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We implement and analyse a sparse / indirect-addressing data structure for the Lattice Boltzmann Method to support efficient compute kernels for fluid dynamics problems with a high number of non-fluid nodes in the domain, such as in porous media flows. The data structure is integrated into a code generation pipeline to enable sparse Lattice Boltzmann Methods with a variety of stencils and collision operators and to generate efficient code for kernels for CPU as well as for AMD and NVIDIA accelerator cards. We optimize these sparse kernels with an in-place streaming pattern to save memory accesses and memory consumption and we implement a communication hiding technique to prove scalability. We present single GPU performance results with up to 99% of maximal bandwidth utilization. We integrate the optimized generated kernels in the high performance framework WALBERLA and achieve a scaling efficiency of at least 82% on up to 1024 NVIDIA A100 GPUs and up to 4096 AMD MI250X GPUs on modern HPC systems. Further, we set up three different applications to test the sparse data structure for realistic demonstrator problems. We show performance results for flow through porous media, free flow over a particle bed, and blood flow in a coronary artery. We achieve a maximal performance speed-up of 2 and a significantly reduced memory consumption by up to 75% with the sparse / indirect-addressing data structure compared to the direct-addressing data structure for these applications., Comment: 16 pages, 19 figures

Density functional theory has become the workhorse of quantum physics, chemistry, and materials science. Within these fields, a broad range of applications needs to be covered. These applications range from solids to molecular systems, from organic to inorganic chemistry, or even from electrons to other fermions such as protons or muons. This is emphasized by the plethora of density functional approximations that have been developed for various cases. In this work, a new local hybrid exchange-correlation density functional is constructed from first principles, promoting generality and transferability. We show that constraint satisfaction can be achieved even for admixtures with full exact exchange, without sacrificing accuracy. The performance of the new functional for electronic structure theory is assessed for thermochemical properties, excitation energies, M\"ossbauer isomer shifts, NMR spin--spin coupling constants, NMR shieldings and shifts, magnetizabilities, as well as EPR hyperfine coupling constants. Here, the new density functional shows excellent performance throughout all tests and is numerically robust only requiring small grids for converged results. Additionally, the functional can be easily generalized to arbitrary fermions as shown for electron-proton correlation energies. Therefore, we outline that density functionals generated in this way are general purpose tools for quantum mechanical studies.

Temporal logics are powerful tools that are widely used for the synthesis and verification of reactive systems. The recent progress on Large Language Models (LLMs) has the potential to make the process of writing such specifications more accessible. However, writing specifications in temporal logics remains challenging for all but the most expert users. A key question in using LLMs for temporal logic specification engineering is to understand what kind of guidance is most helpful to the LLM and the users to easily produce specifications. Looking specifically at the problem of reactive program synthesis, we explore the impact of providing an LLM with guidance on the separation of control and data--making explicit for the LLM what functionality is relevant for the specification, and treating the remaining functionality as an implementation detail for a series of pre-defined functions and predicates. We present a benchmark set and find that this separation of concerns improves specification generation. Our benchmark provides a test set against which to verify future work in LLM generation of temporal logic specifications.

This paper presents a novel approach to quantum architecture search by integrating the techniques of ZX-calculus with Genetic Programming (GP) to optimize the structure of parameterized quantum circuits employed in Quantum Machine Learning (QML). Recognizing the challenges in designing efficient quantum circuits for QML, we propose a GP framework that utilizes mutations defined via ZX-calculus, a graphical language that can simplify visualizing and working with quantum circuits. Our methodology focuses on evolving quantum circuits with the aim of enhancing their capability to approximate functions relevant in various machine learning tasks. We introduce several mutation operators inspired by the transformation rules of ZX-calculus and investigate their impact on the learning efficiency and accuracy of quantum circuits. The empirical analysis involves a comparative study where these mutations are applied to a diverse set of quantum regression problems, measuring performance metrics such as the percentage of valid circuits after the mutation, improvement of the objective, as well as circuit depth and width. Our results indicate that certain ZX-calculus-based mutations perform significantly better than others for Quantum Architecture Search (QAS) in all metrics considered. They suggest that ZX-diagram based QAS results in shallower circuits and more uniformly allocated gates than crude genetic optimization based on the circuit model., Comment: 10 Pages, 10 figures, 1 algorithm

