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We present a data-driven approach to use the Koopman generator for prediction and optimal control of control-affine stochastic systems. We provide a novel conceptual approach and a proof-of-principle for the determination of optimal control policies which accelerate the simulation of rare events in metastable stochastic systems.

The hyperfine structure of bound electrons in hydrogen-like ions is considered with corrections to the energy levels due to vacuum polarization (VP). Corrections to the wave function as well as the magnetic potential are determined for both leptonic and hadronic VP. Hadronic VP is treated with a semi-empirical approach. Uncertainties due to the nuclear charge distribution are given and discussed. Point-like, spherical and Fermi distributed nuclear models are considered and the differences of the results are discussed., Comment: 10 pages, 2 figures

We consider the task of data-driven identification of dynamical systems, specifically for systems whose behavior at large frequencies is non-standard, as encoded by a non-trivial relative degree of the transfer function or, alternatively, a non-trivial index of a corresponding realization as a descriptor system. We develop novel surrogate modeling strategies that allow state-of-the-art rational approximation algorithms (e.g., AAA and vector fitting) to better handle data coming from such systems with non-trivial relative degree. Our contribution is twofold. On one hand, we describe a strategy to build rational surrogate models with prescribed relative degree, with the objective of mirroring the high-frequency behavior of the high-fidelity problem, when known. The surrogate model's desired degree is achieved through constraints on its barycentric coefficients, rather than through ad-hoc modifications of the rational form. On the other hand, we present a degree-identification routine that allows one to estimate the unknown relative degree of a system from low-frequency data. By identifying the degree of the system that generated the data, we can build a surrogate model that, in addition to matching the data well (at low frequencies), has enhanced extrapolation capabilities (at high frequencies). We showcase the effectiveness and robustness of the newly proposed method through a suite of numerical tests., Comment: 20 pages, 5 figures

Multiscale models provide a unique tool for studying complex processes that study events occurring at different scales across space and time. In the context of biological systems, such models can simulate mechanisms happening at the intracellular level such as signaling, and at the extracellular level where cells communicate and coordinate with other cells. They aim to understand the impact of genetic or environmental deregulation observed in complex diseases, describe the interplay between a pathological tissue and the immune system, and suggest strategies to revert the diseased phenotypes. The construction of these multiscale models remains a very complex task, including the choice of the components to consider, the level of details of the processes to simulate, or the fitting of the parameters to the data. One additional difficulty is the expert knowledge needed to program these models in languages such as C++ or Python, which may discourage the participation of non-experts. Simplifying this process through structured description formalisms -- coupled with a graphical interface -- is crucial in making modeling more accessible to the broader scientific community, as well as streamlining the process for advanced users. This article introduces three examples of multiscale models which rely on the framework PhysiBoSS, an add-on of PhysiCell that includes intracellular descriptions as continuous time Boolean models to the agent-based approach. The article demonstrates how to easily construct such models, relying on PhysiCell Studio, the PhysiCell Graphical User Interface. A step-by-step tutorial is provided as a Supplementary Material and all models are provided at: https://physiboss.github.io/tutorial/.

In this paper, we propose a method for aligning models with their realization through the application of model-based systems engineering. Our approach is divided into three steps. (1) Firstly, we leverage domain expertise and the Unified Architecture Framework to establish a reference model that fundamentally describes some domain. (2) Subsequently, we instantiate the reference model as specific models tailored to different scenarios within the domain. (3) Finally, we incorporate corresponding run logic directly into both the reference model and the specific models. In total, we thus provide a practical means to ensure that every implementation result is justified by business demand. We demonstrate our approach using the example of maritime object detection as a specific application (specific model / implementation element) of automatic target recognition as a service reoccurring in various forms (reference model element). Our approach facilitates a more seamless integration of models and implementation, fostering enhanced Business-IT alignment.

