or linear increasing wall velocity.
Article
Mechanics
Yong Shi
Summary: This article presents a novel approach for simulating low-speed gas flows at the micro- and nanoscale with high accuracy by proposing different integration methods and analyzing the numerical evaluation of involved functions.
Article
Mechanics
Yong Shi
Summary: This article verifies the poor accuracy of the linearized lattice Boltzmann (LB) models based on half-range Gauss-Hermite quadrature in simulating noncontinuum bounded gas flows at large Knudsen numbers. By analyzing the numerical evaluation of the involved Abramowitz functions, a different thought on velocity discretization using Gauss-Legendre quadrature is proposed. The resulting LB models, based on GL quadrature, achieve high accuracy in simulating micro- and nanoscale low-speed gas flows with strong noncontinuum effects.
Article
Mechanics
W. Liu, Y. Y. Liu, L. M. Yang, Z. J. Liu, Z. Y. Yuan, C. Shu, C. J. Teo
Summary: In this paper, a simple hybrid strategy is proposed to couple the improved discrete velocity method (IDVM) and the G13-based gas kinetic flux solver (G13-GKFS) in the process of flux reconstruction for rarefied flow. By dividing the flow field into different areas and eliminating the storage of distribution functions, computational effort and memory storage can be reduced without sacrificing accuracy. Testing on different non-equilibrium cases shows good performance and higher efficiency under this hybrid method.
Article
Computer Science, Interdisciplinary Applications
Qin Lou, Xuhui Meng, George Em Karniadakis
Summary: In this study, physics-informed neural networks (PINNs) are utilized to solve forward and inverse problems via the Boltzmann-BGK formulation, enabling simulations of both continuous and rarefied flows. The PINN-BGK model, consisting of three sub-networks, successfully approximates various benchmark flows and infers flow fields in the entire computational domain through minimizing residuals and mismatches. Results show that PINN-BGK can accurately infer velocity fields in the entire domain and transfer learning can accelerate the training process significantly.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Engineering, Multidisciplinary
Shashank Jaiswal
Summary: This work introduces isogeometric kinetic schemes for modeling flows in topologically complex multi-patch geometries, aiming for high order accuracy, non-linear stability, and nearly-linear parallel efficiency due to the six-dimensional nature of the Boltzmann equation. These schemes perform well when surface properties need to be computed in aerodynamic applications.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Mechanics
Linying Zhang, Wenjun Ma, Qin Lou, Jun Zhang
Summary: In this study, a new surrogate model (PINN-DVM) is developed to simulate rarefied gas flows by combining physics-informed neural networks (PINNs) with the discrete velocity method (DVM). The linearized Bhatnagar-Gross-Krook equation is directly encoded into the residual of an artificial neural network in the PINN-DVM model. A new loss function for the boundary condition, based on the impermeable diffusion model, accurately captures the velocity slip and temperature jump at the boundary. PINN-DVM overcomes the limitations of conventional numerical methods and exhibits superiority compared to original PINNs in solving rarefied gas flows, as demonstrated by four representative numerical cases.
Article
Mechanics
Mario De Florio, Enrico Schiassi, Barry D. Ganapol, Roberto Furfaro
Summary: This study accurately solves a thermal creep flow problem in a plane channel using Physics-Informed Neural Networks. By developing a specific framework that utilizes Constrained Expressions based on the Theory of Functional Connections, the study demonstrates that accurate solutions can be achieved with fast training times using shallow neural networks, such as Chebyshev NN and Legendre NN. The results show that the approach is effective in matching benchmarks and providing accurate solutions.
Article
Computer Science, Interdisciplinary Applications
M. Hossein Gorji, Manuel Torrilhon
Summary: The diffusion limit of kinetic systems has garnered significant attention, particularly from the perspective of rarefied gas simulations. Fokker-Planck based kinetic models offer novel approximations of the Boltzmann equation, suitable for small/vanishing Knudsen numbers.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Physics, Multidisciplinary
Neeraj Sarna, Georgii Oblapenko, Manuel Torrilhon
Summary: This passage discusses the study on solving the Boltzmann equation of chemically reacting rarefied gas flows using the Grad's-14 moment method. It introduces a novel mathematical model for describing collision dynamics, an algorithm for computing moments of the collision operator, and derivation of reaction rates for chemical reactions outside of equilibrium. The importance of considering a fourteen moment system over a thirteen one is highlighted, along with numerical experiments studying the relaxation of the Grad's-14 moment system to equilibrium.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2021)
Article
Computer Science, Artificial Intelligence
Xu Liu, Wen Yao, Wei Peng, Weien Zhou
Summary: In this paper, a novel Bayesian physics-informed extreme learning machine (BPIELM) is proposed to solve forward and inverse linear partial differential equation (PDE) problems with noisy data. BPIELM not only quantifies uncertainty arising from noisy data and provides more accurate predictions, but also has a considerably lower computational cost compared to PINN.
