4,957 research outputs found

    Linear Amplification in Nonequilibrium Turbulent Boundary Layers

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    Resolvent analysis is applied to nonequilibrium incompressible adverse pressure gradient (APG) turbulent boundary layers (TBL) and hypersonic boundary layers with high temperature real gas effects, including chemical nonequilibrium. Resolvent analysis is an equation-based, scale-dependent decomposition of the Navier Stokes equations, linearized about a known mean flow field. The decomposition identifies the optimal response and forcing modes, ranked by their linear amplification. To treat the nonequilibrium APG TBL, a biglobal resolvent analysis approach is used to account for the streamwise and wall-normal inhomogeneities in the streamwise developing flow. For the hypersonic boundary layer in chemical nonequilibrium, the resolvent analysis is constructed using a parallel flow assumption, incorporating N₂, O₂, NO, N, and O as a mixture of chemically reacting gases. Biglobal resolvent analysis is first applied to the zero pressure gradient (ZPG) TBL. Scaling relationships are determined for the spanwise wavenumber and temporal frequency that admit self-similar resolvent modes in the inner layer, mesolayer, and outer layer regions of the ZPG TBL. The APG effects on the inner scaling of the biglobal modes are shown to diminish as their self-similarity improves with increased Reynolds number. An increase in APG strength is shown to increase the linear amplification of the large-scale biglobal modes in the outer region, similar to the energization of large scale modes observed in simulation. The linear amplification of these modes grows linearly with the APG history, measured as the streamwise averaged APG strength, and relates to a novel pressure-based velocity scale. Resolvent analysis is then used to identify the length scales most affected by the high-temperature gas effects in hypersonic TBLs. It is shown that the high-temperature gas effects primarily affect modes localized near the peak mean temperature. Due to the chemical nonequilibrium effects, the modes can be linearly amplified through changes in chemical concentration, which have non-negligible effects on the higher order modes. Correlations in the components of the small-scale resolvent modes agree qualitatively with similar correlations in simulation data. Finally, efficient strategies for resolvent analysis are presented. These include an algorithm to autonomously sample the large amplification regions using a Bayesian Optimization-like approach and a projection-based method to approximate resolvent analysis through a reduced eigenvalue problem, derived from calculus of variations.</p

    Meta-learning algorithms and applications

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    Meta-learning in the broader context concerns how an agent learns about their own learning, allowing them to improve their learning process. Learning how to learn is not only beneficial for humans, but it has also shown vast benefits for improving how machines learn. In the context of machine learning, meta-learning enables models to improve their learning process by selecting suitable meta-parameters that influence the learning. For deep learning specifically, the meta-parameters typically describe details of the training of the model but can also include description of the model itself - the architecture. Meta-learning is usually done with specific goals in mind, for example trying to improve ability to generalize or learn new concepts from only a few examples. Meta-learning can be powerful, but it comes with a key downside: it is often computationally costly. If the costs would be alleviated, meta-learning could be more accessible to developers of new artificial intelligence models, allowing them to achieve greater goals or save resources. As a result, one key focus of our research is on significantly improving the efficiency of meta-learning. We develop two approaches: EvoGrad and PASHA, both of which significantly improve meta-learning efficiency in two common scenarios. EvoGrad allows us to efficiently optimize the value of a large number of differentiable meta-parameters, while PASHA enables us to efficiently optimize any type of meta-parameters but fewer in number. Meta-learning is a tool that can be applied to solve various problems. Most commonly it is applied for learning new concepts from only a small number of examples (few-shot learning), but other applications exist too. To showcase the practical impact that meta-learning can make in the context of neural networks, we use meta-learning as a novel solution for two selected problems: more accurate uncertainty quantification (calibration) and general-purpose few-shot learning. Both are practically important problems and using meta-learning approaches we can obtain better solutions than the ones obtained using existing approaches. Calibration is important for safety-critical applications of neural networks, while general-purpose few-shot learning tests model's ability to generalize few-shot learning abilities across diverse tasks such as recognition, segmentation and keypoint estimation. More efficient algorithms as well as novel applications enable the field of meta-learning to make more significant impact on the broader area of deep learning and potentially solve problems that were too challenging before. Ultimately both of them allow us to better utilize the opportunities that artificial intelligence presents

    Techniques for high-multiplicity scattering amplitudes and applications to precision collider physics

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    In this thesis, we present state-of-the-art techniques for the computation of scattering amplitudes in Quantum Field Theories. Following an introduction to the topic, we describe a robust framework that enables the calculation of multi-scale two-loop amplitudes directly relevant to modern particle physics phenomenology at the Large Hadron Collider and beyond. We discuss in detail the use of finite fields to bypass the algebraic complexity of such computations, as well as the method of integration-by-parts relations and differential equations. We apply our framework to calculate the two-loop amplitudes contributing to three process: Higgs boson production in association with a bottom-quark pair, W boson production with a photon and a jet, as well as lepton-pair scattering with an off-shell and an on-shell photon. Finally, we draw our conclusions and discuss directions for future progress of amplitude computations

