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Disturbance rejection in high-precision control applications can be significantly improved upon via online convex optimization (OCO). This includes classical techniques such as recursive least squares (RLS) and more recent, regret-based formulations. However, these methods can cause instabilities in the presence of model uncertainty. This paper introduces a safety filter for systems with OCO in the form of adaptive finite impulse response (FIR) filtering to ensure robust disturbance rejection. The safety filter enforces a robust stability constraint on the FIR coefficients while minimally altering the OCO command in the $\infty$-norm cost. Additionally, we show that the induced $\ell_\infty$-norm allows for easy online implementation of the safety filter by directly limiting the OCO command. The constraint can be tuned to trade off robustness and performance. We provide a simple example to demonstrate the safety filter., Comment: Submitted to the 2025 European Control Conference. This paper builds on the work done in arXiv:2405.07037

This paper introduces a novel method for inter-camera color calibration for multispectral imaging with camera arrays using a consensus image. Capturing images using multispectral camera arrays has gained importance in medical, agricultural, and environmental processes. Due to fabrication differences, noise, or device altering, varying pixel sensitivities occur, influencing classification processes. Therefore, color calibration between the cameras is necessary. In existing methods, one of the camera images is chosen and considered as a reference, ignoring the color information of all other recordings. Our new approach does not just take one image as reference, but uses statistical information such as the location parameter to generate a consensus image as basis for calibration. This way, we managed to improve the PSNR values for the linear regression color correction algorithm by 1.15 dB and the improved color difference (iCID) values by 2.81.

Using techniques coming from the theory of marked bases, we develop new computational methods for detection and construction of Cohen-Macaulay, Gorenstein and complete intersection homogeneous polynomial ideals. Thanks to the functorial properties of marked bases, an elementary and effective proof of the openness of arithmetically Cohen-Macaulay, arithmetically Gorenstein and strict complete intersection loci in a Hilbert scheme follows, for a non-constant Hilbert polynomial., Comment: 29 pages, comments are welcome

Since performance improvements of computers are stagnating, new technologies and computer paradigms are hot research topics. Memristor-based In-Memory Computing is one of the promising candidates for the post-CMOS era, which comes in many flavors. Processing In memory Array (PIA) or using memory, is on of them which is a relatively new approach, and substantially different than traditional CMOS-based logic design. Consequently, there is a lack of publicly available CAD tools for memristive PIA design and evaluation. Here, we present ATOMIC: an Automatic Tool for Memristive IMPLY-based Circuit-level Simulation and Validation. Using our tool, a large portion of the simulation, evaluation, and validation process can be performed automatically, drastically reducing the development time for memristive PIA systems, in particular those using IMPLY logic. The code is available at https://github.com/fabianseiler/ATOMIC., Comment: 4 pages, 5 figures, Submitted and Presented at the Embedded Systems Software Competition 2024 at ESWEEK

Control system design is a crucial aspect of modern engineering with far-reaching applications across diverse sectors including aerospace, automotive systems, power grids, and robotics. Despite advances made by Large Language Models (LLMs) in various domains, their application in control system design remains limited due to the complexity and specificity of control theory. To bridge this gap, we introduce ControlAgent, a new paradigm that automates control system design via novel integration of LLM agents and control-oriented domain expertise. ControlAgent encodes expert control knowledge and emulates human iterative design processes by gradually tuning controller parameters to meet user-specified requirements for stability, performance, and robustness. ControlAgent integrates multiple collaborative LLM agents, including a central agent responsible for task distribution and task-specific agents dedicated to detailed controller design for various types of systems and requirements. ControlAgent also employs a Python computation agent that performs complex calculations and controller evaluations based on standard design information provided by task-specified LLM agents. Combined with a history and feedback module, the task-specific LLM agents iteratively refine controller parameters based on real-time feedback from prior designs. Overall, ControlAgent mimics the design processes used by (human) practicing engineers, but removes all the human efforts and can be run in a fully automated way to give end-to-end solutions for control system design with user-specified requirements. To validate ControlAgent's effectiveness, we develop ControlEval, an evaluation dataset that comprises 500 control tasks with various specific design goals. The effectiveness of ControlAgent is demonstrated via extensive comparative evaluations between LLM-based and traditional human-involved toolbox-based baselines.

