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Accurate load forecasting is crucial for predictive control in many energy domain applications, with significant economic and ecological implications. To address these implications, this study provides an extensive benchmark of state-of-the-art deep learning models for short-term load forecasting in energy communities. Namely, LSTM, xLSTM, and Transformers are compared with benchmarks such as KNNs, synthetic load models, and persistence forecasting models. This comparison considers different scales of aggregation (e.g., number of household loads) and varying training data availability (e.g., training data time spans). Further, the impact of transfer learning from synthetic (standard) load profiles and the deep learning model size (i.e., parameter count) is investigated in terms of forecasting error. Implementations are publicly available and other researchers are encouraged to benchmark models using this framework. Additionally, a comprehensive case study, comprising an energy community of 50 households and a battery storage demonstrates the beneficial financial implications of accurate predictions. Key findings of this research include: (1) Simple persistence benchmarks outperform deep learning models for short-term load forecasting when the available training data is limited to six months or less; (2) Pretraining with publicly available synthetic load profiles improves the normalized Mean Absolute Error (nMAE) by an average of 1.28%pt during the first nine months of training data; (3) Increased aggregation significantly enhances the performance of deep learning models relative to persistence benchmarks; (4) Improved load forecasting, with an nMAE reduction of 1.1%pt, translates to an economic benefit of approximately 600EUR per year in an energy community comprising 50 households., Comment: This preprint was submitted to the Elsevier journal Energy and AI on December 18, 2024

Complex Langevin simulations are an attempt to solve the sign (or complex-action) problem encountered in various physical systems of interest. The method is based on a complexification of the underlying degrees of freedom and an evolution in an auxiliary time dimension. The complexification, however, does not come without drawbacks, the most severe of which is the infamous 'wrong convergence' problem, stating that complex Langevin simulations sometimes fail to produce correct answers despite their apparent convergence. It has long been realized that wrong convergence may - in principle - be fixed by the introduction of a suitable kernel into the complex Langevin equation, such that the conventional correctness criteria are met. However, as we discuss in this work, complex Langevin results may - especially in the presence of a kernel - still be affected by unwanted so-called integration cycles of the theory spoiling them. Indeed, we confirm numerically that in the absence of boundary terms the complex Langevin results are given by a linear combination of such integration cycles, as put forward by Salcedo & Seiler. In particular, we shed light on the way different choices of kernel affect which integration cycles are being sampled in a simulation and how this knowledge can be used to ensure correct convergence in simple toy models., Comment: 19 pages + 5 pages appendix, 19 figures

To overcome the performance limitations in modern computing, such as the power wall, emerging computing paradigms are gaining increasing importance. Approximate computing offers a promising solution by substantially enhancing energy efficiency and reducing latency, albeit with a trade-off in accuracy. Another emerging method is memristor-based In-Memory Computing (IMC) which has the potential to overcome the Von Neumann bottleneck. In this work, we combine these two approaches and propose two Serial APProximate IMPLY-based full adders (SAPPI). When embedded in a Ripple Carry Adder (RCA), our designs reduce the number of steps by 39%-41% and the energy consumption by 39%-42% compared to the exact algorithm. We evaluated our approach at the circuit level and compared it with State-of-the-Art (SoA) approximations where our adders improved the speed by up to 10% and the energy efficiency by up to 13%. We applied our designs in three common image processing applications where we achieved acceptable image quality with up to half of the RCA approximated. We performed a case study to demonstrate the applicability of our approximations in Machine Learning (ML) underscoring the potential gains in more complex scenarios. The proposed approach demonstrates energy savings of up to 296 mJ (21%) and a reduction of 1.3 billion (20%) computational steps when applied to Convolutional Neural Networks (CNNs) trained on the MNIST dataset while maintaining accuracy.