Article
Computer Science, Interdisciplinary Applications
G. Oblapenko, D. Goldstein, P. Varghese, C. Moore
Summary: This paper proposes a new scheme for simulating collisions with multiple possible outcomes in variable-weight DSMC computations. The scheme is applied to the computation of 0-D ionization rate coefficients and 1-D electrical breakdown simulation. The results show a significant improvement in stochastic noise level compared to the usual acceptance-rejection algorithm, even with slight additional computational costs. The benefits and performance of the scheme are analyzed in detail, and possible extensions are suggested.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Physics, Mathematical
Thierry Bodineau, Isabelle Gallagher, Laure Saint-Raymond, Sergio Simonella
Summary: In this paper, an alternative approach is introduced to study the hard sphere dynamics in the low density limit by directly applying cluster expansion to the real trajectories of the particle system. This method allows us to reproduce previous results and describe the actual clustering of particle trajectories.
JOURNAL OF MATHEMATICAL PHYSICS
(2022)
Article
Computer Science, Artificial Intelligence
Enrico Schiassi, Roberto Furfaro, Carl Leake, Mario De Florio, Hunter Johnston, Daniele Mortari
Summary: X-TFC is a physics-informed neural network method that combines the Theory of Functional Connections and Neural Networks to solve differential equation problems accurately and quickly. It achieves high accuracy with low computational time, even for large scale problems, by using a single-layer neural network trained via the Extreme Learning Machine algorithm.
Article
Physics, Mathematical
Zhicheng Hu, Guanghan Li
Summary: In this study, a nonlinear multigrid solver is proposed to efficiently simulate steady state for multi-dimensional rarefied gas flow. The solver shows excellent efficiency and robustness through numerical experiments.
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
(2023)
Article
Engineering, Aerospace
Enrico Schiassi, Andrea D'Ambrosio, Kristofer Drozd, Fabio Curti, Roberto Furfaro
Summary: This paper presents a novel framework that combines the indirect method and Physics-Informed Neural Networks (PINNs) to learn optimal control actions for a series of optimal planar orbit transfer problems. The framework utilizes the indirect method to retrieve the optimal control by applying the Pontryagin minimum principle, and PINNs are used to model a neural network representation of the state-costate pair while satisfying the physics constraints of the problem.
JOURNAL OF SPACECRAFT AND ROCKETS
(2022)
Article
Engineering, Aerospace
Tanner Campbell, Roberto Furfaro, Vishnu Reddy, Adam Battle, Peter Birtwhistle, Tyler Linder, Scott Tucker, Neil Pearson
Summary: This study estimates the spin state and reflective properties of Near Earth Object (NEO) 2020 SO, confirming it as a Centaur rocket booster from the mid 1960's. The research reveals that 2020 SO rotates much faster than any known asteroid and the method used in this study can be applied to other NEOs as well.
JOURNAL OF THE ASTRONAUTICAL SCIENCES
(2022)
Article
Engineering, Aerospace
Andrea D'Ambrosio, Enrico Schiassi, Hunter Johnston, Fabio Curti, Daniele Mortari, Roberto Furfaro
Summary: In this paper, a unified approach is proposed to solve the time-energy optimal landing problem on planetary bodies. The indirect optimization method based on the derivation of the first order necessary conditions from the Hamiltonian is used, and the Two-Point Boundary Value Problem arising from the application of the Pontryagin Minimum Principle is solved using the Theory of Functional Connections. The proposed method accurately computes the optimal landing trajectories in a short computational time, making it suitable for real-time applications.
ADVANCES IN SPACE RESEARCH
(2022)
Article
Nuclear Science & Technology
Laura Laghi, Enrico Schiassi, Mario De Florio, Roberto Furfaro, Domiziano Mostacci
Summary: This study aims to address six problems using four different physics-informed machine learning frameworks and compare their results in terms of accuracy and computational cost. The diffusion-advection-reaction equations, which are second-order linear differential equations with two boundary conditions, are considered. The Classic Physics-Informed Neural Networks, Physics-Informed Extreme Learning Machine, Deep Theory of Functional Connections, and Extreme Theory of Functional Connections (X-TFC) algorithms were used. The results indicate that ELM-based frameworks, particularly X-TFC, outperform deep neural networks in terms of accuracy and computational time for these types of problems.
