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Accurate 3D object detection is vital for automated driving. While lidar sensors are well suited for this task, they are expensive and have limitations in adverse weather conditions. 3+1D imaging radar sensors offer a cost-effective, robust alternative but face challenges due to their low resolution and high measurement noise. Existing 3+1D imaging radar datasets include radar and lidar data, enabling cross-modal model improvements. Although lidar should not be used during inference, it can aid the training of radar-only object detectors. We explore two strategies to transfer knowledge from the lidar to the radar domain and radar-only object detectors: 1. multi-stage training with sequential lidar point cloud thin-out, and 2. cross-modal knowledge distillation. In the multi-stage process, three thin-out methods are examined. Our results show significant performance gains of up to 4.2 percentage points in mean Average Precision with multi-stage training and up to 3.9 percentage points with knowledge distillation by initializing the student with the teacher's weights. The main benefit of these approaches is their applicability to other 3D object detection networks without altering their architecture, as we show by analyzing it on two different object detectors. Our code is available at https://github.com/rst-tu-dortmund/lerojd, Comment: Accepted for publication as ECCV 2024

A neural network architecture is presented that exploits the multilevel properties of high-dimensional parameter-dependent partial differential equations, enabling an efficient approximation of parameter-to-solution maps, rivaling best-in-class methods such as low-rank tensor regression in terms of accuracy and complexity. The neural network is trained with data on adaptively refined finite element meshes, thus reducing data complexity significantly. Error control is achieved by using a reliable finite element a posteriori error estimator, which is also provided as input to the neural network. The proposed U-Net architecture with CNN layers mimics a classical finite element multigrid algorithm. It can be shown that the CNN efficiently approximates all operations required by the solver, including the evaluation of the residual-based error estimator. In the CNN, a culling mask set-up according to the local corrections due to refinement on each mesh level reduces the overall complexity, allowing the network optimization with localized fine-scale finite element data. A complete convergence and complexity analysis is carried out for the adaptive multilevel scheme, which differs in several aspects from previous non-adaptive multilevel CNN. Moreover, numerical experiments with common benchmark problems from Uncertainty Quantification illustrate the practical performance of the architecture.

This work proposes stochastic partial differential equations (SPDEs) as a practical tool to replicate clustering effects of more detailed particle-based dynamics. Inspired by membrane-mediated receptor dynamics on cell surfaces, we formulate a stochastic particle-based model for diffusion and pairwise interaction of particles, leading to intriguing clustering phenomena. Employing numerical simulation and cluster detection methods, we explore the approximation of the particle-based clustering dynamics through mean-field approaches. We find that SPDEs successfully reproduce spatiotemporal clustering dynamics, not only in the initial cluster formation period, but also on longer time scales where the successive merging of clusters cannot be tracked by deterministic mean-field models. The computational efficiency of the SPDE approach allows us to generate extensive statistical data for parameter estimation in a simpler model that uses a Markov jump process to capture the temporal evolution of the cluster number.

This paper is concerned with collective variables, or reaction coordinates, that map a discrete-in-time Markov process $X_n$ in $\mathbb{R}^d$ to a (much) smaller dimension $k \ll d$. We define the effective dynamics under a given collective variable map $\xi$ as the best Markovian representation of $X_n$ under $\xi$. The novelty of the paper is that it gives strict criteria for selecting optimal collective variables via the properties of the effective dynamics. In particular, we show that the transition density of the effective dynamics of the optimal collective variable solves a relative entropy minimization problem from certain family of densities to the transition density of $X_n$. We also show that many transfer operator-based data-driven numerical approaches essentially learn quantities of the effective dynamics. Furthermore, we obtain various error estimates for the effective dynamics in approximating dominant timescales / eigenvalues and transition rates of the original process $X_n$ and how optimal collective variables minimize these errors. Our results contribute to the development of theoretical tools for the understanding of complex dynamical systems, e.g. molecular kinetics, on large timescales. These results shed light on the relations among existing data-driven numerical approaches for identifying good collective variables, and they also motivate the development of new methods.