Pairs of entangled photons are important for applications in quantum nanophotonics, where their theoretical description must accommodate their bipartite character. Such character is shared at the other end of the intensity range by, for example, the two degenerate instances of the pump field involved in second-harmonic generation. Describing the interaction of nanophotonic structures with bipartite states of light is, regardless of their intensity, a challenge with important technological applications. Here, we develop a theoretical framework for studying the interaction of material structures with bipartite states of light. The basic element is the symmetrized tensor product space of two copies of an electromagnetic Hilbert space. One of the benefits inherited from the single Hilbert space is that consequences of material symmetries are readily deduced. We derive selection rules for second-order non-linear processes in objects with rotational and/or mirror symmetries. We numerically verify several selection rules by combining quantum-chemical calculations with a Maxwell solver to simulate second-harmonic generation in two different MoS$_2$ clusters. The computationally convenient scattering matrix method is also extended to the tensor product space when the response of the object to one part of the state is independent of the other. For such a case, we obtain the relation between the scattering matrix in the single Hilbert space and the scattering matrix for bipartite states. Such a separable case is relevant for the entanglement evolution of biphoton states interacting with nanostructures. We discuss some possibilities for accommodating the computations of non-linear effects in the framework, for example, through a non-separable scattering operator, where the response of the object to one part of the state depends on the other part., Comment: 17 pages, 3 figures

Fully distributed learning schemes such as Gossip Learning (GL) are gaining momentum due to their scalability and effectiveness even in dynamic settings. However, they often imply a high utilization of communication and computing resources, whose energy footprint may jeopardize the learning process, particularly on battery-operated IoT devices. To address this issue, we present Optimized Gossip Learning (OGL)}, a distributed training approach based on the combination of GL with adaptive optimization of the learning process, which allows for achieving a target accuracy while minimizing the energy consumption of the learning process. We propose a data-driven approach to OGL management that relies on optimizing in real-time for each node the number of training epochs and the choice of which model to exchange with neighbors based on patterns of node contacts, models' quality, and available resources at each node. Our approach employs a DNN model for dynamic tuning of the aforementioned parameters, trained by an infrastructure-based orchestrator function. We performed our assessments on two different datasets, leveraging time-varying random graphs and a measurement-based dynamic urban scenario. Results suggest that our approach is highly efficient and effective in a broad spectrum of network scenarios., Comment: IEEE AIIOT 2024

Spin-orbit coupling induces a current density in the ground state, which consequently requires a generalization for meta-generalized gradient approximations. That is, the exchange-correlation energy has to be constructed as an explicit functional of the current density and a generalized kinetic energy density has to be formed to satisfy theoretical constraints. Herein, we generalize our previously presented formalism of spin-orbit current density functional theory [Holzer et al., J. Chem. Phys. 157, 204102 (2022)] to non-magnetic and magnetic periodic systems of arbitrary dimension. Besides the ground-state exchange-correlation potential, analytical derivatives such as geometry gradients and stress tensors are implemented. The importance of the current density is assessed for band gaps, lattice constants, magnetic transitions, and Rashba splittings. For the latter, the impact of the current density may be larger than the deviation between different density functional approximations.

In the last years, Infrared Reflection-Absorption Spectroscopy (IRRAS) became a standard technique to study vibrational excitations of molecules. These investigations are strongly motivated by perspective applications in monitoring chemical processes. For a better understanding of the adsorption mechanism of molecules on dielectrics, the polarization-dependence of an interaction of infrared light with adsorbates at dielectric surfaces is commonly used. Thus, the peak positions in absorption spectra could be different for s- and p-polarized light. This shift between the peak positions depends on both the molecule itself and the dielectric substrate. While the origin of this shift is well understood for infinite two-dimensional adsorbate layers, finite-size samples, which consist of 2D islands of a small number of molecules, have never been considered. Here, we present a study on polarization-dependent finite-size effects in the optical response of such islands on dielectric substrates. The study uses a multi-scale modeling approach that connects quantum chemistry calculations to Maxwell scattering simulations. We distinguish the optical response of a single molecule, a finite number of molecules, and a two-dimensional adsorbate layer. We analyze CO and CO$_2$ molecules deposited on CeO$_2$ and Al$_2$O$_3$ substrates. The evolution of the shift between the polarization-dependent absorbance peaks is firstly studied for a single molecule, which it does not exhibit for at all, and for finite molecular islands, which it increases with increasing island size for, as well as for an infinite two-dimensional adsorbate layer. In the latter case, the agreement between the obtained results and the experimental IRRAS data and more traditional three/four-layer-model theoretical studies supports the predictive power of the multi-scale approach.

