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Data-Driven Mori-Zwanzig: Approaching a Reduced Order Model for Hypersonic Boundary Layer Transition

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arXiv 2023年

作者： Woodward, Michael Tian, Yifeng Mohan, Arvind Lin, Yen Ting Hader, Christoph Fasel, Hermann Chertkov, Misha Livescu, Daniel Graduate Interdisciplinary Program in Applied Mathematics Department of Mathematics University of Arizona TucsonAZ85721 United States Computer Computational and Statistical Sciences Division Los Alamos National Laboratory Los AlamosNM87544 United States Department of Aerospace and Mechanical Engineering University of Arizona TucsonAZ85721 United States

In this work, we apply, for the first time to spatially inhomogeneous flows, a recently developed data-driven learning algorithm of Mori-Zwanzig (MZ) operators, which is based on a generalized Koopman’s description of dynamical systems. The MZ formalism provides a mathematically exact procedure for constructing non-Markovian reduced-order models of resolved variables from high-dimensional dynamical systems, where the effects due to the unresolved dynamics are captured in the memory kernel and orthogonal dynamics. The algorithm developed in this work applies Mori’s linear projection operator and an SVD based compression to the selection of the resolved variables (equivalently, a low rank approximation of the two time covariance matrices). We show that this MZ decomposition not only identifies the same spatio-temporal structures found by DMD, but it can also be used to extract spatio-temporal structures of the hysteresis effects present in the memory kernels. We perform an analysis of these structures in the context of a laminar-turbulent boundary-layer transition flow over a flared cone at Mach 6, and show the dynamical relevance of the memory kernels. Additionally, by including these memory terms learned in our data-driven MZ approach, we show improvement in prediction accuracy over DMD at the same level of truncation and at a similar computational cost. Furthermore, an analysis of the spatio-temporal structures of the MZ operators shows identifiable structures associated with the nonlinear generation of the so-called "hot" streaks on the surface of the flared cone, which have previously been observed in experiments and direct numerical simulations. Copyright © 2023, The Authors. All rights reserved.

关键词： Dynamic mode decomposition

CONSTRUCTING AND COMPRESSING GLOBAL MOMENT DESCRIPTORS FROM LOCAL ATOMIC ENVIRONMENTS

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arXiv 2023年

作者： Gharakhanyan, Vahe Aalto, Max S. Alsoulah, Aminah Artrith, Nongnuch Urban, Alexander Department of Applied Physics and Applied Mathematics Columbia University New YorkNY United States Physics and Informatics Laboratories NTT Research Inc. SunnyvaleCA United States Department of Chemical Engineering Columbia University New YorkNY United States Debye Institute for Nanomaterials Science Utrecht University Utrecht Netherlands

Local atomic environment descriptors (LAEDs) are used in the materials science and chemistry communities, for example, for the development of machine learning interatomic potentials. Despite the fact that LAEDs have been extensively studied and benchmarked for various applications, global structure descriptors (GSDs), i.e., descriptors for entire molecules or crystal structures, have been mostly developed independently based on other approaches. Here, we propose a systematically improvable methodology for constructing a space of representations of GSDs from LAEDs by incorporating statistical information and information about chemical elements. We apply the method to construct GSDs of varying complexity for lithium thiophosphate structures that are of interest as solid electrolytes and use an information-theoretic approach to obtain an optimally compressed GSD. Finally, we report the performance of the compressed GSD for energy prediction tasks. Copyright © 2023, The Authors. All rights reserved.