Upon a polarization reversal within a ferroelectric material, one stable state changes into another which is typically described by a progression of switching events of smaller fractions of the material. These events give rise to crackling or Barkhausen noise and follow a characteristic distribution in their sizes. Barkhausen noise has been studied to better understand the switching processes of ferroelectrics and has been applied for inorganic ferroelectric materials and perovskites. In this work, we present results from kinetic Monte Carlo simulations investigating the switching process of the small organic molecular ferroelectric benzene-1,3,5-tricarboxamides (BTAs). For temperatures below 175 K and sufficiently strong structural disorder, the system exhibits self-organized critical behavior; for higher temperatures, a creep regime is entered. Our extracted power-law exponents are smaller than those typically measured in inorganic crystals and ceramics which indicates that in the more disordered material BTA larger spanning avalanches are possible. The system was experimentally investigated with a high-sensitivity setup. No Barkhausen noise was observed which is consistent with the simulated event sizes, lying several orders beneath the noise threshold of the experimental setup. This finding corroborates the notion that switching in BTA progresses along the 1D columns in the hexagonal liquid crystal lattice, with little coupling between the columns that could give rise to larger lateral avalanches.

Polarization reversal within a ferroelectric material is commonly described as a progression of smaller switching events, giving rise to crackling or Barkhausen noise. While studies on Barkhausen noise, and particularly the associated event size distribution, allow for better understanding of switching processes in ferroelectrics, they were not yet conducted experimentally on organic ferroelectric materials. In this work, Barkhausen noise in the organic ferroelectric copolymer poly(vinylidene fluoride-co-trifluoroethylene) (P(VDF:TrFE)) is experimentally investigated under different electric fields, increasing at various rates. A weak dependence of the structure of the Barkhausen noise on both the magnitude and rise time of the applied electric field is observed, which manifests as a trend in the probability density function power-law exponents. Specifically, an increase in maximum electric field leads to an increase of the power-law exponent; increasing the rise time causes a parallel shift towards lower exponents. While these findings do not allow to conclusively confirm or refute universal self-organized critical behavior of the polarization reversal avalanches in P(VDF:TrFE), the exponents were found to seemingly converge to the universal value of 1.5 for fast and strong driving, suggesting the system is close to this limit.

This paper considers the discrete-time, stochastic LQR problem with $p$ steps of disturbance preview information where $p$ is finite. We first derive the solution for this problem on a finite horizon with linear, time-varying dynamics and time-varying costs. Next, we derive the solution on the infinite horizon with linear, time-invariant dynamics and time-invariant costs. Our proofs rely on the well-known principle of optimality. We provide an independent proof for the principle of optimality that relies only on nested information structure. Finally, we show that the finite preview controller converges to the optimal noncausal controller as the preview horizon $p$ tends to infinity. We also provide a simple example to illustrate both the finite and infinite horizon results.

Two-dimensional transition metal dichalcogenides (TMDs) and organic semiconductors (OSCs) have emerged as promising material platforms for next-generation optoelectronic devices. The combination of both is predicted to yield emergent properties while retaining the advantages of their individual components. In OSCs the optoelectronic response is typically dominated by localized Frenkel-type excitons, whereas TMDs host delocalized Wannier-type excitons. However, much less is known about the spatial and electronic characteristics of excitons at hybrid TMD/OSC interfaces, which ultimately determine the possible energy and charge transfer mechanisms across the 2D-organic interface. Here, we use ultrafast momentum microscopy and many-body perturbation theory to elucidate a hybrid exciton at an TMD/OSC interface that forms via the ultrafast resonant F\"orster energy transfer process. We show that this hybrid exciton has both Frenkel- and Wannier-type contributions: Concomitant intra- and interlayer electron-hole transitions within the OSC layer and across the TMD/OSC interface, respectively, give rise to an exciton wavefunction with mixed Frenkel-Wannier character. By combining theory and experiment, our work provides previously inaccessible insights into the nature of hybrid excitons at TMD/OSC interfaces. It thus paves the way to a fundamental understanding of charge and energy transfer processes across 2D-organic heterostructures.

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