The method of complex Langevin simulations is a tool that can be used to tackle the complex-action problem encountered, for instance, in finite-density lattice quantum chromodynamics or real-time lattice field theories. The method is based on a stochastic evolution of the dynamical degrees of freedom via (complex) Langevin equations, which, however, sometimes converge to the wrong equilibrium distributions. While the convergence properties of the evolution can to some extent be assessed by studying so-called boundary terms, we demonstrate in this contribution that boundary terms on their own are not sufficient as a correctness criterion. Indeed, in their absence complex Langevin simulation results might still be spoiled by unwanted so-called integration cycles. In particular, we elaborate on how the introduction of a kernel into the complex Langevin equation can - in principle - be used to control which integration cycles are sampled in a simulation such that correct convergence is restored., Comment: 7 pages, 3 figures; Proceedings of the 41st International Symposium on Lattice Field Theory (LATTICE 2024), 28th July - 3rd August 2024, Liverpool, United Kingdom

A pseudodifferential calculus for parameter-dependent operators on smooth manifolds with boundary in the spirit of Boutet de Monvel's algebra is constructed. The calculus contains, in particular, the resolvents of realizations of differential operators subject to global projection boundary conditions (spectral boundary conditions are a particular example); resolvent trace asymptotics are easily derived. The calculus is related to but different from the calculi developed by Grubb and Grubb-Seeley. We use ideas from the theory of pseudodifferential operators on manifolds with edges due to Schulze, in particular the concept of operator-valued symbols twisted by a group-action. Parameter-ellipticity in the calculus is characterized by the invertibility of three principal symbols: the homogeneous principal symbol, the principal boundary symbol, and the so-called principal limit symbol. The principal boundary symbol has, in general, a singularity in the co-variable/parameter space, the principal limit symbol is a new ingredient of our calculus., Comment: 75 pages

Capturing images using multispectral camera arrays has gained importance in medical, agricultural and environmental processes. However, using all available spectral bands is infeasible and produces much data, while only a fraction is needed for a given task. Nearby bands may contain similar information, therefore redundant spectral bands should not be considered in the evaluation process to keep complexity and the data load low. In current methods, a restricted and pre-determined number of spectral bands is selected. Our approach improves this procedure by including preset conditions such as noise or the bandwidth of available filters, minimizing spectral redundancy. Furthermore, a minimal filter selection can be conducted, keeping the hardware setup at low costs, while still obtaining all important spectral information. In comparison to the fast binary search filter band selection method, we managed to reduce the amount of misclassified objects of the SMM dataset from 318 to 124 using a random forest classifier.

We present a method to train neural network controllers with guaranteed stability margins. The method is applicable to linear time-invariant plants interconnected with uncertainties and nonlinearities that are described by integral quadratic constraints. The type of stability margin we consider is the disk margin. Our training method alternates between a training step to maximize reward and a stability margin-enforcing step. In the stability margin enforcing-step, we solve a semidefinite program to project the controller into the set of controllers for which we can certify the desired disk margin.

AB-stacked bilayer graphene has emerged as a fascinating yet simple platform for exploring macroscopic quantum phenomena of correlated electrons. Unexpectedly, a phase with negative dR/dT has recently been observed when a large electric displacement field is applied and the charge carrier density is tuned to the vicinity of an ultra-low-density van Hove singularity. This phase exhibits features consistent with Wigner crystallization, including a characteristic temperature dependence and non-linear current bias behavior. However, more direct evidence for the emergence of an electron crystal in AB-stacked bilayer graphene at zero magnetic field remains elusive. Here we explore the low-frequency noise consistent with depinning and sliding of a Wigner crystal lattice. The current bias and frequency dependence of these noise spectra align well with findings from previous experimental and theoretical studies on the quantum electron solids. Our results offer transport signatures consistent with Wigner crystallization in AB-stacked bilayer graphene at zero and finite magnetic fields, paving the way for further substantiating an anomalous Hall crystal in its original form.

Multispectral imaging is very beneficial in diverse applications, like healthcare and agriculture, since it can capture absorption bands of molecules in different spectral areas. A promising approach for multispectral snapshot imaging are camera arrays. Image processing is necessary to warp all different views to the same view to retrieve a consistent multispectral datacube. This process is also called multispectral image registration. After a cross spectral disparity estimation, an occlusion detection is required to find the pixels that were not recorded by the peripheral cameras. In this paper, a novel fast edge-aware occlusion detection is presented, which is shown to reduce the runtime by at least a factor of 12. Moreover, an evaluation on ground truth data reveals better performance in terms of precision and recall. Finally, the quality of a final multispectral datacube can be improved by more than 1.5 dB in terms of PSNR as well as in terms of SSIM in an existing multispectral registration pipeline. The source code is available at \url{https://github.com/FAU-LMS/fast-occlusion-detection}.