关键词： Solid electrolytes

One Set to Rule Them All: How to Obtain General chemical Conditions via Bayesian Optimization over Curried Functions

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arXiv 2025年

作者： Schmid, Stefan P. Rajaonson, Ella Miray Ser, Cher Tian Haddadnia, Mohammad Leong, Shi Xuan Aspuru-Guzik, Alán Kristiadi, Agustinus Jorner, Kjell Strieth-Kalthoff, Felix Institute of Chemical and Bioengineering Department of Chemistry and Applied Biosciences ETH Zurich ZurichCH-8093 Switzerland Catalysis ETH Zurich ZurichCH-8093 Switzerland Department of Chemistry University of Toronto Toronto Canada Vector Institute Toronto Canada Department of Biological Chemistry & Molecular Pharmacology Harvard University CambridgeMA United States Dana-Farber Cancer Institute BostonMA United States School of Chemistry Chemical Engineering and Biotechnology Nanyang Technological University Singarpore Singapore Department of Computer Science University of Toronto Toronto Canada Department of Chemical Engineering and Applied Chemistry University of Toronto Toronto Canada Department of Materials Science and Engineering University of Toronto Toronto Canada Acceleration Consortium University of Toronto Toronto Canada Canada School of Mathematics and Natural Sciences University of Wuppertal Wuppertal Germany

General parameters are highly desirable in the natural sciences — e.g., chemical reaction conditions that enable high yields across a range of related transformations. This has a significant practical impact since those general parameters can be transferred to related tasks without the need for laborious and time-intensive re-optimization. While Bayesian optimization (BO) is widely applied to find optimal parameter sets for specific tasks, it has remained underused in experiment planning towards such general optima. In this work, we consider the real-world problem of condition optimization for chemical reactions to study how performing generality-oriented BO can accelerate the identification of general optima, and whether these optima also translate to unseen examples. This is achieved through a careful formulation of the problem as an optimization over curried functions, as well as systematic evaluations of generality-oriented strategies for optimization Copyright © 2025, The Authors. All rights reserved.

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chemical compounds in essential oil of nutmeg leaves (Myristica fragrans) from Batang Indonesia 10

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Chemical compounds in essential oil of nutmeg leaves (Myrist...

10th International Seminar on New Paradigm and Innovation of Natural Sciences and itsApplication, ISNPINSA 2020

作者： Kusumaningrum, H.P. Zainuri, M. Endrawati, H. Loka, B.D. Widiasa, I.N. Sulistyowati, E. Laboratory of Biotechnology Study Program of Biotechnology Faculty of Science and Mathematics Universitas Diponegoro Semarang Indonesia Laboratory of Oceanography Department of Oceanography Food Technology Department Faculty of Animal and Agricultural Sciences Diponegoro University Indonesia Chemical Engineering Department Faculty of Engineering Universitas Diponegoro Semarang Indonesia Architecture Department Faculty of Engineering Universitas Diponegoro Semarang Indonesia

Nutmeg oil has an important function as natural tropical biomedicine activity which commonly found in Batang region. This essential oil is one of the dominant traditional export product from Batang instead of patchouli oil, Clove oil, and lemongrass oil. The objective of the research was to analyze chemical compound of essential oil of nutmeg leaves from Batang region produced by traditional destillation. Research methods was conducted by GCMS method. The biomedical activity against some tropical diseases was analysed in-silico. The results showed that essential oil from nutmeg leaves showed potential antimicroabial activities in silico againts several tropical diseases in skin. The GCMS result showed 2-.BETA.-PINENE and .gamma.-Terpinene as the major compound with values 34,46% and 30,28%. © Published under licence by IOP Publishing Ltd.

关键词： Essential oils

BRAIN-TO-TEXT BENCHMARK’24: LESSONS LEARNED

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arXiv 2024年

作者： Willett, Francis R. Li, Jingyuan Le, Trung Fan, Chaofei Chen, Mingfei Shlizerman, Eli Chen, Yue Zheng, Xin Okubo, Tatsuo S. Benster, Tyler Lee, Hyun Dong Kounga, Maxwell Buchanan, E. Kelly Zoltowski, David Linderman, Scott W. Henderson, Jaimie M. Department of Neurosurgery Stanford University United States Department of Electrical & Computer Engineering University of Washington United States Department of Computer Science Stanford University United States Department of Applied Mathematics University of Washington United States China Neurosciences Phd Program Stanford University United States Wu Tsai Neurosciences Institute Department of Statistics Stanford University United States