Reference models in form of best practices are an essential element to ensured knowledge as design for reuse. Popular modeling approaches do not offer mechanisms to embed reference models in a supporting way, let alone a repository of it. Therefore, it is hardly possible to profit from this expertise. The problem is that the reference models are not described formally enough to be helpful in developing solutions. Consequently, the challenge is about the process, how a user can be supported in designing dedicated solutions assisted by reference models. In this paper, we present a generic approach for the formal description of reference models using semantic technologies and their application. Our modeling assistant allows the construction of solution models using different techniques based on reference building blocks. This environment enables the subsequent verification of the developed designs against the reference models for conformity. Therefore, our reference modeling assistant highlights the interdependency. The application of these techniques contributes to the formalization of requirements and finally to quality assurance in context of maturity model. It is possible to use multiple reference models in context of system of system designs. The approach is evaluated in industrial area and it can be integrated into different modeling landscapes.

Polytopic autoencoders provide low-dimensional parametrizations of states in a polytope. For nonlinear PDEs, this is readily applied to low-dimensional linear parameter-varying (LPV) approximations as they have been exploited for efficient nonlinear controller design via series expansions of the solution to the state-dependent Riccati equation. In this work, we develop a polytopic autoencoder for control applications and show how it outperforms standard linear approaches in view of LPV approximations of nonlinear systems and how the particular architecture enables higher order series expansions at little extra computational effort. We illustrate the properties and potentials of this approach to computational nonlinear controller design for large-scale systems with a thorough numerical study., Comment: 9 pages, 6 figures, 2 tables

Numerical algorithms and computational tools are instrumental in navigating and addressing complex simulation and data processing tasks. The exponential growth of metadata and parameter-driven simulations has led to an increasing demand for automated workflows that can replicate computational experiments across platforms. In general, a computational workflow is defined as a sequential description for accomplishing a scientific objective, often described by tasks and their associated data dependencies. If characterized through input-output relation, workflow components can be structured to allow interchangeable utilization of individual tasks and their accompanying metadata. In the present work, we develop a novel computational framework, namely, MaRDIFlow, that focuses on the automation of abstracting meta-data embedded in an ontology of mathematical objects. This framework also effectively addresses the inherent execution and environmental dependencies by incorporating them into multi-layered descriptions. Additionally, we demonstrate a working prototype with example use cases and methodically integrate them into our workflow tool and data provenance framework. Furthermore, we show how to best apply the FAIR principles to computational workflows, such that abstracted components are Findable, Accessible, Interoperable, and Reusable in nature., Comment: 13 pages, 7 figures

With the advancement of neural networks, there has been a notable increase, both in terms of quantity and variety, in research publications concerning the application of autoencoders to reduced-order models. We propose a polytopic autoencoder architecture that includes a lightweight nonlinear encoder, a convex combination decoder, and a smooth clustering network. Supported by several proofs, the model architecture ensures that all reconstructed states lie within a polytope, accompanied by a metric indicating the quality of the constructed polytopes, referred to as polytope error. Additionally, it offers a minimal number of convex coordinates for polytopic linear-parameter varying systems while achieving acceptable reconstruction errors compared to proper orthogonal decomposition (POD). To validate our proposed model, we conduct simulations involving two flow scenarios with the incompressible Navier-Stokes equation. Numerical results demonstrate the guaranteed properties of the model, low reconstruction errors compared to POD, and the improvement in error using a clustering network., Comment: 28 pages, 18 figures

The reduced-order modeling of a system from data (also known as system identification) is a classical task in system and control theory and well understood for standard linear systems with the so-called Loewner framework as one of many established approaches. In the case of descriptor systems for which the transfer function is not proper anymore, recent research efforts have addressed strategies to deal with the non-proper parts more or less explicitly. In this work, we propose a variant of a Loewner matrix-based interpolation algorithm that implicitly addresses possibly non-proper components of the system response. We evaluate the performance of the suggested approach by comparing against recently-developed explicit algorithms for which we propose a linearized Navier-Stokes model with a significant non-proper behavior as a benchmark example., Comment: 8 pages, 4 Figures, submitted for presentation at ECC24

The control of nonlinear large-scale dynamical models such as the incompressible Navier-Stokes equations is a challenging task. The computational challenges in the controller design come from both the possibly large state space and the nonlinear dynamics. A general purpose approach certainly will resort to numerical linear algebra techniques which can handle large system sizes or to model order reduction. In this work we propose a two-folded model reduction approach tailored to nonlinear controller design for incompressible Navier-Stokes equations and similar PDE models that come with quadratic nonlinearities. Firstly, we approximate the nonlinear model within in the class of LPV systems with a very low dimension in the parametrization. Secondly, we reduce the system size to a moderate number of states. This way, standard robust LPV theory for nonlinear controller design becomes feasible. We illustrate the procedure and its potentials by numerical simulations.