The generation of terawatt (TW) near-single-cycle laser pulses is of high interest for applications including attosecond science. Here we demonstrate a three-stage post-compression scheme in a non-guided geometry using He as the nonlinear medium, resulting in the generation of multi-mJ pulses with a duration of 3.7 fs. Key features of this approach are its simplicity, robustness and high stability, making it ideally suited for highly demanding applications such as attosecond-pump attosecond-probe spectroscopy (APAPS). This is demonstrated by performing two-color APAPS in Ar and Ne, where both simultaneous and sequential two-photon absorption are observed. Our approach is scalable to multi-TW powers., Comment: 9 pages, 4 figures

To solve high-dimensional parameter-dependent partial differential equations (pPDEs), a neural network architecture is presented. It is constructed to map parameters of the model data to corresponding finite element solutions. To improve training efficiency and to enable control of the approximation error, the network mimics an adaptive finite element method (AFEM). It outputs a coarse grid solution and a series of corrections as produced in an AFEM, allowing a tracking of the error decay over successive layers of the network. The observed errors are measured by a reliable residual based a posteriori error estimator, enabling the reduction to only few parameters for the approximation in the output of the network. This leads to a problem adapted representation of the solution on locally refined grids. Furthermore, each solution of the AFEM is discretized in a hierarchical basis. For the architecture, convolutional neural networks (CNNs) are chosen. The hierarchical basis then allows to handle sparse images for finely discretized meshes. Additionally, as corrections on finer levels decrease in amplitude, i.e., importance for the overall approximation, the accuracy of the network approximation is allowed to decrease successively. This can either be incorporated in the number of generated high fidelity samples used for training or the size of the network components responsible for the fine grid outputs. The architecture is described and preliminary numerical examples are presented.

We determine the uncorrelated modes that characterize the fluctuations in a semi-realistic model for the initial state of high-energy nuclear collisions, consisting of hot spots whose positions are distributed independently. Varying the number of hot spots, their size, and the weights with which they contribute to the initial state, we find that the parameter that has the largest influence on the relative importance of the fluctuation modes is the source size, with more extended hot spots leading to a more marked predominance of the principal modes., Comment: 14 pages, 7 figures + supplemental material: 16 figures on 15 pages

The thermal plasma filling the early universe generated a stochastic gravitational wave background that peaks in the microwave frequency range today. If the graviton production rate is expressed as a series in a fine-structure constant, $\alpha$, and the temperature over the Planck mass, $T^2_{ } / m_{\rm pl}^2$, then the lowest-order contributions come from single ($\sim \alpha T^2_{ }/m_{\rm pl}^2$) and double ($\sim T^4_{ }/m_{\rm pl}^4$) graviton production via $2\to 2$ scatterings. We show that in the Standard Model, single-graviton production dominates if the maximal temperature is smaller than $4\times 10^{18}_{ }$ GeV. This justifies previous calculations which relied solely on single-graviton production. We mention Beyond the Standard Model scenarios in which the single and double-graviton contributions could be of comparable magnitudes. Finally, we elaborate on what these results imply for the range of applicability of General Relativity as an effective theory., Comment: 16 pages. v2: clarifications added

We report on the mechanism of energy transfer in van der Waals heterostructures of the two-dimensional semiconductor WS$_2$ and graphene with varying interlayer distances, achieved through spacer layers of hexagonal boron nitride (hBN). We record photoluminescence and reflection spectra at interlayer distances between 0.5 nm and 5.8 nm (0-16 hBN layers). We find that the energy transfer is dominated by states outside the light cone, indicative of a F\"orster transfer process, with an additional contribution from a Dexter process at 0.5 nm interlayer distance. We find that the measured dependence of the luminescence intensity on interlayer distances above 1 nm can be quantitatively described using recently reported values of the F\"orster transfer rates of thermalized charge carriers. At smaller interlayer distances, the experimentally observed transfer rates exceed the predictions and furthermore depend on excess energy as well as on excitation density. Since the transfer probability of the F\"orster mechanism depends on the momentum of electron-hole pairs, we conclude that at these distances, the transfer is driven by non-thermalized charge carrier distributions.

