Article
Mathematics, Interdisciplinary Applications
Alvaro H. Salas, Wedad Albalawi, M. R. Alharthi, S. A. El-Tantawy
Summary: This paper introduces novel analytical and numerical techniques for solving and analyzing nonlinear second-order ordinary differential equations. Two different analytical approximations and numerical approximations are presented and applied to real-life nonlinear oscillator equations. The accuracy of these approximations is evaluated through comparisons with the Runge-Kutta numerical approximation.
Article
Geochemistry & Geophysics
F. Zyserman, L. B. Monachesi, A. H. Thompson, T. D'Biassi, L. Jouniaux, P. Gauzellino
Summary: This work presents numerical modelling of electroseismic conversions with electric field sources in the atmosphere. It shows that layered structures of conductivity anomalies can generate rotated electric fields at reservoir depths. However, the high-power dipole sources limit the practical application of these methods in hydrocarbon exploration. The research explores the potential use of environmental electric fields to create useful electroseismic conversions.
GEOPHYSICAL JOURNAL INTERNATIONAL
(2022)
Article
Physics, Applied
Mohammad Partohaghighi, Tukur A. Sulaiman, Abdullahi Yusuf, Mustafa Inc, Mustafa Bayram
Summary: This study successfully constructs new topological kink-type, non-topological, singular solitons, periodic waves and singular periodic wave solutions to the nonlinear Klein-Gordon equation (KGE) using the extended ShGEEM, rational sine-cosine extended (ERSC), and sinh-cosh (ERSCh) methods. Additionally, a numerical method for solving the KGE is described, which utilizes the fictitious time integration method and the group preserving scheme (GPS). Experimental results demonstrate the correctness of the approach.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2023)
Article
Mathematics, Interdisciplinary Applications
Xiaoying Dai, Stefano De Gironcoli, Bin Yang, Aihui Zhou
Summary: This paper investigates the energy minimization model in ensemble Kohn-Sham density functional theory for metallic systems and proposes an algorithm to solve the problem. Numerical experiments show that the algorithm is efficient for large scale metallic systems and produces convergent numerical approximations.
MULTISCALE MODELING & SIMULATION
(2023)
Article
Mathematics, Applied
Stefano Maset
Summary: This study focuses on the relative error in the numerical integration of the long-time solution of a linear ordinary differential equation, showing that some A-stable approximants exhibit instability in the stiff situation with perturbations in the initial value of the long-time solution.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Ghazala Akram, Muhammad Abbas, Hira Tariq, Maasoomah Sadaf, Thabet Abdeljawad, Manar A. Alqudah
Summary: Developing mathematical models of fractional order and constructing numerical solutions for physical phenomena is important in mathematics, physics, and engineering. This paper presents a numerical solution for higher order fractional temporal evolution problems using the sextic polynomial spline technique. The accuracy and applicability of the proposed technique are demonstrated through numerical simulations.
FRACTAL AND FRACTIONAL
(2022)
Article
Computer Science, Interdisciplinary Applications
Fatemeh Mohammadizadeh, Saeede Rashidi, S. Reza Hejazi
Summary: This paper investigates the symmetry operators and conservation laws of the fractional Klein-Gordon equation, and extends the Chebyshev spectral collocation method to the space-time-fractional case to provide numerical results and conservation laws for the equation.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
Article
Acoustics
Xuhong Miao, Pei Jiang, Fuzhen Pang, Yang Tang, Haichao Li, Guanglei Qu, Jun Li
Summary: This paper establishes an electromagnetic-mechanical-acoustic coupled three-dimensional finite element method for oil-immersed transformers, and explores the influences of radiating grids and input voltage on their vibration and noise characteristics. The study proves the effectiveness of the calculation model and quantitatively analyzes the effects of different factors.
Article
Mathematics, Applied
Abdulghani R. Alharbi
Summary: This article presents new solutions for the Novikov-Veselov system using various methods, including soliton solutions of hyperbolic, rational, and trigonometric functions. The study examines magneto-sound and ion waves in plasma through partial differential equations, utilizing the Generalized Algebraic and Modified F-expansion methods. Numerical simulations are conducted using the finite difference method, and the stability and error analysis of the numerical schemes are discussed. Comparison between exact and numerical solutions is made to validate the accuracy of the methods proposed in this paper.