Speech brain-computer interfaces aim to decipher what a person is trying to say from neural activity alone, restoring communication to people with paralysis who have lost the ability to speak intelligibly. The Brain-to-Text Benchmark’24 and associated competition was created to foster the advancement of decoding algorithms that convert neural activity to text. Here, we summarize the lessons learned from the competition ending on June 1, 2024 (the top 4 entrants also presented their experiences in a recorded webinar). The largest improvements in accuracy were achieved using an ensembling approach, where the output of multiple independent decoders was merged using a fine-tuned large language model (an approach used by all 3 top entrants). Performance gains were also found by improving how the baseline recurrent neural network (RNN) model was trained, including by optimizing learning rate scheduling and by using a diphone training objective. Improving upon the model architecture itself proved more difficult, however, with attempts to use deep state space models or transformers not yet appearing to offer a benefit over the RNN baseline. The benchmark will remain open indefinitely to support further work towards increasing the accuracy of brain-to-text algorithms. © 2024, CC BY.

关键词： Recurrent neural networks

Surfactant-laden bubble bursting: dynamics of capillary waves and Worthington jet at large Bond number

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arXiv 2024年

作者： Pico, Paula Kahouadji, Lyes Shin, Seungwon Chergui, Jalel Juric, Damir Matar, Omar K. Department of Chemical Engineering Imperial College London South Kensington Campus LondonSW7 2AZ United Kingdom Department of Mechanical and System Design Engineering Hongik University Seoul04066 Korea Republic of Orsay91400 France Department of Applied Mathematics and Theoretical Physics University of Cambridge CambridgeCB3 0WA United Kingdom

We present a numerical study of the main sub-stages preceding aerosol formation via bursting bubbles: capillary wave propagation along the bubble, convergence at the bubble’s apex, the ascent of a Worthington jet and its break-up to release liquid drops. We focus on two crucial yet overlooked aspects of the system: the presence of surface-active agents and dynamics driven by non-negligible gravitational effects, quantified by the Bond number. Our results propose, for the first time, a mechanism explaining capillary wave retardation in the presence of surfactants, involving the transition from bi- to uni-directional Marangoni stresses, which pull the interface upwards, countering the motion of the waves. We also quantitatively elucidate the variable nature of the waves’ velocity with various surfactant parameters, including surfactant solubility and elasticity, a departure from the constant behaviour well-documented in clean interfaces. Copyright © 2024, The Authors. All rights reserved.

关键词： Surface active agents

Questionnaires to PDEs: From Disorganized Data to Emergent Generative Dynamic Models

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arXiv 2022年

作者： Sroczynski, David W. Kemeth, Felix P. Coifman, Ronald R. Kevrekidis, Ioannis G. Department of Chemical and Biological Engineering Princeton University PrincetonNJ08544 United States Department of Chemical and Biomolecular Engineering Johns Hopkins University BaltimoreMD21218 United States Department of Mathematics Yale University New HavenCT06520 United States Department of Applied Mathematics and Statistics Johns Hopkins University BaltimoreMD21218 United States

Starting with sets of disorganized observations of spatially varying and temporally evolving systems, obtained at different (also disorganized) sets of parameters, we demonstrate the data-driven derivation of parameter dependent, evolutionary partial differential equation (PDE) models capable of generating the data. This tensor type of data is reminiscent of shuffled (multi-dimensional) puzzle tiles. The independent variables for the evolution equations (their "space" and "time") as well as their effective parameters are all "emergent", i.e., determined in a data-driven way from our disorganized observations of behavior in them. We use a diffusion map based "questionnaire" approach to build a parametrization of our emergent space/time/parameter space for the data. This approach iteratively processes the data by successively observing them on the "space", the "time" and the "parameter" axes of a tensor. Once the data are organized, we use machine learning (here, neural networks) to approximate the operators governing the evolution equations in this emergent space. Our illustrative example is based on a previously developed vertex-plus-signaling model of Drosophila embryonic development. This allows us to discuss features of the process like symmetry breaking, translational invariance, and autonomousness of the emergent PDE model, as well as its interpretability. © 2022, CC BY-NC-ND.