Continuous transportation of material in the mining industry is achieved by the dispatch of autonomous haul-trucks with discrete haulage capacities. Recently, Monte Carlo Tree Search (MCTS) was successfully deployed in tackling challenges of long-run optimality, scalability and adaptability in haul-truck dispatch. Typically, operational constraints imposed on the mine site are satisfied by heuristic controllers or human operators independent of the dispatch planning. This article incorporates operational constraint satisfaction into the dispatch planning by utilising the MCTS based dispatch planner Flow-Achieving Scheduling Tree (FAST). Operational constraint violation and satisfaction are modelled as opportunity costs in the combinatorial optimisation problem of dispatch. Explicit cost formulations are avoided by utilising MCTS generator models to derive opportunity costs. Experimental studies with four types of operational constraints demonstrate the success of utilising opportunity costs for constraint satisfaction, and the effectiveness of integrating constraints into dispatch planning., Comment: International Conference on Automation Science and Engineering (CASE), 2024

The recently introduced structured input-output analysis is a powerful method for capturing nonlinear phenomena associated with incompressible flows, and this paper extends that method to the compressible regime. The proposed method relies upon a reformulation of the compressible Navier-Stokes equations, which allows for an exact quadratic formulation of the dynamics of perturbations about a steady base flow. To facilitate the structured input-output analysis, a pseudo-linear model for the quadratic nonlinearity is proposed and the structural information of the nonlinearity is embedded into a structured uncertainty comprising unknown `perturbations'. The structured singular value framework is employed to compute the input-output gain, which provides an estimate of the robust stability margin of the flow perturbations, as well as the forcing and response modes that are consistent with the nonlinearity structure. The analysis is then carried out on a plane, laminar compressible Couette flow over a range of Mach numbers. The structured input-output gains identify an instability mechanism, characterized by a spanwise elongated structure in the streamwise-spanwise wavenumber space at a subsonic Mach number, that evolves into an oblique structure at sonic and supersonic Mach numbers. In addition, the structured input-output forcing and response modes provide insight into the thermodynamic and momentum characteristics associated with a source of instability. Comparisons with a resolvent/unstructured analysis reveal discrepancies in the distribution of input-output gains over the wavenumber space as well as in the modal behavior of an instability, thus highlighting the strong correlation between the structural information of the nonlinearity and the underlying flow physics., Comment: Submitted to the Journal of Fluid Mechanics

Retrieving the reflectance spectrum from objects is an essential task for many classification and detection problems, since many materials and processes have a unique spectral behaviour. In many cases, it is highly desirable to capture hyperspectral images due to the high spectral flexibility. Often, it is even necessary to capture hyperspectral videos or at least to be able to record a hyperspectral image at once, also called snapshot hyperspectral imaging, to avoid spectral smearing. For this task, a high-resolution snapshot hyperspectral camera array using a hexagonal shape is introduced.The hexagonal array for hyperspectral imaging uses off-the-shelf hardware, which enables high flexibility regarding employed cameras, lenses and filters. Hence, the spectral range can be easily varied by mounting a different set of filters. Moreover, the concept of using off-the-shelf hardware enables low prices in comparison to other approaches with highly specialized hardware. Since classical industrial cameras are used in this hyperspectral camera array, the spatial and temporal resolution is very high, while recording 37 hyperspectral channels in the range from 400 nm to 760 nm in 10 nm steps. A registration process is required for near-field imaging, which maps the peripheral camera views to the center view. It is shown that this combination using a hyperspectral camera array and the corresponding image registration pipeline is superior in comparison to other popular snapshot approaches. For this evaluation, a synthetic hyperspectral database is rendered. On the synthetic data, the novel approach outperforms its best competitor by more than 3 dB in reconstruction quality. This synthetic data is also used to show the superiority of the hexagonal shape in comparison to an orthogonal-spaced one. Moreover, a real-world high resolution hyperspectral video database is provided.