Article
Materials Science, Multidisciplinary
Beenish Khan, Muhammad Abbas, Ahmed S. M. Alzaidi, Farah Aini Abdullah, Muhammad Bilal Riaz
Summary: In this study, a new approximation method using B-spline functions is proposed to approximate the numerical solution of the time fractional advection diffusion equation. The finite difference scheme is used to discretize the time fractional derivative, and the stability and convergence of the proposed method are analyzed to ensure its feasibility and accuracy.
RESULTS IN PHYSICS
(2022)
Article
Engineering, Electrical & Electronic
Orell Garten, Christoph Statz, Steffen Gerling, Jochen Jebramcik, Jan Barowski, Dirk Plettemeier, Ilona Rolfes
Summary: This work addresses volume scattering effects using the physical optics approach, reducing modeling and computational effort for simulating scattering from complex materials. The results show a natural progression from classical PO to the proposed formulation. Four specializations of the algorithm highlight its versatility.
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION
(2021)
Review
Computer Science, Interdisciplinary Applications
Hefeng Chen, Tobias Gleim
Summary: This paper establishes different axisymmetric and two-dimensional models for a levitation device by combining the Maxwell equations with the balance of linear momentum. A high order finite element discretization using Galerkin's method in space and the generalized Newmark-alpha method in time are developed for the electro-magneto-mechanical approach. Several studies on spatial and temporal discretization with respect to convergence will be investigated, along with examining the boundary influences and the domain size with respect to the levitation device.
ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING
(2021)
Article
Mathematics, Applied
Farid Bozorgnia, Sonia Seyed Allaei
Summary: A numerical scheme based on modified method of characteristics with adjusted advection (MMOCAA) is proposed to approximate the solution of the system liquid chromatography with multi components case. Various examples and computational tests numerically verify the accuracy and efficiency of the approach.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics
Igor Mezic
Summary: This paper studies numerical methods for computing spectral properties of composition operators. It provides a characterization of Koopman Modes in Banach spaces using Generalized Laplace Analysis. The paper also applies Dynamic Mode Decomposition-type methods in the context of the Finite Section theory of infinite dimensional operators, and gives an example where the finite section method fails. Under assumptions on the underlying dynamics, the paper provides the first result on the convergence rate under sample size increase in the finite-section approximation. Moreover, it studies the error in the Krylov subspace version of the finite section method and proves convergence in pseudospectral sense for operators with pure point spectrum.
Article
Electrochemistry
Gabriele Pozzato, Aki Takahashi, Xueyan Li, Donghoon Lee, Johan Ko, Simona Onori
Summary: In this paper, a core-shell enhanced single particle model for iron-phosphate battery cells is formulated, implemented, and verified. The positive electrode intercalation and deintercalation phenomena and associated phase transitions are described with the core-shell modeling paradigm. The best setting for numerical solutions is determined through a sensitivity analysis.
JOURNAL OF THE ELECTROCHEMICAL SOCIETY
(2022)
Article
Computer Science, Artificial Intelligence
Lars Ruthotto, Eldad Haber
JOURNAL OF MATHEMATICAL IMAGING AND VISION
(2020)
Article
Multidisciplinary Sciences
Lars Ruthotto, Stanley J. Osher, Wuchen Li, Levon Nurbekyan, Samy Wu Fung
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2020)
Article
Engineering, Electrical & Electronic
Jonathan Ephrath, Moshe Eliasof, Lars Ruthotto, Eldad Haber, Eran Treister
IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING
(2020)
Article
Engineering, Multidisciplinary
Meenarli Sharma, Mirko Hahn, Sven Leyffer, Lars Ruthotto, Bart van Bloemen Waanders
Summary: This study introduces a convection-diffusion inverse problem that aims to identify an unknown number of sources and their locations. It is shown that the problem can be formulated as a large-scale mixed-integer nonlinear optimization problem, which current state-of-the-art solvers cannot solve. Two new rounding heuristics are developed to tackle the issue, along with a steepest-descent improvement heuristic to obtain satisfactory solutions for both two- and three-dimensional inverse problems. The code used in the numerical experiments is also provided in open-source format.
