Article
Automation & Control Systems
Mathieu Bajodek, Frederic Gouaisbaut, Alexandre Seuret
Summary: Recently, the necessary conditions of stability for time-delay systems based on the handling of the Lyapunov-Krasovskii functional have been studied. This article proposes an extension of the existing results, where the uniform discretization of the state has been replaced by projections on the first Legendre polynomials. The improved method allows for a significantly reduced order to ensure stability and provides an analytical expression for the matrix size and convergence rate.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2023)
Article
Automation & Control Systems
Alexey Aliseyko
Summary: In this article, we study general linear systems with right-hand sides represented by the Riemann-Stieltjes integral using matrix functions of bounded variation. We establish minimal requirements on the convergence of the kernels to ensure the convergence of Lyapunov matrices for the perturbed systems. By employing functional analytic approach, we analyze the continuity of the dependence of Lyapunov matrices on the right-hand sides. The results obtained improve upon previous findings for multiple delay systems and distributed delay systems, without assuming exponential stability.
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
(2022)
Article
Automation & Control Systems
M. Vidyasagar
Summary: This paper studies the almost sure boundedness and convergence of the stochastic approximation (SA) algorithm. Most existing convergence proofs are based on the ODE method, and the almost sure boundedness of the iterations is an assumption rather than a conclusion. The objective of this paper is to provide an alternate proof based on martingale methods, which are simpler and less technical. Through examples, it is shown that our theory covers situations not covered by currently known results, specifically Borkar and Meyn (2000).
MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS
(2023)
Article
Geosciences, Multidisciplinary
Tongya Liu, Ryan Abernathey
Summary: In this study, a global Lagrangian eddy dataset GLED v1.0 is presented using the Lagrangian-averaged vorticity deviation (LAVD) method. The dataset includes general features of eddies and particle trajectories trapped by coherent eddies. The statistical features of Lagrangian eddies are compared with those of the widely used sea surface height (SSH) eddies.
EARTH SYSTEM SCIENCE DATA
(2023)
Review
Chemistry, Multidisciplinary
Benjamin W. J. Chen, Lang Xu, Manos Mavrikakis
Summary: Computational heterogeneous catalysis shows great promise for designing and discovering novel catalysts, with recent advances in electronic structure methods, atomistic catalyst models, and microkinetic modeling bridging the gap between nanoscale insights and macroscale experimental data. Remaining challenges include improving model accuracy and addressing discrepancies between experimental and computational results.
Review
Chemistry, Physical
Nicola Marzari, Andrea Ferretti, Chris Wolverton
Summary: Simulations, using electronic-structure methods such as density functional theory, have driven a new paradigm in research by accelerating the identification, characterization, and optimization of materials. The accuracy and efficiency of these methods rely on the predictive accuracy of underlying physical descriptions and the ability to capture system complexity. Continuous progress in theory, algorithms, and hardware, along with the adaptation of tools from computer science, play a key role in advancing materials science.
Article
Computer Science, Artificial Intelligence
Usman Qamar, Muhammad Summair Raza
Summary: This article introduces a computationally efficient dominance-based rough set approach that updates the approximations based on the preference order, reducing computation time and memory consumption while producing the same results as the conventional approach.
APPLIED SOFT COMPUTING
(2023)
Article
Mechanics
Yangwei Liu, Weibo Zhong, Yumeng Tang
Summary: The paper establishes theoretical relationships between Q series vortex criteria, eigenvalue-based vortex criteria, and the Rortex method based on LT criterion, and visually analyzes their physical meanings and interrelations on the LT-plane. The LTcri-based method effectively reflects local swirling patterns, provides new interpretations of vortex criteria, and shows potential in analyzing vortex dynamics and distinguishing swirling patterns of complex vortices.
Article
Computer Science, Artificial Intelligence
Liu Liu, Ji Liu, Dacheng Tao
Summary: This paper explores the optimization problem of non-convex composition with a large number of component functions, which is important in applications such as nonlinear embedding and reinforcement learning. The authors propose the stochastic composition via variance reduction (SCVR) method to improve the query complexity of existing approaches. They also analyze the query complexity under different numbers of inner and outer functions, and present the SCVRII algorithm for different estimation methods of inner functions. Additionally, an extension is proposed to handle mini-batch cases.
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
(2022)
Article
Automation & Control Systems
Haishan Ye, Luo Luo, Zhihua Zhang
Summary: The paper proposes a unified framework to analyze the local and global convergence properties of second order methods, bridging the gap between current convergence theory and empirical performance in real applications.
JOURNAL OF MACHINE LEARNING RESEARCH
(2021)
Article
Materials Science, Multidisciplinary
Zhi-Feng Zhang, Qing-Rui Wang, Peng Ye
Summary: This article studies the fusion and shrinking rules of loops in three dimensions through field theory, and finds that the fusion may have non-Abelian properties.