According to a conservative estimate, a 1% reduction in forecast error for a 10 GW energy utility can save up to $ 1.6 million annually. In our context, achieving precise forecasts of future power consumption is crucial for operating flexible energy assets using model predictive control approaches. Specifically, this work focuses on the load profile forecast of a first-year energy community with the common practical challenge of limited historical data availability. We propose to pre-train the load prediction models with open-access synthetic load profiles using transfer learning techniques to tackle this challenge. Results show that this approach improves both, the training stability and prediction error. In a test case with 74 households, the prediction mean squared error (MSE) decreased from 0.34 to 0.13, showing transfer learning based on synthetic load profiles to be a viable approach to compensate for a lack of historic data., Comment: The paper has been accepted for the IEEE RTSI 2024 conference

This paper derives a complete set of quadratic constraints (QCs) for the repeated ReLU. The complete set of QCs is described by a collection of matrix copositivity conditions. We also show that only two functions satisfy all QCs in our complete set: the repeated ReLU and flipped ReLU. Thus our complete set of QCs bounds the repeated ReLU as tight as possible up to the sign invariance inherent in quadratic forms. We derive a similar complete set of incremental QCs for repeated ReLU, which can potentially lead to less conservative Lipschitz bounds for ReLU networks than the standard LipSDP approach. The basic constructions are also used to derive the complete sets of QCs for other piecewise linear activation functions such as leaky ReLU, MaxMin, and HouseHolder. Finally, we illustrate the use of the complete set of QCs to assess stability and performance for recurrent neural networks with ReLU activation functions. We rely on a standard copositivity relaxation to formulate the stability/performance condition as a semidefinite program. Simple examples are provided to illustrate that the complete sets of QCs and incremental QCs can yield less conservative bounds than existing sets.

The implementation of modern monitoring systems for power quality disturbances have the potential to generate substantial amounts of data, reaching a point where transmission and storage of high-frequency measurements become impractical. This research paper addresses this challenge by presenting a new, AI-based data compression method. It is based on existing, multi-level compression schemes; however, it uses state-of-the-art technologies, such as autoencoders, to improve the performance. Furthermore, it solves the problem that such algorithms usually cannot ensure an error bound. The scheme is tested on synthetically generated power quality disturbance samples. The evaluation is performed using different metrics such as final compression rate and overhead size. Compression rates between 5 and 68 were achieved depending on the error bound and noise level. Additionally, the impact of the compression on the performance of subsequent algorithms is determined by applying a classification algorithm to the decompressed data. The classification accuracy only declined by 0.8--11.9 \%, depending on the chosen error bound., Comment: 6 pages, 7 figures, 1 table, conference, SEST 2024

In this work, we present a comparison between color spaces namely YUV, LAB, RGB and their effect on learned image compression. For this we use the structure and color based learned image codec (SLIC) from our prior work, which consists of two branches - one for the luminance component (Y or L) and another for chrominance components (UV or AB). However, for the RGB variant we input all 3 channels in a single branch, similar to most learned image codecs operating in RGB. The models are trained for multiple bitrate configurations in each color space. We report the findings from our experiments by evaluating them on various datasets and compare the results to state-of-the-art image codecs. The YUV model performs better than the LAB variant in terms of MS-SSIM with a Bj{\o}ntegaard delta bitrate (BD-BR) gain of 7.5\% using VTM intra-coding mode as the baseline. Whereas the LAB variant has a better performance than YUV model in terms of CIEDE2000 having a BD-BR gain of 8\%. Overall, the RGB variant of SLIC achieves the best performance with a BD-BR gain of 13.14\% in terms of MS-SSIM and a gain of 17.96\% in CIEDE2000 at the cost of a higher model complexity., Comment: Accepter pre-print version for ICIP 2024

The contact process is a simple model for the spread of an infection in a structured population. We investigate the case when the underlying structure evolves dynamically as a degree-dependent dynamical percolation model. Starting with a connected locally finite base graph we initially declare edges independently open with a probability that is allowed to depend on the degree of the adjacent vertices and closed otherwise. Edges are independently updated with a rate depending on the degrees and then are again declared open and closed with the same probabilities. We are interested in the contact process, where infections are only allowed to spread via open edges. Our aim is to analyze the impact of the update speed and the probability for edges to be open on the existence of a phase transition. For a general connected locally finite graph, our first result gives sufficient conditions for the critical value for survival to be strictly positive. Furthermore, in the setting of Bienaym\'e-Galton-Watson trees, we show that the process survives strongly with positive probability for any infection rate if the offspring distribution has a stretched exponential tail with an exponent depending on the percolation probability and the update speed. In particular, if the offspring distribution follows a power law and the connection probability is given by a product kernel and the update speed exhibits polynomial behaviour, we provide a complete characterisation of the phase transition., Comment: 56 pages, 4 figures