OPTIMIZATION AND ENGINEERING
(2021)
Editorial Material
Mathematics, Applied
M. Burger, W. E, L. Ruthotto, S. J. . Osher
EUROPEAN JOURNAL OF APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Kelvin Kan, Samy Wu Fung, Lars Ruthotto
Summary: PNKH-B is a projected Newton-Krylov method designed for solving large-scale optimization problems with bound constraints, particularly in scenarios where function and gradient evaluations are expensive and the (approximate) Hessian is only available through matrix-vector products. By utilizing a low-rank approximation of the Hessian to determine the search direction and construct the metric, PNKH-B achieves fast convergence, especially in the initial iterations.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2021)
Article
Mathematics, Applied
Elizabeth Newman, Julianne Chung, Matthias Chung, Lars Ruthotto
Summary: Deep neural networks (DNNs) have been successful in many applications but training them can be challenging due to nonconvexity, nonsmoothness, inadequate regularization, and complex data distributions. In this study, slimTrain is proposed to address the challenges by exploiting separability in DNN architectures, reducing sensitivity to hyperparameter choice and achieving fast initial convergence. Numerical experiments demonstrate the superior performance of slimTrain in function approximation tasks, outperforming existing DNN training methods.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2022)
Article
Automation & Control Systems
Derek Onken, Levon Nurbekyan, Xingjian Li, Samy Wu Fung, Stanley Osher, Lars Ruthotto
Summary: In this study, a neural network approach is proposed to solve high-dimensional optimal control problems using approximate solutions. The approach combines the Hamilton-Jacobi-Bellman and Pontryagin maximum principle methods and provides real-time control through feedback. The method is effective in multiagent path finding and offers advantages in terms of time efficiency and scalability in high dimensions. Offline training of the neural network enables fast generation of control policies.
IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY
(2023)
Article
Mathematics, Applied
Moshe Eliasof, Jonathan Ephrath, Lars Ruthotto, Eran Treister
Summary: In this paper, a multigrid-in-channels (MGIC) approach is presented to address the quadratic growth of parameters in standard convolutional neural networks (CNNs) with respect to the number of channels. The proposed approach replaces each CNN block with an MGIC counterpart that utilizes nested grouped convolutions to reduce the number of parameters while maintaining coupling of the channels. Experimental results demonstrate the effectiveness of the proposed approach in various architectures, achieving parameter reduction without sacrificing accuracy.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2023)
Proceedings Paper
Computer Science, Artificial Intelligence
Kelvin Kan, Youngsuk Park, Francois-Xavier Aubet, Konstantinos Benidis, Jan Gasthaus, Tim Januschowski, Lars Ruthotto
Summary: We propose a global probabilistic forecasting method called Multivariate Quantile Function Forecaster (MQF(2)) and investigate its application to multi-horizon forecasting. MQF(2) combines the benefits of autoregressive and multi-horizon sequence-to-sequence models, achieving accurate predictions while capturing the time dependency structure.
INTERNATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE AND STATISTICS, VOL 151
(2022)
Proceedings Paper
Automation & Control Systems
Derek Onken, Levon Nurbekyan, Xingjian Li, Samy Wu Fung, Stanley Osher, Lars Ruthotto
Summary: "The proposed neural network approach combines different control theories, parameterizes the value function with neural networks, efficiently solves multi-agent control problems, and maintains robustness to system disturbances during training. By training on a distribution of initial states, it ensures optimality of controls across a large portion of state-space."
2021 EUROPEAN CONTROL CONFERENCE (ECC)
(2021)
Article
Mathematics, Applied
Elizabeth Newman, Lars Ruthotto, Joseph Hart, Bart van Bloemen Waanders
Summary: Deep neural networks (DNNs) have achieved state-of-the-art performance across various machine learning tasks by effectively approximating high-dimensional functions. This paper focuses on supervised training of DNNs and proposes the Gauss-Newton VarPro method (GNvpro) for optimizing weights to accurately approximate the relation between input and target data. Through numerical experiments, GNvpro is shown to be more efficient than commonly used stochastic gradient descent (SGD) schemes, providing solutions with good generalization performance.
SIAM JOURNAL ON MATHEMATICS OF DATA SCIENCE
(2021)
Article
Mathematics, Applied
Samy Wu Fung, Sanna Tyrvainen, Lars Ruthotto, Eldad Haber
ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS
(2020)
Article
Engineering, Electrical & Electronic
James Lincoln Herring, James Nagy, Lars Ruthotto
IEEE TRANSACTIONS ON COMPUTATIONAL IMAGING
(2020)
Article
Mathematics, Applied
Stefanie Guenther, Lars Ruthotto, Jacob B. Schroder, Eric C. Cyr, Nicolas R. Gauger
SIAM JOURNAL ON MATHEMATICS OF DATA SCIENCE
(2020)