Article
Computer Science, Artificial Intelligence
Fahimeh Baghbani, Mohammad Reza Akbarzadeh Totonchi
Summary: This paper proposes a modified thalamic connection method based on a radial basis emotional network (RBEN-ATC) to address the challenges in theoretical and cognitive aspects of emotional controllers. The RBEN-ATC mapping has the universal function approximation property and can handle network weights continuously and differentiably. The resulting control system follows the fundamental laws of the emotional brain and is interpretable from a biological perspective. It achieves stable adaptive control of nonlinear systems by incorporating compensators for nonsymmetric actuator saturation and uncertainties.
NEURAL COMPUTING & APPLICATIONS
(2023)
Article
Computer Science, Artificial Intelligence
Shu Li, Liang Ding, Miao Zheng, Zixuan Liu, Xinyu Li, Huaiguang Yang, Haibo Gao, Zongquan Deng
Summary: Based on actor-critic neural networks, an optimal controller is proposed for solving the constrained control problem of an affine nonlinear discrete-time system with disturbances. The relationship between the optimal control input and worst-case disturbance is obtained using Game theory. Lyapunov stability theory ensures that the control signals are uniformly ultimately bounded. The effectiveness of the control algorithms is tested through a numeral simulation using a third-order dynamic system.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2023)
Article
Mathematics, Applied
Daniel Potts, Michael Schmischke
Summary: The proposed method utilizes multivariate ANOVA decomposition to approximate high-dimensional periodic functions, showing advantages in achieving importance ranking on dimensions and dimension interactions in scattered data or black-box approximation scenarios.
SIAM JOURNAL ON NUMERICAL ANALYSIS
(2021)
Article
Biochemistry & Molecular Biology
Divya Srivastava, Jouni Ahopelto, Antti J. Karttunen
Summary: The phonon properties and thermodynamics of four crystalline cellulose allomorphs have been investigated using dispersion-corrected density functional theory. The results show that the free energy differences between the cellulose allomorphs are small and the specific heat behavior is similar within the studied temperature range.
Article
Mathematics, Applied
Steven L. Brunton, Marko Budisic, Eurika Kaiser, J. Nathan Kutz
Summary: The field of dynamical systems is undergoing a transformation due to the emergence of mathematical tools and algorithms from modern computing and data science. Data-driven approaches that use operator-theoretic or probabilistic frameworks are replacing first-principles derivations and asymptotic reductions. The Koopman spectral theory, which represents nonlinear dynamics using an infinite-dimensional linear operator, has the potential to enable the prediction, estimation, and control of nonlinear systems with standard textbook methods developed for linear systems. However, a challenge remains in obtaining finite-dimensional coordinate systems and embeddings that approximately linearize the dynamics. The success of Koopman analysis is attributed to its rigorous theoretical connections, measurement-based approach suitable for leveraging big data and machine learning techniques, and the development of simple yet powerful numerical algorithms.
Article
Multidisciplinary Sciences
Jared L. Callaham, Georgios Rigas, Jean-Christophe Loiseau, Steven L. Brunton
Summary: Improved turbulence modeling remains a major open problem in mathematical physics due to the multiscale nature of turbulence. This study presents a data-driven modeling approach to approximate turbulent fluctuations by learning nonlinear models of coherent structures. Experimental results on a high-Reynolds number turbulent wake validate the effectiveness of the proposed approach in reproducing empirical power spectra and probability distributions. The interpretable model also provides insights into the physical mechanisms underlying the symmetry-breaking behavior in the wake. This work suggests a potential path to low-dimensional models of globally unstable turbulent flows from experimental measurements, with broad implications for other multiscale systems.
Article
Multidisciplinary Sciences
Yuying Liu, J. Nathan Kutz, Steven L. Brunton
Summary: Nonlinear differential equations are difficult to solve analytically, so numerical methods are needed. This work introduces a deep neural network time-stepping approach that approximates the dynamics of the system over various timescales. The method is data-driven, accurate, and efficient, and can be combined with classical numerical methods.
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2022)
Article
Engineering, Aerospace
Michelle K. Hickner, Urban Fasel, Aditya G. Nair, Bingni W. Brunton, Steven L. Brunton
Summary: This study extends the classical unsteady aerodynamic models to include the deformation of a flexible wing, and develops low-order linear models based on data from direct numerical simulations. Model predictive control is used to track maneuvers and limit wing deformation, providing an interpretable and accurate representation of the aeroelastic system for applications where transients are important.
Article
Physics, Fluids & Plasmas
J. D. Lore, S. De Pascuale, P. Laiu, B. Russo, J. -S. Park, J. M. Park, S. L. Brunton, J. N. Kutz, A. A. Kaptanoglu
Summary: Time-dependent SOLPS-ITER simulations were used to identify reduced models using the SINDy method and develop model-predictive control of the boundary plasma state. The identified reduced models show good predictive accuracy and can be applied to other time-dependent data from boundary simulations or experimental data.