Multispectral imaging aims at recording images in different spectral bands. This is extremely beneficial in diverse discrimination applications, for example in agriculture, recycling or healthcare. One approach for snapshot multispectral imaging, which is capable of recording multispectral videos, is by using camera arrays, where each camera records a different spectral band. Since the cameras are at different spatial positions, a registration procedure is necessary to map every camera to the same view. In this paper, we present a multispectral snapshot image registration with three novel components. First, a cross spectral disparity estimation network is introduced, which is trained on a popular stereo database using pseudo spectral data augmentation. Subsequently, this disparity estimation is used to accurately detect occlusions by warping the disparity map in a layer-wise manner. Finally, these detected occlusions are reconstructed by a learned deep guided neural network, which leverages the structure from other spectral components. It is shown that each element of this registration process as well as the final result is superior to the current state of the art. In terms of PSNR, our registration achieves an improvement of over 3 dB. At the same time, the runtime is decreased by a factor of over 3 on a CPU. Additionally, the registration is executable on a GPU, where the runtime can be decreased by a factor of 111. The source code and the data is available at https://github.com/FAU-LMS/MSIR.

Conservation laws are of great theoretical and practical interest. We describe a novel approach to machine learning conservation laws of finite-dimensional dynamical systems using trajectory data. It is the first such approach based on kernel methods instead of neural networks which leads to lower computational costs and requires a lower amount of training data. We propose the use of an "indeterminate" form of kernel ridge regression where the labels still have to be found by additional conditions. We use here a simple approach minimising the length of the coefficient vector to discover a single conservation law.

Forward stagewise regression is a simple algorithm that can be used to estimate regularized models. The updating rule adds a small constant to a regression coefficient in each iteration, such that the underlying optimization problem is solved slowly with small improvements. This is similar to gradient boosting, with the essential difference that the step size is determined by the product of the gradient and a step length parameter in the latter algorithm. One often overlooked challenge in gradient boosting for distributional regression is the issue of a vanishing small gradient, which practically halts the algorithm's progress. We show that gradient boosting in this case oftentimes results in suboptimal models, especially for complex problems certain distributional parameters are never updated due to the vanishing gradient. Therefore, we propose a stagewise boosting-type algorithm for distributional regression, combining stagewise regression ideas with gradient boosting. Additionally, we extend it with a novel regularization method, correlation filtering, to provide additional stability when the problem involves a large number of covariates. Furthermore, the algorithm includes best-subset selection for parameters and can be applied to big data problems by leveraging stochastic approximations of the updating steps. Besides the advantage of processing large datasets, the stochastic nature of the approximations can lead to better results, especially for complex distributions, by reducing the risk of being trapped in a local optimum. The performance of our proposed stagewise boosting distributional regression approach is investigated in an extensive simulation study and by estimating a full probabilistic model for lightning counts with data of more than 9.1 million observations and 672 covariates.

We study monolayer WSe2 using ultrafast electron diffraction. We introduce an approach to quantitatively extract atomic-site-specific information, providing an element-specific view of incoherent atomic vibrations following femtosecond excitation. Via differences between W and Se vibrations, we identify stages in the nonthermal evolution of the lattice. Combined with a calculated phonon dispersion, this element specificity enables us to identify a long-lasting overpopulation of specific optical phonons, and to interpret the stages as energy transfer processes between specific phonon groups. These results demonstrate the appeal of resolving element-specific vibrational information in the ultrafast time domain., Comment: 13 pages, 3 figures

D-xylose is the second most abundant monosaccharide found in lignocellulose and is of biotechnological importance for producing second-generation ethanol and other high-value chemical compounds. D-xylose conversion to ethanol is promoted by microbial fermentation, mainly by bacteria, yeasts, or filamentous fungi. Considering yeasts, species belonging to the CTG(Ser1) or CTG(Ala) clade display a remarkable ability to ferment D-xylose to ethanol and other compounds; however, these yeasts are not employed on an industrial scale due to the poor fermentative performance compared to conventional yeasts, like Saccharomyces cerevisiae, and also due to the lack of a molecular toolbox for development of new strains tailored to fermentation stress tolerance and performance. Thus, the purpose of this review is to evaluate the major molecular tools (e.g., transformation markers and techniques, vectors, regulatory sequences, and gene editing techniques) available for the most studied yeasts of CTG(Ser1) clade, like Scheffersomyces, Spathaspora, Candida and Yamadazyma species, and the CTG(Ala) clade representative Pachysolen tannophilus. Furthermore, we synthesized the current state-of-the-art molecular developments and perspectives for D-xylose fermenting yeast strain design., Comment: 32 pages, 4 tables

Online convex optimization (OCO) is a powerful tool for learning sequential data, making it ideal for high precision control applications where the disturbances are arbitrary and unknown in advance. However, the ability of OCO-based controllers to accurately learn the disturbance while maintaining closed-loop stability relies on having an accurate model of the plant. This paper studies the performance of OCO-based controllers for linear time-invariant (LTI) systems subject to disturbance and model uncertainty. The model uncertainty can cause the closed-loop to become unstable. We provide a sufficient condition for robust stability based on the small gain theorem. This condition is easily incorporated as an on-line constraint in the OCO controller. Finally, we verify via numerical simulations that imposing the robust stability condition on the OCO controller ensures closed-loop stability.