关键词： Tensors

Drop encapsulation and bubble bursting in surfactant-laden flows in capillary channels

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Physical Review Fluids 2024年第3期9卷 034001-034001页

作者： P. Pico L. Kahouadji S. Shin J. Chergui D. Juric O. K. Matar Department of Chemical Engineering Imperial College London South Kensington Campus London SW7 2AZ United Kingdom Department of Mechanical and System Design Engineering Hongik University Seoul 121-791 Republic of Korea Université Paris Saclay Centre National de la Recherche Scientifique (CNRS) Laboratoire Interdisciplinaire des Sciences du Numérique (LISN) 91400 Orsay France Department of Applied Mathematics and Theoretical Physics University of Cambridge Cambridge CB3 0WA United Kingdom

We present a parametric study of the unsteady phenomena associated with the flow of elongated gas bubbles traveling through liquid-filled square capillaries under high Weber number conditions. These conditions induce the formation of an indentation at the back of the bubble that commonly gives way to a deep reentrant liquid jet penetrating the bubble. Subsequent steps include pinch-off events in the penetrating liquid to generate one or multiple encapsulated drops which may coalesce, in conjunction with the bursting of the bubble-liquid interface by either the liquid jet or the drops. Some of these interfacial instabilities have previously been reported experimentally and numerically for liquid-liquid flow in microchannels. We carry out three-dimensional direct numerical simulations based on a hybrid interface-tracking/level-set method capable of accounting for the presence and dynamic exchange of surfactants between the liquid bulk phase and the liquid-gas interface. Our results indicate that the delicate interplay among inertia, capillarity, viscosity, surfactant adsorption/desorption kinetics, and Marangoni stresses has a dramatic influence over the nonaxisymmetric morphological structures of the encapsulated drops-elongated bubble. This strong coupling also influences the pinch-off time, penetration depth of the liquid, and number, size, and velocity of the encapsulated drops across the bubble. The observed phenomena are summarized in three main morphological regimes based on surfactant-related parameters and dimensionless groups. A discussion of the flow regime maps is also provided.

关键词： Drop & bubble phenomena Interfacial flows Multiphase flows Surface tension effects

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arXiv 2023年

作者： Jon Chapman, S. Kavousanakis, M. Charalampidis, E.G. Kevrekidis, I.G. Kevrekidis, P.G. Mathematical Institute University of Oxford AWB ROQ Woodstock Road OxfordOX2 6GG United Kingdom School of Chemical Engineering National Technical University of Athens Athens15780 Greece Mathematics Department California Polytechnic State University San Luis ObispoCA93407-0403 United States Department of Chemical and Biomolecular Engineering Department of Applied Mathematics and Statistics Johns Hopkins University BaltimoreMD21218 United States Department of Mathematics and Statistics University of Massachusetts AmherstMA1003-4515 United States

In the present work we revisit the problem of the generalized Korteweg-de Vries equation parametrically, as a function of the relevant nonlinearity exponent, to examine the emergence of blow-up solutions, as traveling waveforms lose their stability past a critical point of the relevant parameter p, here at p = 5. We provide a normal form of the associated collapse dynamics and illustrate how this captures the collapsing branch bifurcating from the unstable traveling branch. We also systematically characterize the linearization spectrum of not only the traveling states, but importantly of the emergent collapsing waveforms in the so-called co-exploding frame where these waveforms are identified as stationary states. This spectrum, in addition to two positive real eigenvalues which are shown to be associated with the symmetries of translation and scaling invariance of the original (non-exploding) frame features complex patterns of negative eigenvalues that we also fully characterize. We show that the phenomenology of the latter is significantly affected by the boundary conditions and is far more complicated than in the corresponding symmetric Laplacian case of the nonlinear Schrödinger problem that has recently been explored. In addition, we explore the dynamics of the unstable solitary waves for p > 5 in the co-exploding frame. Copyright © 2023, The Authors. All rights reserved.

关键词： Korteweg-de Vries equation