Article
Physics, Fluids & Plasmas
Alan A. Kaptanoglu, Christopher Hansen, Jeremy D. Lore, Matt Landreman, Steven L. Brunton
Summary: Many scientific problems can be solved by sparse regression, which finds parsimonious and interpretable solutions by exploring high-dimensional spaces and assuming that some parameters are zero or negligible. This technique has been widely used in signal and image processing, system identification, optimization, and parameter estimation methods like Gaussian process regression. In this paper, the authors illustrate the importance of sparse regression in plasma physics and discuss recent contributions and challenges in solving related problems, especially in constrained and high-dimensional scenarios.
PHYSICS OF PLASMAS
(2023)
Article
Multidisciplinary Sciences
Peter J. J. Baddoo, Benjamin Herrmann, BeverleyJ. J. McKeon, J. Nathan Kutz, Steven L. L. Brunton
Summary: In this work, the integration of physical principles into the dynamic mode decomposition (DMD) is demonstrated. A physics-informed DMD (piDMD) optimization is proposed to restrict the models to a matrix manifold that respects the physical structure of the system. Several closed-form solutions and efficient algorithms for the corresponding piDMD optimizations are derived based on fundamental physical principles. The piDMD models outperform standard DMD algorithms in various applications, showing advantages in spectral identification, state prediction, and estimation.
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2023)
Article
Mechanics
Jared L. Callaham, Jean-Christophe Loiseau, Steven L. Brunton
Summary: In this study, we introduce a projection-based model reduction method that takes into account the nonlinear interactions between the resolved and unresolved scales of the flow in a low-dimensional dynamical systems model. The method uses a separation of time scales and a perturbation series approximation to derive a reduced-order model with closure terms, which improves the stability and accuracy of the flow models.
JOURNAL OF FLUID MECHANICS
(2023)
Article
Multidisciplinary Sciences
Joseph Bakarji, Kathleen Champion, J. Nathan Kutz, Steven L. Brunton
Summary: A central challenge in data-driven model discovery is the presence of hidden, or latent, variables that are not directly measured but are dynamically important. We designed a deep autoencoder network to learn a coordinate transformation from the delay embedded space into a new space, where it is possible to represent the dynamics in a sparse, closed form. This framework combines deep learning and the sparse identification of nonlinear dynamics methods to uncover interpretable models within effective coordinates.
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2023)
Article
Computer Science, Information Systems
Kartik Krishna, Steven L. Brunton, Zhuoyuan Song
Summary: Finite-time Lyapunov exponents (FTLEs) can be used to compute time-varying analogs of invariant manifolds in unsteady fluid flow fields, providing insight into optimal transport routes and effective deployment locations for controlled agents.
Article
Computer Science, Interdisciplinary Applications
Ricardo Vinuesa, Steven L. L. Brunton
Summary: The renewed interest in machine learning has opened up new research opportunities in computational fluid dynamics. The synergies between machine learning and CFD have already proven beneficial, and there are other areas still under development that may have significant impact in the future. It is important to approach these emerging approaches with cautious optimism.
COMPUTING IN SCIENCE & ENGINEERING
(2022)
Article
Computer Science, Interdisciplinary Applications
Ricardo Vinuesa, Steven L. Brunton
Summary: Machine learning is rapidly integrating into scientific computing, offering significant opportunities for advancing computational fluid dynamics. Key areas of impact include accelerating numerical simulations, enhancing turbulence modeling, and developing simplified models, while potential limitations should also be taken into consideration.
NATURE COMPUTATIONAL SCIENCE
(2022)
Article
Quantum Science & Technology
Andy J. Goldschmidt, Jonathan L. DuBois, Steven L. Brunton, J. Nathan Kutz
Summary: Model predictive control (MPC) is introduced in this work as a method for quantum control applications. It is shown that MPC can successfully realize model-based control even when the model is inadequate, making it an important addition to quantum engineering control suite.
Article
Computer Science, Information Systems
Emma Hansen, Steven L. Brunton, Zhuoyuan Song
Summary: This study applies a purely data-driven method to learn and generate similar swarming behavior by observing data of homogeneous swarms. The developed swarmDMD method successfully reconstructs swarm dynamics and provides a short prediction window for data extrapolation with a trade-off between prediction accuracy and horizon.
Article
Computer Science, Artificial Intelligence
Kadierdan Kaheman, Steven L. Brunton, J. Nathan Kutz
Summary: The Sparse Identification of Nonlinear Dynamics (SINDy) is a regression framework used for discovering dynamic models and equations from time-series data. This study presents an improved SINDy algorithm that combines automatic differentiation and constraint techniques to denoise the data, learn the noise probability distribution, and identify the underlying dynamic system. The algorithm achieves higher accuracy and robustness in handling noise compared to existing methods.
MACHINE LEARNING-SCIENCE AND TECHNOLOGY
(2022)