    Classical and quantum algorithms for scaling problems

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    This thesis is concerned with scaling problems, which have a plethora of connections to different areas of mathematics, physics and computer science. Although many structural aspects of these problems are understood by now, we only know how to solve them efficiently in special cases.We give new algorithms for non-commutative scaling problems with complexity guarantees that match the prior state of the art. To this end, we extend the well-known (self-concordance based) interior-point method (IPM) framework to Riemannian manifolds, motivated by its success in the commutative setting. Moreover, the IPM framework does not obviously suffer from the same obstructions to efficiency as previous methods. It also yields the first high-precision algorithms for other natural geometric problems in non-positive curvature.For the (commutative) problems of matrix scaling and balancing, we show that quantum algorithms can outperform the (already very efficient) state-of-the-art classical algorithms. Their time complexity can be sublinear in the input size; in certain parameter regimes they are also optimal, whereas in others we show no quantum speedup over the classical methods is possible. Along the way, we provide improvements over the long-standing state of the art for searching for all marked elements in a list, and computing the sum of a list of numbers.We identify a new application in the context of tensor networks for quantum many-body physics. We define a computable canonical form for uniform projected entangled pair states (as the solution to a scaling problem), circumventing previously known undecidability results. We also show, by characterizing the invariant polynomials, that the canonical form is determined by evaluating the tensor network contractions on networks of bounded size

    Digitalization and Development

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    This book examines the diffusion of digitalization and Industry 4.0 technologies in Malaysia by focusing on the ecosystem critical for its expansion. The chapters examine the digital proliferation in major sectors of agriculture, manufacturing, e-commerce and services, as well as the intermediary organizations essential for the orderly performance of socioeconomic agents. The book incisively reviews policy instruments critical for the effective and orderly development of the embedding organizations, and the regulatory framework needed to quicken the appropriation of socioeconomic synergies from digitalization and Industry 4.0 technologies. It highlights the importance of collaboration between government, academic and industry partners, as well as makes key recommendations on how to encourage adoption of IR4.0 technologies in the short- and long-term. This book bridges the concepts and applications of digitalization and Industry 4.0 and will be a must-read for policy makers seeking to quicken the adoption of its technologies

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    An Optimized, Easy-to-use, Open-source GPU Solver for Large-scale Inverse Homogenization Problems

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    We propose a high-performance GPU solver for inverse homogenization problems to design high-resolution 3D microstructures. Central to our solver is a favorable combination of data structures and algorithms, making full use of the parallel computation power of today's GPUs through a software-level design space exploration. This solver is demonstrated to optimize homogenized stiffness tensors, such as bulk modulus, shear modulus, and Poisson's ratio, under the constraint of bounded material volume. Practical high-resolution examples with 512^3(134.2 million) finite elements run in less than 32 seconds per iteration with a peak memory of 21 GB. Besides, our GPU implementation is equipped with an easy-to-use framework with less than 20 lines of code to support various objective functions defined by the homogenized stiffness tensors. Our open-source high-performance implementation is publicly accessible at https://github.com/lavenklau/homo3d

    Data-assisted modeling of complex chemical and biological systems

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    Complex systems are abundant in chemistry and biology; they can be multiscale, possibly high-dimensional or stochastic, with nonlinear dynamics and interacting components. It is often nontrivial (and sometimes impossible), to determine and study the macroscopic quantities of interest and the equations they obey. One can only (judiciously or randomly) probe the system, gather observations and study trends. In this thesis, Machine Learning is used as a complement to traditional modeling and numerical methods to enable data-assisted (or data-driven) dynamical systems. As case studies, three complex systems are sourced from diverse fields: The first one is a high-dimensional computational neuroscience model of the Suprachiasmatic Nucleus of the human brain, where bifurcation analysis is performed by simply probing the system. Then, manifold learning is employed to discover a latent space of neuronal heterogeneity. Second, Machine Learning surrogate models are used to optimize dynamically operated catalytic reactors. An algorithmic pipeline is presented through which it is possible to program catalysts with active learning. Third, Machine Learning is employed to extract laws of Partial Differential Equations describing bacterial Chemotaxis. It is demonstrated how Machine Learning manages to capture the rules of bacterial motility in the macroscopic level, starting from diverse data sources (including real-world experimental data). More importantly, a framework is constructed though which already existing, partial knowledge of the system can be exploited. These applications showcase how Machine Learning can be used synergistically with traditional simulations in different scenarios: (i) Equations are available but the overall system is so high-dimensional that efficiency and explainability suffer, (ii) Equations are available but lead to highly nonlinear black-box responses, (iii) Only data are available (of varying source and quality) and equations need to be discovered. For such data-assisted dynamical systems, we can perform fundamental tasks, such as integration, steady-state location, continuation and optimization. This work aims to unify traditional scientific computing and Machine Learning, in an efficient, data-economical, generalizable way, where both the physical system and the algorithm matter