Quantum Neural Networks (QNNs) are a popular approach in Quantum Machine Learning due to their close connection to Variational Quantum Circuits, making them a promising candidate for practical applications on Noisy Intermediate-Scale Quantum (NISQ) devices. A QNN can be expressed as a finite Fourier series, where the set of frequencies is called the frequency spectrum. We analyse this frequency spectrum and prove, for a large class of models, various maximality results. Furthermore, we prove that under some mild conditions there exists a bijection between classes of models with the same area $A = RL$ that preserves the frequency spectrum, where $R$ denotes the number of qubits and $L$ the number of layers, which we consequently call spectral invariance under area-preserving transformations. With this we explain the symmetry in $R$ and $L$ in the results often observed in the literature and show that the maximal frequency spectrum depends only on the area $A = RL$ and not on the individual values of $R$ and $L$. Moreover, we extend existing results and specify the maximum possible frequency spectrum of a QNN with arbitrarily many layers as a function of the spectrum of its generators. If the generators of the QNN can be further decomposed into 2-dimensional sub-generators, then this specification follows from elementary number-theoretical considerations. In the case of arbitrary dimensional generators, we extend existing results based on the so-called Golomb ruler and introduce a second novel approach based on a variation of the turnpike problem, which we call the relaxed turnpike problem.

The goal of this work is to identify steady-state solutions to dynamical systems defined on large, random families of networks. We do so by passing to a continuum limit where the adjacency matrix is replaced by a non-local operator with kernel called a graphon. This graphon equation is often more amenable to analysis and provides a single equation to study instead of the infinitely many variations of networks that lead to the limit. Our work establishes a rigorous connection between steady-states of the continuum and network systems. Precisely, we show that if the graphon equation has a steady-state solution whose linearization is invertible, there exists related steady-state solutions to the finite-dimensional networked dynamical system over all sufficiently large graphs converging to the graphon. The proof involves setting up a Newton--Kantorovich type iteration scheme which is shown to be a contraction on a suitable metric space. Interestingly, we show that the first iterate of our defined operator in general fails to be a contraction mapping, but the second iterate is proven to contract on the space. We extend our results to show that linear stability properties further carry over from the graphon system to the graph dynamical system. Our results are applied to twisted states in a Kuramoto model of coupled oscillators, steady-states in a model of neuronal network activity, and a Lotka--Volterra model of ecological interaction.

This study develops a computationally efficient phase-field lattice Boltzmann model with the capability to simulate thermocapillary flows. The model was implemented into the open-source simulation framework, waLBerla, and extended to conduct the collision stage using central moments. The multiphase model was coupled with both a passive-scalar thermal LB, and a RK solution to the energy equation in order to resolve temperature-dependent surface tension phenomena. Various lattice stencils (D3Q7, D3Q15, D3Q19, D3Q27) were tested for the passive-scalar LB and both the second- and fourth-order RK methods were investigated. There was no significant difference observed in the accuracy of the LB or RK schemes. The passive scalar D3Q7 LB discretisation tended to provide computational benefits, while the second order RK scheme is superior in memory usage. This paper makes contributions relating to the modelling of thermocapillary flows and to understanding the behaviour of droplet capture with thermal sources analogous to thermal tweezers. Four primary contributions to the literature are identified. First, a new 3D thermocapillary, central-moment phase-field LB model is presented and implemented in the open-source software, waLBerla. Second, the accuracy and computational performance of various techniques to resolve the energy equation for multiphase, incompressible fluids is investigated. Third, the dynamic droplet transport behaviour in the presence of thermal sources is studied and insight is provided on the potential ability to manipulate droplets based on local domain heating. Finally, a concise analysis of the computational performance together with near-perfect scaling results on NVIDIA and AMD GPU-clusters is shown. This research enables the detailed study of droplet manipulation and control in thermocapillary devices.