NUCLEAR SCIENCE AND ENGINEERING
(2023)
Article
Astronomy & Astrophysics
Bryn Bowen, Vishnu Reddy, Mario De Florio, Theodore Kareta, Neil Pearson, Roberto Furfaro, Benjamin Sharkey, Allison McGraw, David Cantillo, Juan A. Sanchez, Adam Battle
Summary: Remote spectral characterization of near-Earth asteroids relies on laboratory spectral calibration to understand their surface composition. A study was conducted on meteorites to examine the effects of grain size on spectral properties and its impact on ground-based characterization of asteroids. The results show that grain size affects the spectral parameters of ordinary chondrites, but has less impact on HED meteorites.
PLANETARY SCIENCE JOURNAL
(2023)
Correction
Nuclear Science & Technology
Enrico Schiassi, Mario De Florio, Barry D. Ganapol, Paolo Picca, Roberto Furfaro
ANNALS OF NUCLEAR ENERGY
(2023)
Article
Engineering, Aerospace
Lorenzo Federici, Andrea Scorsoglio, Alessandro Zavoli, Roberto Furfaro
Summary: This paper investigates the use of reinforcement learning for fuel-optimal guidance of a spacecraft during a time-free low-thrust transfer. A deep neural network is trained to map spacecraft state to optimal control action using proximal policy optimization. The study compares the learned control policies with optimal solutions provided by a direct method and evaluates their robustness through Monte Carlo simulations.
JOURNAL OF SPACECRAFT AND ROCKETS
(2023)
Article
Chemistry, Analytical
Luca Ghilardi, Roberto Furfaro
Summary: Hazard detection is crucial for safe lunar landing, and the current advanced method relies on 2D image and 3D Lidar systems for autonomous detection. However, vision-based methods face challenges in the lunar south pole due to shadow covering terrain features. This study proposes a method using a deep learning architecture called ViT model to extract terrain feature information from low-light RGB images, which outperforms the popular convolutional neural network UNet in high-altitude scenarios.
Article
Mathematics
Kristofer Drozd, Roberto Furfaro, Enrico Schiassi, Andrea D'Ambrosio
Summary: In this manuscript, we explore how to compute the solution of the matrix differential Riccati equation (MDRE) using the Extreme Theory of Functional Connections (X-TFC). Two approaches for solving the MDRE with X-TFC are utilized: direct and indirect implementation. Both approaches are validated by solving a fluid catalytic reactor problem and comparing the results with several state-of-the-art methods. Our work demonstrates that the first approach should be performed for a highly accurate solution, while the second approach should be used for quicker computation time.
Article
Astronomy & Astrophysics
David C. Cantillo, Vishnu Reddy, Adam Battle, Benjamin N. L. Sharkey, Neil C. Pearson, Tanner Campbell, Akash Satpathy, Mario De Florio, Roberto Furfaro, Juan Sanchez
Summary: Carbonaceous chondrites play a crucial role in understanding the origin and evolution of our solar system, but the linkages between asteroids and meteorites remain uncertain. This study obtained reflectance spectra of seven carbonaceous chondrite meteorite groups to investigate the effects of grain size on spectral properties. The results show correlations between grain size and reflectance, spectral slope, band depth, and band center, indicating the influence of grain size on interpreting asteroid surfaces and classifications.
PLANETARY SCIENCE JOURNAL
(2023)
Article
Engineering, Aerospace
Andrea Scorsoglio, Luca Ghilardi, Roberto Furfaro
Summary: This paper presents a method called Physics Informed Orbit Determination for solving orbit determination problems. It utilizes a type of neural network called Extreme Learning Machines with random input weights and biases to estimate the state of the spacecraft. The method incorporates a regularizing term based on the differential equations modeling the dynamics of the problem, ensuring that the learned relationship between input and output is consistent with the physics of the problem. It is tested on synthetic data with and without perturbations and achieves comparable results to the batch least-squares solution.
JOURNAL OF THE ASTRONAUTICAL SCIENCES
(2023)
Article
Mathematics, Applied
Mario De Florio, Enrico Schiassi, Francesco Calabro, Roberto Furfaro
Summary: This work compares four different methods based on Physics-Informed Neural Networks (PINNs) for solving Differential Equations (DE): Classic-PINN, Deep-TFC, PIELM, and X-TFC. They are compared by solving the boundary value problem arising from the 1D Steady-State Advection-Diffusion Equation for different diffusion coefficient values. X-TFC outperforms the other three methods in solving challenging problems affected by discontinuity.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