This paper presents sufficient conditions for the stability and $\ell_2$-gain performance of recurrent neural networks (RNNs) with ReLU activation functions. These conditions are derived by combining Lyapunov/dissipativity theory with Quadratic Constraints (QCs) satisfied by repeated ReLUs. We write a general class of QCs for repeated RELUs using known properties for the scalar ReLU. Our stability and performance condition uses these QCs along with a "lifted" representation for the ReLU RNN. We show that the positive homogeneity property satisfied by a scalar ReLU does not expand the class of QCs for the repeated ReLU. We present examples to demonstrate the stability / performance condition and study the effect of the lifting horizon.

This letter considers assignment problems consisting of n pursuers attempting to intercept n targets. We consider stationary targets as well as targets maneuvering toward an asset. The assignment algorithm relies on an n x n cost matrix where entry (i, j) is the minimum time for pursuer i to intercept target j. Each entry of this matrix requires the solution of a nonlinear optimal control problem. This subproblem is computationally intensive and hence the computational cost of the assignment is dominated by the construction of the cost matrix. We propose to use neural networks for function approximation of the minimum time until intercept. The neural networks are trained offline, thus allowing for real-time online construction of cost matrices. Moreover, the function approximators have sufficient accuracy to obtain reasonable solutions to the assignment problem. In most cases, the approximators achieve assignments with optimal worst case intercept time. The proposed approach is demonstrated on several examples with increasing numbers of pursuers and targets., Comment: 6 pages, 6 tables, 1 figure. Presented at the 2022 American Control Conference

In this paper, a method is presented to synthesize neural network controllers such that the feedback system of plant and controller is dissipative, certifying performance requirements such as L2 gain bounds. The class of plants considered is that of linear time-invariant (LTI) systems interconnected with an uncertainty, including nonlinearities treated as an uncertainty for convenience of analysis. The uncertainty of the plant and the nonlinearities of the neural network are both described using integral quadratic constraints (IQCs). First, a dissipativity condition is derived for uncertain LTI systems. Second, this condition is used to construct a linear matrix inequality (LMI) which can be used to synthesize neural network controllers. Finally, this convex condition is used in a projection-based training method to synthesize neural network controllers with dissipativity guarantees. Numerical examples on an inverted pendulum and a flexible rod on a cart are provided to demonstrate the effectiveness of this approach., Comment: Submitted to the journal Automatica, 14 pages, 7 figures

We present the formalism and implementation of quasi-particle self-consistent GW (qsGW) and eigenvalue only quasi-particle self-consistent GW (evGW) adapted to standard quantum chemistry packages. Our implementation is benchmarked against high-level quantum chemistry computations (coupled-cluster theory) and experimental results using a representative set of molecules. Furthermore, we compare the qsGW approach for five molecules relevant for organic photovoltaics to self-consistent GW results (scGW) and analyze the effects of the self-consistency on the ground state density by comparing calculated dipole moments to their experimental values. We show that qsGW makes a significant improvement over conventional G0W0 and that partially self-consistent flavors (in particular evGW) can be excellent alternatives.

To align mobile robot navigation policies with user preferences through reinforcement learning from human feedback (RLHF), reliable and behavior-diverse user queries are required. However, deterministic policies fail to generate a variety of navigation trajectory suggestions for a given navigation task. In this paper, we introduce EnQuery, a query generation approach using an ensemble of policies that achieve behavioral diversity through a regularization term. For a given navigation task, EnQuery produces multiple navigation trajectory suggestions, thereby optimizing the efficiency of preference data collection with fewer queries. Our methodology demonstrates superior performance in aligning navigation policies with user preferences in low-query regimes, offering enhanced policy convergence from sparse preference queries. The evaluation is complemented with a novel explainability representation, capturing full scene navigation behavior of the mobile robot in a single plot. Our code is available online at https://github.com/hrl-bonn/EnQuery.

