5,702 research outputs found

    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

    Sampling with Barriers: Faster Mixing via Lewis Weights

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    We analyze Riemannian Hamiltonian Monte Carlo (RHMC) for sampling a polytope defined by mm inequalities in Rn\R^n endowed with the metric defined by the Hessian of a convex barrier function. The advantage of RHMC over Euclidean methods such as the ball walk, hit-and-run and the Dikin walk is in its ability to take longer steps. However, in all previous work, the mixing rate has a linear dependence on the number of inequalities. We introduce a hybrid of the Lewis weights barrier and the standard logarithmic barrier and prove that the mixing rate for the corresponding RHMC is bounded by O~(m1/3n4/3)\tilde O(m^{1/3}n^{4/3}), improving on the previous best bound of O~(mn2/3)\tilde O(mn^{2/3}) (based on the log barrier). This continues the general parallels between optimization and sampling, with the latter typically leading to new tools and more refined analysis. To prove our main results, we have to overcomes several challenges relating to the smoothness of Hamiltonian curves and the self-concordance properties of the barrier. In the process, we give a general framework for the analysis of Markov chains on Riemannian manifolds, derive new smoothness bounds on Hamiltonian curves, a central topic of comparison geometry, and extend self-concordance to the infinity norm, which gives sharper bounds; these properties appear to be of independent interest

    A convergent stochastic scalar auxiliary variable method

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    We discuss an extension of the scalar auxiliary variable approach which was originally introduced by Shen et al.~([Shen, Xu, Yang, J.~Comput.~Phys., 2018]) for the discretization of deterministic gradient flows. By introducing an additional scalar auxiliary variable, this approach allows to derive a linear scheme, while still maintaining unconditional stability. Our extension augments the approximation of the evolution of this scalar auxiliary variable with higher order terms, which enables its application to stochastic partial differential equations. Using the stochastic Allen--Cahn equation as a prototype for nonlinear stochastic partial differential equations with multiplicative noise, we propose an unconditionally energy stable, linear, fully discrete finite element scheme based on our stochastic scalar auxiliary variable method. Recovering a discrete version of the energy estimate and establishing Nikolskii estimates with respect to time, we are able to prove convergence of appropriate subsequences of discrete solutions towards pathwise unique martingale solutions by applying Jakubowski's generalization of Skorokhod's theorem. A generalization of the Gy\"ongy--Krylov characterization of convergence in probability to quasi-Polish spaces finally provides convergence of fully discrete solutions towards strong solutions of the stochastic Allen--Cahn equation

    Proceedings of SIRM 2023 - The 15th European Conference on Rotordynamics

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    It was our great honor and pleasure to host the SIRM Conference after 2003 and 2011 for the third time in Darmstadt. Rotordynamics covers a huge variety of different applications and challenges which are all in the scope of this conference. The conference was opened with a keynote lecture given by Rainer Nordmann, one of the three founders of SIRM “Schwingungen in rotierenden Maschinen”. In total 53 papers passed our strict review process and were presented. This impressively shows that rotordynamics is relevant as ever. These contributions cover a very wide spectrum of session topics: fluid bearings and seals; air foil bearings; magnetic bearings; rotor blade interaction; rotor fluid interactions; unbalance and balancing; vibrations in turbomachines; vibration control; instability; electrical machines; monitoring, identification and diagnosis; advanced numerical tools and nonlinearities as well as general rotordynamics. The international character of the conference has been significantly enhanced by the Scientific Board since the 14th SIRM resulting on one hand in an expanded Scientific Committee which meanwhile consists of 31 members from 13 different European countries and on the other hand in the new name “European Conference on Rotordynamics”. This new international profile has also been emphasized by participants of the 15th SIRM coming from 17 different countries out of three continents. We experienced a vital discussion and dialogue between industry and academia at the conference where roughly one third of the papers were presented by industry and two thirds by academia being an excellent basis to follow a bidirectional transfer what we call xchange at Technical University of Darmstadt. At this point we also want to give our special thanks to the eleven industry sponsors for their great support of the conference. On behalf of the Darmstadt Local Committee I welcome you to read the papers of the 15th SIRM giving you further insight into the topics and presentations

    AI: Limits and Prospects of Artificial Intelligence

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    The emergence of artificial intelligence has triggered enthusiasm and promise of boundless opportunities as much as uncertainty about its limits. The contributions to this volume explore the limits of AI, describe the necessary conditions for its functionality, reveal its attendant technical and social problems, and present some existing and potential solutions. At the same time, the contributors highlight the societal and attending economic hopes and fears, utopias and dystopias that are associated with the current and future development of artificial intelligence