Black hole X-ray binaries (BHXRBs) play a crucial role in understanding the accretion of matter onto a black hole. Here, we focus on exploring the transient BHXRB \source~discovered by Swift/BAT and MAXI/GSC during its January 2019 outburst. We present measurements on its accretion properties, long time-scale variability, and spin. To probe these properties we make use of several NICER observations and an unexplored data set from NuSTAR, as well as long term light curves from MAXI/GSC. In our timing analysis we provide estimates of the cross-correlation functions between light curves in various energy bands. In our spectral analysis we employ numerous phenomenological models to constrain the parameters of the system, including flavours of the relativistic reflection model Relxill to model the Fe K$\alpha$ line and the $>15$ keV reflection hump. Our analysis reveals that: (i) Over the course of the outburst the total energy released was $\sim 5.2 \times 10^{44}$~ergs, corresponding to roughly 90\% the mass of Mars being devoured. (ii) We find a continuum lag of $8.4 \pm 1.9$ days between light curves in the $2-4$ keV and $10-20$ keV bands which could be related to the viscous inflow time-scale of matter in the standard disc. (iii) Spectral analysis reveals a spin parameter of $\sim 0.6 - 0.7$ with an inclination angle of $\sim 45^{\circ}-70^{\circ}$, and an accretion rate during the NuSTAR observation of $\sim 17\% ~L_{\rm Edd}$., Comment: 13 pages 6 figures, Accepted for publication in MNRAS, Comments are welcome

The generalized Kalman-Yakubovich-Popov lemma as established by Iwasaki and Hara in 2005 marks a milestone in the analysis and synthesis of linear systems from a finite-frequency perspective. Given a pre-specified frequency band, it allows us to produce passive controllers with excellent in-band disturbance attenuation performance at the expense of some of the out-of-band performance. This paper focuses on control design of linear systems in the presence of disturbances with non-strictly or non-stationary limited frequency spectrum. We first propose a class of frequency-dependent excited energy functions (FD-EEF) as well as frequency-dependent excited power functions (FD-EPF), which possess a desirable frequency-selectiveness property with regard to the in-band and out-of-band excited energy as well as excited power of the system. Based upon a group of frequency-selective passive controllers, we then develop a frequency-dependent switching control (FDSC) scheme that selects the most appropriate controller at runtime. We show that our FDSC scheme is capable to approximate the solid in-band performance while maintaining acceptable out-of-band performance with regard to global time horizons as well as localized time horizons. The method is illustrated by a commonly used benchmark model.

Systems with artificial intelligence components, so-called AI-based systems, have gained considerable attention recently. However, many organizations have issues with achieving production readiness with such systems. As a means to improve certain software quality attributes and to address frequently occurring problems, design patterns represent proven solution blueprints. While new patterns for AI-based systems are emerging, existing patterns have also been adapted to this new context. The goal of this study is to provide an overview of design patterns for AI-based systems, both new and adapted ones. We want to collect and categorize patterns, and make them accessible for researchers and practitioners. To this end, we first performed a multivocal literature review (MLR) to collect design patterns used with AI-based systems. We then integrated the created pattern collection into a web-based pattern repository to make the patterns browsable and easy to find. As a result, we selected 51 resources (35 white and 16 gray ones), from which we extracted 70 unique patterns used for AI-based systems. Among these are 34 new patterns and 36 traditional ones that have been adapted to this context. Popular pattern categories include "architecture" (25 patterns), "deployment" (16), "implementation" (9), or "security & safety" (9). While some patterns with four or more mentions already seem established, the majority of patterns have only been mentioned once or twice (51 patterns). Our results in this emerging field can be used by researchers as a foundation for follow-up studies and by practitioners to discover relevant patterns for informing the design of AI-based systems., Comment: Accepted for publication at the International Conference on AI Engineering (CAIN) 2023