    From a causal representation of multiloop scattering amplitudes to quantum computing in the Loop-Tree Duality

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    La teoría cúantica de campos con enfoque perturbativo ha logrado de manera exitosa proporcionar predicciones teóricas increíblemente precisas en física de altas energías. A pesar del desarrollo de diversas técnicas con el objetivo de incrementar la eficiencia de estos cálculos, algunos ingredientes continuan siendo un verdadero reto. Este es el caso de las amplitudes de dispersión con lazos múltiples, las cuales describen las fluctuaciones cuánticas en los procesos de dispersión a altas energías. La Dualidad Lazo-Árbol (LTD) es un método innovador, propuesto con el objetivo de afrontar estas dificultades abriendo las amplitudes de lazo a amplitudes conectadas de tipo árbol. En esta tesis presentamos tres logros fundamentales: la reformulación de la Dualidad Lazo-Árbol a todos los órdenes en la expansión perturbativa, una metodología general para obtener expresiones LTD con un comportamiento manifiestamente causal, y la primera aplicación de un algoritmo cuántico a integrales de lazo de Feynman. El cambio de estrategia propuesto para implementar la metodología LTD, consiste en la aplicación iterada del teorema del residuo de Cauchy a un conjunto de topologías con lazos m\'ultiples y configuraciones internas arbitrarias. La representación LTD que se obtiene, sigue una estructura factorizada en términos de subtopologías más simples, caracterizada por un comportamiento causal bien conocido. Además, a través de un proceso avanzado desarrollamos representaciones duales analíticas explícitamente libres de singularidades no causales. Estas propiedades permiten escribir cualquier amplitud de dispersión, hasta cinco lazos, de forma factorizada con una mejor estabilidad numérica en comparación con otras representaciones, debido a la ausencia de singularidades no causales. Por último, establecemos la conexión entre las integrales de lazo de Feynman y la computación cuántica, mediante la asociación de los dos estados sobre la capa de masas de un propagador de Feynman con los dos estados de un qubit. Proponemos una modificación del algoritmo cuántico de Grover para encontrar las configuraciones singulares causales de los diagramas de Feynman con lazos múltiples. Estas configuraciones son requeridas para establecer la representación causal de topologías con lazos múltiples.The perturbative approach to Quantum Field Theories has successfully provided incredibly accurate theoretical predictions in high-energy physics. Despite the development of several techniques to boost the efficiency of these calculations, some ingredients remain a hard bottleneck. This is the case of multiloop scattering amplitudes, describing the quantum fluctuations at high-energy scattering processes. The Loop-Tree Duality (LTD) is a novel method aimed to overcome these difficulties by opening the loop amplitudes into connected tree-level diagrams. In this thesis we present three core achievements: the reformulation of the Loop-Tree Duality to all orders in the perturbative expansion, a general methodology to obtain LTD expressions which are manifestly causal, and the first flagship application of a quantum algorithm to Feynman loop integrals. The proposed strategy to implement the LTD framework consists in the iterated application of the Cauchy's residue theorem to a series of mutiloop topologies with arbitrary internal configurations. We derive a LTD representation exhibiting a factorized cascade form in terms of simpler subtopologies characterized by a well-known causal behaviour. Moreover, through a clever approach we extract analytic dual representations that are explicitly free of noncausal singularities. These properties enable to open any scattering amplitude of up to five loops in a factorized form, with a better numerical stability than in other representations due to the absence of noncausal singularities. Last but not least, we establish the connection between Feynman loop integrals and quantum computing by encoding the two on-shell states of a Feynman propagator through the two states of a qubit. We propose a modified Grover's quantum algorithm to unfold the causal singular configurations of multiloop Feynman diagrams used to bootstrap the causal LTD representation of multiloop topologies

    Unobstructed Lagrangian cobordism groups of surfaces

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    We study Lagrangian cobordism groups of closed symplectic surfaces of genus g2g \geq 2 whose relations are given by unobstructed, immersed Lagrangian cobordisms. Building upon work of Abouzaid and Perrier, we compute these cobordism groups and show that they are isomorphic to the Grothendieck group of the derived Fukaya category of the surface.Comment: 60 pages, 15 figure
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