Second harmonic generation (SHG) is forbidden in centrosymmetric molecular materials. However, a signal is frequently observed from interfaces where the symmetry is broken. Whereas the effect can be phenomenologically accommodated, an ab initio qualitative and quantitative description has remained elusive, preventing the exploration of fascinating questions such as how deep below the surface the second harmonic can still be generated. To answer such questions, we present an ab initio multiscale approach to compute the total and layer-dependent intensity of surface SHG from molecular crystals. The microscopic origin of surface SHG is identified in layer-dependent models with embedding partial charges combined with density functional theory. The models show increasing symmetry-breaking distortions of the electron cloud around the molecules as the surface layer is approached. The SHG at the molecular level is determined using time-dependent density functional theory and then brought to the scale of macroscopic films through a rigorous self-consistent multiple scattering formalism capable of predicting the measurable optical intensities of the generated second harmonic signal. We study crystalline molecular films with centrosymmetric unit cells of 7,9-Dibromobenzo[h]quinolin-10-ol. The intensity of the SHG at the surface layer is two orders of magnitude larger than at the next layer below and three orders of magnitude larger than two layers below. Besides providing fundamental understanding, our approach can be used for designing and optimizing optical devices containing nonlinear molecular materials, such as molecular laminates. We show that a relatively basic Kretschmann-like setup can enhance the surface SHG of a crystalline film of centrosymmetric molecular unit cells a thousand times., Comment: 12 pages, 6 figures

Federated clustering, an integral aspect of federated machine learning, enables multiple data sources to collaboratively cluster their data, maintaining decentralization and preserving privacy. In this paper, we introduce a novel federated clustering algorithm named Dynamically Weighted Federated k-means (DWF k-means) based on Lloyd's method for k-means clustering, to address the challenges associated with distributed data sources and heterogeneous data. Our proposed algorithm combines the benefits of traditional clustering techniques with the privacy and scalability benefits offered by federated learning. The algorithm facilitates collaborative clustering among multiple data owners, allowing them to cluster their local data collectively while exchanging minimal information with the central coordinator. The algorithm optimizes the clustering process by adaptively aggregating cluster assignments and centroids from each data source, thereby learning a global clustering solution that reflects the collective knowledge of the entire federated network. We address the issue of empty clusters, which commonly arises in the context of federated clustering. We conduct experiments on multiple datasets and data distribution settings to evaluate the performance of our algorithm in terms of clustering score, accuracy, and v-measure. The results demonstrate that our approach can match the performance of the centralized classical k-means baseline, and outperform existing federated clustering methods like k-FED in realistic scenarios.

Nanophotonic concepts can improve many measurement techniques by enhancing and tailoring the light-matter interaction. However, the optical response of devices that implement such techniques can be intricate, depending on the sample under investigation. That combination of a promise and a challenge makes nanophotonics a ripe field for applying the concept of a digital twin: a digital representation of an entire real-world device. In this work, we detail the concept of a digital twin with the example of a nanophotonically-enhanced chiral sensing platform. In that platform, helicity-preserving cavities with diffractive mirrors enhance the light-matter interaction between chiral molecules and circularly polarized light, allowing a faster measurement of the circular dichroism of the molecules. However, the sheer presence of the molecules affects the cavity's functionality, demanding a holistic treatment to understand the device's performance. In our digital twin, optical and quantum chemistry simulations are fused to provide a comprehensive description of the device with the molecules across all length scales and predict the circular dichroism spectrum of the device containing molecules to be sensed. Performing simulations in lockstep with the experiment will allow a clear interpretation of the results of complex measurements. We also demonstrate how to design a cavity-enhanced circular dichroism spectrometer by utilizing our digital twin. The digital twin can be used to guide experiments and analyze results, and its underlying concept can be translated to many other optical experiments., Comment: 17 pages, 6 figures

The study of the operational complexity of minimal pumping constants started in [J. DASSOW and I. JECKER. Operational complexity and pumping lemmas. Acta Inform., 59:337-355, 2022], where an almost complete picture of the operational complexity of minimal pumping constants for two different variants of pumping lemmata from the literature was given. We continue this research by considering a pumping lemma for regular languages that allows pumping of sub-words at any position of the considered word, if the sub-word is long enough [S. J. SAVITCH. Abstract Machines and Grammars. 1982]. First we improve on the simultaneous regulation of minimal pumping constants induced by different pumping lemmata including Savitch's pumping lemma. In this way we are able to simultaneously regulate four different minimal pumping constants. This is a novel result in the field of descriptional complexity. Moreover, for Savitch's pumping lemma we are able to completely classify the range of the minimal pumping constant for the operations Kleene star, reversal, complement, prefix- and suffix-closure, union, set-subtraction, concatenation, intersection, and symmetric difference. In this way, we also solve some of the open problems from the paper that initiated the study of the operational complexity of minimal pumping constants mentioned above., Comment: In Proceedings AFL 2023, arXiv:2309.01126