In this paper, we explore the capabilities of state-of-the-art large language models (LLMs) such as GPT-4, Claude 3 Opus, and Gemini 1.0 Ultra in solving undergraduate-level control problems. Controls provides an interesting case study for LLM reasoning due to its combination of mathematical theory and engineering design. We introduce ControlBench, a benchmark dataset tailored to reflect the breadth, depth, and complexity of classical control design. We use this dataset to study and evaluate the problem-solving abilities of these LLMs in the context of control engineering. We present evaluations conducted by a panel of human experts, providing insights into the accuracy, reasoning, and explanatory prowess of LLMs in control engineering. Our analysis reveals the strengths and limitations of each LLM in the context of classical control, and our results imply that Claude 3 Opus has become the state-of-the-art LLM for solving undergraduate control problems. Our study serves as an initial step towards the broader goal of employing artificial general intelligence in control engineering.

Spin-orbit coupling (SOC) and electron-electron interaction can mutually influence each other and give rise to a plethora of intriguing phenomena in condensed matter systems. In pristine bilayer graphene, which has weak SOC, intrinsic Lifshitz transitions and concomitant van-Hove singularities lead to the emergence of many-body correlated phases. Layer-selective SOC can be proximity induced by adding a layer of tungsten diselenide (WSe2) on its one side. By applying an electric displacement field, the system can be tuned across a spectrum wherein electronic correlation, SOC, or a combination of both dominates. Our investigations reveal an intricate phase diagram of proximity-induced SOC-selective bilayer graphene. Not only does this phase diagram include those correlated phases reminiscent of SOC-free doped bilayer graphene, but it also hosts unique SOC-induced states allowing a compelling measurement of valley g-factor and a seemingly impossible correlated insulator at charge neutrality, thereby showcasing the remarkable tunability of the interplay between interaction and SOC in WSe2 enriched bilayer graphene.

In this paper, we revisit model-free policy search on an important robust control benchmark, namely $\mu$-synthesis. In the general output-feedback setting, there do not exist convex formulations for this problem, and hence global optimality guarantees are not expected. Apkarian (2011) presented a nonconvex nonsmooth policy optimization approach for this problem, and achieved state-of-the-art design results via using subgradient-based policy search algorithms which generate update directions in a model-based manner. Despite the lack of convexity and global optimality guarantees, these subgradient-based policy search methods have led to impressive numerical results in practice. Built upon such a policy optimization persepctive, our paper extends these subgradient-based search methods to a model-free setting. Specifically, we examine the effectiveness of two model-free policy optimization strategies: the model-free non-derivative sampling method and the zeroth-order policy search with uniform smoothing. We performed an extensive numerical study to demonstrate that both methods consistently replicate the design outcomes achieved by their model-based counterparts. Additionally, we provide some theoretical justifications showing that convergence guarantees to stationary points can be established for our model-free $\mu$-synthesis under some assumptions related to the coerciveness of the cost function. Overall, our results demonstrate that derivative-free policy optimization offers a competitive and viable approach for solving general output-feedback $\mu$-synthesis problems in the model-free setting., Comment: Submitted to L4DC 2024

Let $I$ be a monomial ideal in two variables generated by three monomials and let $\mathcal{R}(I)$ be its Rees ideal. We describe an algorithm to compute the minimal generating set of $\mathcal{R}(I)$. Based on the data obtained by this algorithm, we build a graph that encodes the minimal free resolution of $\mathcal{R}(I)$. We explicitly describe the modules and differentials on the minimal free resolution of $\mathcal{R}(I)$.

Quadratic systems with lossless quadratic terms arise in many applications, including models of atmosphere and incompressible fluid flows. Such systems have a trapping region if all trajectories eventually converge to and stay within a bounded set. Conditions for the existence and characterization of trapping regions have been established in prior works for boundedness analysis. However, prior solutions have used non-convex optimization methods, resulting in conservative estimates. In this paper, we build on this prior work and provide a convex semidefinite programming condition for the existence of a trapping region. The condition allows precise verification or falsification of the existence of a trapping region. If a trapping region exists, then we provide a second semidefinite program to compute the least conservative trapping region in the form of a ball. Two low-dimensional systems are provided as examples to illustrate the results. A third high-dimensional example is also included to demonstrate that the computation required for the analysis can be scaled to systems of up to $\sim O(100)$ states. The proposed method provides a precise and computationally efficient numerical approach for computing trapping regions. We anticipate this work will benefit future studies on modeling and control of lossless quadratic dynamical systems.

