Uncovering spatio-temporal patterns in semiconductor superlattices by efficient data processing tools

Time periodic patterns in a semiconductor superlattice, relevant to microwave generation, are obtained upon numerical integration of a known set of drift-diffusion equations. The associated spatiotemporal transport mechanisms are uncovered by applying (to the computed data) two recent data processing tools, known as the higher order dynamic mode decomposition and the spatiotemporal Koopman decomposition. Outcomes include a clear identification of the asymptotic self-sustained oscillations of the current density (isolated from the transient dynamics) and an accurate description of the electric field traveling pulse in terms of its dispersion diagram. In addition, a preliminary version of a data-driven reduced order model is constructed, which allows for extremely fast online simulations of the system response over a range of different configurations.The authors are indebted to two anonymous referees for some useful comments and suggestions on an earlier version of the paper. This work has been supported by the Fondo Europeo de Desarrollo Regional Ministerio de Ciencia, Innovación y Universidades–Agencia Estatal de Investigación, under Grants No. TRA2016-75075-R, No. MTM2017-84446-C2-2-R, and No. PID2020-112796RB-C22, and by the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M in the line of Excellence of University Professors (EPUC3M23) and in the context of the V PRICIT (Regional Programme of Research and Technological Innovation)

ModelFLOWs-app: data-driven post-processing and reduced order modelling tools

This article presents an innovative open-source software named ModelFLOWs-app, written in Python, which has been created and tested to generate precise and robust hybrid reduced order models (ROMs) fully data-driven. By integrating modal decomposition and deep learning methods in diverse ways, the software uncovers the fundamental patterns in dynamic systems. This acquired knowledge is then employed to enrich the comprehension of the underlying physics, reconstruct databases from limited measurements, and forecast the progression of system dynamics. These hybrid models combine experimental and numerical database, and serve as accurate alternatives to numerical simulations, effectively diminishing computational expenses, and also as tools for optimization and control. The ModelFLOWs-app software has demonstrated in a wide range of applications its great capability to develop reliable data-driven hybrid ROMs, highlighting its potential in understanding complex non-linear dynamical systems and offering valuable insights into various applications. This article presents the mathematical background, review some examples of applications and introduces a short tutorial of ModelFLOWs-app

Energy Modelling and Forecasting for an Underground Agricultural Farm using a Higher Order Dynamic Mode Decomposition Approach

This paper presents an approach based on higher order dynamic mode decomposition (HODMD) to model, analyse, and forecast energy behaviour in an urban agriculture farm situated in a retrofitted London underground tunnel, where observed measurements are influenced by noisy and occasionally transient conditions. HODMD is a data-driven reduced order modelling method typically used to analyse and predict highly noisy and complex flows in fluid dynamics or any type of complex data from dynamical systems. HODMD is a recent extension of the classical dynamic mode decomposition method (DMD), customised to handle scenarios where the spectral complexity underlying the measurement data is higher than its spatial complexity, such as is the environmental behaviour of the farm. HODMD decomposes temporal data as a linear expansion of physically-meaningful DMD-modes in a semi-automatic approach, using a time-delay embedded approach. We apply HODMD to three seasonal scenarios using real data measured by sensors located at at the cross-sectional centre of the the underground farm. Through the study we revealed three physically-interpretable mode pairs that govern the environmental behaviour at the centre of the farm, consistently across environmental scenarios. Subsequently, we demonstrate how we can reconstruct the fundamental structure of the observed time-series using only these modes, and forecast for three days ahead, as one, compact and interpretable reduced-order model. We find HODMD to serve as a robust, semi-automatic modelling alternative for predictive modelling in Digital Twins

Forecasting through deep learning and modal decomposition in multi-phase concentric jets

This work presents a set of neural network (NN) models specifically designed for accurate and efficient fluid dynamics forecasting. In this work, we show how neural networks training can be improved by reducing data complexity through a modal decomposition technique called higher order dynamic mode decomposition (HODMD), which identifies the main structures inside flow dynamics and reconstructs the original flow using only these main structures. This reconstruction has the same number of samples and spatial dimension as the original flow, but with a less complex dynamics and preserving its main features. We also show the low computational cost required by the proposed NN models, both in their training and inference phases. The core idea of this work is to test the limits of applicability of deep learning models to data forecasting in complex fluid dynamics problems. Generalization capabilities of the models are demonstrated by using the same neural network architectures to forecast the future dynamics of four different multi-phase flows. Data sets used to train and test these deep learning models come from Direct Numerical Simulations (DNS) of these flows.Comment: 46 pages, 20 figures. Submitted to Expert Systems with Application

Acoustic characterization of absorbing materials using dynamic mode decomposition techniques