In this work, we present a clear evidence, based on numerical simulations and experiments, that the polarization compensation due to trapped charge strongly influences the ON/ OFF ratio in Hf 0.5 Zr 0.5 O 2 (HZO)-based ferroelectric tunnel junctions (FTJs). Furthermore, we identify and explain compensation conditions that enable an optimal operation of FTJs. Our results provide both key physical insights and design guidelines for the operation of FTJs as multilevel synaptic devices.

Clustering a graph when the clusters can overlap can be seen from three different angles: We may look for cliques that cover the edges of the graph with bounded overlap, we may look to add or delete few edges to uncover the cluster structure, or we may split vertices to separate the clusters from each other. Splitting a vertex $v$ means to remove it and to add two new copies of $v$ and to make each previous neighbor of $v$ adjacent with at least one of the copies. In this work, we study underlying computational problems regarding the three angles to overlapping clusterings, in particular when the overlap is small. We show that the above-mentioned covering problem is NP-complete. We then make structural observations that show that the covering viewpoint and the vertex-splitting viewpoint are equivalent, yielding NP-hardness for the vertex-splitting problem. On the positive side, we show that splitting at most $k$ vertices to obtain a cluster graph has a problem kernel with $O(k)$ vertices. Finally, we observe that combining our hardness results with the so-called critical-clique lemma yields NP-hardness for Cluster Editing with Vertex Splitting, which was previously open (Abu-Khzam et al. [ISCO 2018]) and independently shown to be NP-hard by Arrighi et al. [IPEC 2023]. We observe that a previous version of the critical-clique lemma was flawed; a corrected version has appeared in the meantime on which our hardness result is based., Comment: 30 pages, 9 figures. Appears in SOFSEM 2024

Nonlinear optics is essential for many recent photonic technologies. Here, we introduce a novel multi-scale approach to simulate the nonlinear optical response of molecular nanomaterials combining ab initio quantum-chemical and classical Maxwell-scattering computations. In this approach, the first hyperpolarizability tensor is computed with time-dependent density-functional theory and translated into a multi-scattering formalism that considers the optical interaction between neighboring molecules. A novel object is introduce to perform this transition from quantum-chemistry to classical scattering theory: the Hyper-Transition(T)-matrix. With this object at hand, the nonlinear optical response from single molecules and also from entire photonic devices can be computed, incorporating the full tensorial and dispersive nature of the optical response of the molecules. To demonstrate the applicability of our novel approach, the generation of a second-harmonic signal from a thin film of a Urea molecular crystal is computed and compared to more traditional simulations. Furthermore, an optical cavity is designed, which enhances the second-harmonic response of the molecular film by more than two orders of magnitude. Our approach is highly versatile and accurate and can be the working horse for the future exploration of nonlinear photonic molecular materials in structured photonic environments.

We analyze spatial spreading in a population model with logistic growth and chemorepulsion. In a parameter range of short-range chemo-diffusion, we use geometric singular perturbation theory and functional-analytic farfield-core decompositions to identify spreading speeds with marginally stable front profiles. In particular, we identify a sharp boundary between between linearly determined, pulled propagation, and nonlinearly determined, pushed propagation, induced by the chemorepulsion. The results are motivated by recent work on singular limits in this regime using PDE methods., Comment: 34 pages, 1 figure

The primary goal of the EuroHPC JU project SCALABLE is to develop an industrial Lattice Boltzmann Method (LBM)-based computational fluid dynamics (CFD) solver capable of exploiting current and future extreme scale architectures, expanding current capabilities of existing industrial LBM solvers by at least two orders of magnitude in terms of processor cores and lattice cells, while preserving its accessibility from both the end-user and software developer's point of view. This is accomplished by transferring technology and knowledge between an academic code (waLBerla) and an industrial code (LaBS). This paper briefly introduces the characteristics and main features of both software packages involved in the process. We also highlight some of the performance achievements in scales of up to tens of thousand of cores presented on one academic and one industrial benchmark case.