    Nonlinear and Linearized Analysis of Vibrations of Loaded Anisotropic Beam/Plate/Shell Structures

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    L'abstract è presente nell'allegato / the abstract is in the attachmen

    Development, Implementation, and Optimization of a Modern, Subsonic/Supersonic Panel Method

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    In the early stages of aircraft design, engineers consider many different design concepts, examining the trade-offs between different component arrangements and sizes, thrust and power requirements, etc. Because so many different designs are considered, it is best in the early stages of design to use simulation tools that are fast; accuracy is secondary. A common simulation tool for early design and analysis is the panel method. Panel methods were first developed in the 1950s and 1960s with the advent of modern computers. Despite being reasonably accurate and very fast, their development was abandoned in the late 1980s in favor of more complex and accurate simulation methods. The panel methods developed in the 1980s are still in use by aircraft designers today because of their accuracy and speed. However, they are cumbersome to use and limited in applicability. The purpose of this work is to reexamine panel methods in a modern context. In particular, this work focuses on the application of panel methods to supersonic aircraft (a supersonic aircraft is one that flies faster than the speed of sound). Various aspects of the panel method, including the distributions of the unknown flow variables on the surface of the aircraft and efficiently solving for these unknowns, are discussed. Trade-offs between alternative formulations are examined and recommendations given. This work also serves to bring together, clarify, and condense much of the literature previously published regarding panel methods so as to assist future developers of panel methods

    Nonlinear dynamic analysis of shear- and torsion-free rods using isogeometric discretization, outlier removal and robust time integration

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    In this paper, we present a discrete formulation of nonlinear shear- and torsion-free rods based on \cite{gebhardt_2021_beam} that uses isogeometric discretization and robust time integration. Omitting the director as an independent variable field, we reduce the number of degrees of freedom and obtain discrete solutions in multiple copies of the Euclidean space (R3)\left(\mathbb{R}^3\right), which is larger than the corresponding multiple copies of the manifold \left(\mathbb{R}^3 \cross S^2\right) obtained with standard Hermite finite elements. For implicit time integration, we choose a hybrid form of the mid-point rule and the trapezoidal rule that preserves the linear angular momentum exactly and approximates the energy accurately. In addition, we apply a recently introduced approach for outlier removal \cite{hiemstra_outlier_2021} that reduces high-frequency content in the response without affecting the accuracy, ensuring robustness of our nonlinear discrete formulation. We illustrate the efficiency of our nonlinear discrete formulation for static and transient rods under different loading conditions, demonstrating good accuracy in space, time and the frequency domain. Our numerical example coincides with a relevant application case, the simulation of mooring lines

    Control of McKean--Vlasov SDEs with Contagion Through Killing at a State-Dependent Intensity

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    We consider a novel McKean--Vlasov control problem with contagion through killing of particles and common noise. Each particle is killed at an exponential rate according to an intensity process that increases whenever the particle is located in a specific region. The removal of a particle pushes others towards the removal region, which can trigger cascades that see particles exiting the system in rapid succession. We study the control of such a system by a central agent who intends to preserve particles at minimal cost. Our theoretical contribution is twofold. Firstly, we rigorously justify the McKean--Vlasov control problem as the limit of a corresponding controlled finite particle system. Our proof is based on a controlled martingale problem and tightness arguments. Secondly, we connect our framework with models in which particles are killed once they hit the boundary of the removal region. We show that these models appear in the limit as the exponential rate tends to infinity. As a corollary, we obtain new existence results for McKean--Vlasov SDEs with singular interaction through hitting times which extend those in the established literature. We conclude the paper with numerical investigations of our model applied to government control of systemic risk in financial systems

    Beam scanning by liquid-crystal biasing in a modified SIW structure

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    A fixed-frequency beam-scanning 1D antenna based on Liquid Crystals (LCs) is designed for application in 2D scanning with lateral alignment. The 2D array environment imposes full decoupling of adjacent 1D antennas, which often conflicts with the LC requirement of DC biasing: the proposed design accommodates both. The LC medium is placed inside a Substrate Integrated Waveguide (SIW) modified to work as a Groove Gap Waveguide, with radiating slots etched on the upper broad wall, that radiates as a Leaky-Wave Antenna (LWA). This allows effective application of the DC bias voltage needed for tuning the LCs. At the same time, the RF field remains laterally confined, enabling the possibility to lay several antennas in parallel and achieve 2D beam scanning. The design is validated by simulation employing the actual properties of a commercial LC medium
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