[Abstract] In general, the simulation of physical phenomena through numerical methods tends to be a computationally intensive task, but this is particularly true in the eld of acoustics. Due to the fast changing derivatives and the innately second order formulation, a ne mesh needs to be used, and in order for the time discretization to be well behaved, a small time step needs to be chosen as well. In addition to this, the testing of acoustic propagation in a single domain is rarely of interest, since most applications involve the design of acoustic barriers or transmitters, which means that most problems solved in the eld involve couplings. One of the coupled mediums is usually a uid, and it is common for the other to be a porous material since they are the most e ective sound absorbers. It is in fact because of this absorption that the porous models can get very complex. Time convolutions are usually needed for the modeling of high frequency noise, which makes the simulation process very costly. It becomes apparent that a reduced order method that is able to cut the computation time down is a worthwhile tool to have. Among the reduced order methods (ROMs) the chosen one is a method that is able to make predictions into the future from a reduced amount of snapshots. Dynamic Mode Decomposition (DMD) is a technique developed in 2010 by Peter Schmid [47]. It is based on a Singular Value Decomposition (SVD) into which dynamics are added, making it able to not only reconstruct available data using a reduced order representation, but also able to expand the dimensionality in the time dimension in order to make predictions about the future. This means that a simulation spanning a shorter time can be run and the remaining sector of the time domain can be predicted by DMD, which adds up to a signi cantly faster process. DMD is a data-driven method, which means that no information about the dynamic model is needed, only a series of snapshots are used. It has been used in the uid dynamics community, where it originated, and a number of elds including video processing [21, 14], epidemiology [41] and neuroscience [5]. A number of acoustic models are developed in this work, and then, they are used to test the capabilities of DMD in acoustic problems and to nd its limitations. The motivation of this problem arises from a collaboration between the Technological Institute for Industrial Mathematics (ITMATI) and Micro own Technologies through the ROMSOC project. Together they started a project that became Ashwin Nayak's PhD thesis, in which the objective is to design a multilayer windshield for an acoustic probe by modeling the acoustic eld both inside and outside of the windshield considering acoustic and other physical phenomena such as uid, thermal and poro-elastic e ects in an unbounded domain. The present master thesis project reduces Nayak's problem to a 1D simpli ed problem and attempts to develop a method that could be, in the future, generalized to his problem and reduce the computation time needed.Traballo fin de mestrado (UDC.INF). Matemática industrial. Curso 2019/202

Improving aircraft performance using machine learning: a review

This review covers the new developments in machine learning (ML) that are impacting the multi-disciplinary area of aerospace engineering, including fundamental fluid dynamics (experimental and numerical), aerodynamics, acoustics, combustion and structural health monitoring. We review the state of the art, gathering the advantages and challenges of ML methods across different aerospace disciplines and provide our view on future opportunities. The basic concepts and the most relevant strategies for ML are presented together with the most relevant applications in aerospace engineering, revealing that ML is improving aircraft performance and that these techniques will have a large impact in the near future

Discovering Causal Relations and Equations from Data

Physics is a field of science that has traditionally used the scientific method to answer questions about why natural phenomena occur and to make testable models that explain the phenomena. Discovering equations, laws and principles that are invariant, robust and causal explanations of the world has been fundamental in physical sciences throughout the centuries. Discoveries emerge from observing the world and, when possible, performing interventional studies in the system under study. With the advent of big data and the use of data-driven methods, causal and equation discovery fields have grown and made progress in computer science, physics, statistics, philosophy, and many applied fields. All these domains are intertwined and can be used to discover causal relations, physical laws, and equations from observational data. This paper reviews the concepts, methods, and relevant works on causal and equation discovery in the broad field of Physics and outlines the most important challenges and promising future lines of research. We also provide a taxonomy for observational causal and equation discovery, point out connections, and showcase a complete set of case studies in Earth and climate sciences, fluid dynamics and mechanics, and the neurosciences. This review demonstrates that discovering fundamental laws and causal relations by observing natural phenomena is being revolutionised with the efficient exploitation of observational data, modern machine learning algorithms and the interaction with domain knowledge. Exciting times are ahead with many challenges and opportunities to improve our understanding of complex systems.Comment: 137 page

Causality analysis of large-scale structures in the flow around a wall-mounted square cylinder

The aim of this work is to analyse the formation mechanisms of large-scale coherent structures in the flow around a wall-mounted square cylinder, due to their impact on pollutant transport within cities. To this end, we assess causal relations between the modes of a reduced-order model obtained by applying proper-orthogonal decomposition to high-fidelity-simulation data of the flow case under study. The causal relations are identified using conditional transfer entropy, which is an information-theoretical quantity that estimates the amount of information contained in the past of one variable about another. This allows for an understanding of the origins and evolution of different phenomena in the flow, with the aim of identifying the modes responsible for the formation of the main vortical structures. Our approach unveils that vortex-breaker modes are the most causal modes, in particular, over higher-order modes, and no significant causal relationships were found for vortex-generator modes. We validate this technique by determining the causal relations present in the nine-equation model of near-wall turbulence developed by Moehlis et al. (New J. Phys, vol. 6, 2004, p. 56), which are in good agreement with literature results for turbulent channel flows.Comment: 19 pages, 10 figure

Discovering causal relations and equations from data

Physics is a field of science that has traditionally used the scientific method to answer questions about why natural phenomena occur and to make testable models that explain the phenomena. Discovering equations, laws, and principles that are invariant, robust, and causal has been fundamental in physical sciences throughout the centuries. Discoveries emerge from observing the world and, when possible, performing interventions on the system under study. With the advent of big data and data-driven methods, the fields of causal and equation discovery have developed and accelerated progress in computer science, physics, statistics, philosophy, and many applied fields. This paper reviews the concepts, methods, and relevant works on causal and equation discovery in the broad field of physics and outlines the most important challenges and promising future lines of research. We also provide a taxonomy for data-driven causal and equation discovery, point out connections, and showcase comprehensive case studies in Earth and climate sciences, fluid dynamics and mechanics, and the neurosciences. This review demonstrates that discovering fundamental laws and causal relations by observing natural phenomena is revolutionised with the efficient exploitation of observational data and simulations, modern machine learning algorithms and the combination with domain knowledge. Exciting times are ahead with many challenges and opportunities to improve our understanding of complex systems

Holland City News, Volume 81, Number 12: March 20, 1952

Newspaper published in Holland, Michigan, from 1872-1977, to serve the English-speaking people in Holland, Michigan. Purchased by local Dutch language newspaper, De Grondwet, owner in 1888.https://digitalcommons.hope.edu/hcn_1952/1011/thumbnail.jp