In many recent works, the potential of Exploratory Landscape Analysis (ELA) features to numerically characterize, in particular, single-objective continuous optimization problems has been demonstrated. These numerical features provide the input for all kinds of machine learning tasks on continuous optimization problems, ranging, i.a., from High-level Property Prediction to Automated Algorithm Selection and Automated Algorithm Configuration. Without ELA features, analyzing and understanding the characteristics of single-objective continuous optimization problems is -- to the best of our knowledge -- very limited. Yet, despite their usefulness, as demonstrated in several past works, ELA features suffer from several drawbacks. These include, in particular, (1.) a strong correlation between multiple features, as well as (2.) its very limited applicability to multi-objective continuous optimization problems. As a remedy, recent works proposed deep learning-based approaches as alternatives to ELA. In these works, e.g., point-cloud transformers were used to characterize an optimization problem's fitness landscape. However, these approaches require a large amount of labeled training data. Within this work, we propose a hybrid approach, Deep-ELA, which combines (the benefits of) deep learning and ELA features. Specifically, we pre-trained four transformers on millions of randomly generated optimization problems to learn deep representations of the landscapes of continuous single- and multi-objective optimization problems. Our proposed framework can either be used out-of-the-box for analyzing single- and multi-objective continuous optimization problems, or subsequently fine-tuned to various tasks focussing on algorithm behavior and problem understanding.

Complex-valued Gaussian processes are commonly used in Bayesian frequency-domain system identification as prior models for regression. If each realization of such a process were an $H_\infty$ function with probability one, then the same model could be used for probabilistic robust control, allowing for robustly safe learning. We investigate sufficient conditions for a general complex-domain Gaussian process to have this property. For the special case of processes whose Hermitian covariance is stationary, we provide an explicit parameterization of the covariance structure in terms of a summable sequence of nonnegative numbers. We then establish how an $H_\infty$ Gaussian process can serve as a prior for Bayesian system identification and as a probabilistic uncertainty model for probabilistic robust control. In particular, we compute formulas for refining the uncertainty model by conditioning on frequency-domain data and for upper-bounding the probability that the realizations of the process satisfy a given integral quadratic constraint., Comment: 20 pages, 2 figures. Submission to SICON. arXiv admin note: substantial text overlap with arXiv:2211.15923

Exploiting the infrared area of the spectrum for classification problems is getting increasingly popular, because many materials have characteristic absorption bands in this area. However, sensors in the short wave infrared (SWIR) area and even higher wavelengths have a very low spatial resolution in comparison to classical cameras that operate in the visible wavelength area. Thus, in this paper an upsampling method for SWIR images guided by a visible image is presented. For that, the proposed guided upsampling network (GUNet) uses a graph-regularized optimization problem based on learned affinities is presented. The evaluation is based on a novel synthetic near-field visible-SWIR stereo database. Different guided upsampling methods are evaluated, which shows an improvement of nearly 1 dB on this database for the proposed upsampling method in comparison to the second best guided upsampling network. Furthermore, a visual example of an upsampled SWIR image of a real-world scene is depicted for showing real-world applicability.

Since camera modules become more and more affordable, multispectral camera arrays have found their way from special applications to the mass market, e.g., in automotive systems, smartphones, or drones. Due to multiple modalities, the registration of different viewpoints and the required cross-spectral disparity estimation is up to the present extremely challenging. To overcome this problem, we introduce a novel spectral image synthesis in combination with a color agnostic transform. Thus, any recently published stereo matching network can be turned to a cross-spectral disparity estimator. Our novel algorithm requires only RGB stereo data to train a cross-spectral disparity estimator and a generalization from artificial training data to camera-captured images is obtained. The theoretical examination of the novel color agnostic method is completed by an extensive evaluation compared to state of the art including self-recorded multispectral data and a reference implementation. The novel color agnostic disparity estimation improves cross-spectral as well as conventional color stereo matching by reducing the average end-point error by 41% for cross-spectral and by 22% for mono-modal content, respectively.

In this paper, we consider the learning of a Reduced-Order Linear Parameter-Varying Model (ROLPVM) of a nonlinear dynamical system based on data. This is achieved by a two-step procedure. In the first step, we learn a projection to a lower dimensional state-space. In step two, an LPV model is learned on the reduced-order state-space using a novel, efficient parameterization in terms of neural networks. The improved modeling accuracy of the method compared to an existing method is demonstrated by simulation examples., Comment: Accepted to the 20th IFAC Symposium on System Identification (SYSID 2024)