The recent COVID-19 pandemic has thrown the importance of accurately forecasting contagion dynamics and learning infection parameters into sharp focus. At the same time, effective policy-making requires knowledge of the uncertainty on such predictions, in order, for instance, to be able to ready hospitals and intensive care units for a worst-case scenario without needlessly wasting resources. In this work, we apply a novel and powerful computational method to the problem of learning probability densities on contagion parameters and providing uncertainty quantification for pandemic projections. Using a neural network, we calibrate an ODE model to data of the spread of COVID-19 in Berlin in 2020, achieving both a significantly more accurate calibration and prediction than Markov-Chain Monte Carlo (MCMC)-based sampling schemes. The uncertainties on our predictions provide meaningful confidence intervals e.g. on infection figures and hospitalisation rates, while training and running the neural scheme takes minutes where MCMC takes hours. We show convergence of our method to the true posterior on a simplified SIR model of epidemics, and also demonstrate our method's learning capabilities on a reduced dataset, where a complex model is learned from a small number of compartments for which data is available.

We sample from a given target distribution by constructing a neural network which maps samples from a simple reference, e.g. the standard normal distribution, to samples from the target. To that end, we propose using a neural network architecture inspired by the Langevin Monte Carlo (LMC) algorithm. Based on LMC perturbation results, we show approximation rates of the proposed architecture for smooth, log-concave target distributions measured in the Wasserstein-$2$ distance. The analysis heavily relies on the notion of sub-Gaussianity of the intermediate measures of the perturbed LMC process. In particular, we derive bounds on the growth of the intermediate variance proxies under different assumptions on the perturbations. Moreover, we propose an architecture similar to deep residual neural networks and derive expressivity results for approximating the sample to target distribution map.

The homogeneous precession domain (HPD) of superfluid $^{3}$He has recently been identified as a detection medium which might provide sensitivity to the axion-nucleon coupling $g_{aNN}$ competitive with, or surpassing, existing experimental proposals. In this work, we make a detailed study of the statistical and dynamical properties of the HPD system in order to make realistic projections for a full-fledged experimental program. We include the effects of clock error and measurement error in a concrete readout scheme using superconducting qubits and quantum metrology. This work also provides a more general framework to describe the statistics associated with the axion gradient coupling through the treatment of a transient resonance with a non-stationary background in a time-series analysis. Incorporating an optimal data-taking and analysis strategy, we project a sensitivity approaching $g_{aNN} \sim 10^{-12}$ GeV$^{-1}$ across a decade in axion mass., Comment: 18 pages, 8 figures

We present a numerical algorithm for the computation of invariant Ruelle distributions on convex co-compact hyperbolic surfaces. This is achieved by exploiting the connection between invariant Ruelle distributions and residues of meromorphically continued weighted zeta functions established by the authors together with Barkhofen (2021). To make this applicable for numerics we express the weighted zeta as the logarithmic derivative of a suitable parameter dependent Fredholm determinant similar to Borthwick (2014). As an additional difficulty our transfer operator has to include a contracting direction which we account for with techniques developed by Rugh (1992). We achieve a further improvement in convergence speed for our algorithm in the case of surfaces with additional symmetries by proving and applying a symmetry reduction of weighted zeta functions., Comment: 52 pages, 25 figures

This article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microscopic details with high accuracy. However, they suffer from computational inefficiency if particle numbers and density get too large. Alternative coarse-grained-resolution models reduce computational effort tremendously, e.g., by replacing the particle distribution by a continuous concentration field governed by reaction-diffusion PDEs. We demonstrate how models on the different resolution levels can be combined into hybrid models that seamlessly combine the best of both worlds, describing molecular species with large copy numbers by macroscopic equations with spatial resolution while keeping the stochastic-spatial particle-based resolution level for the species with low copy numbers. To this end, we introduce a simple particle-based model for the binding dynamics of ions and vesicles at the heart of the neurotransmission process. Within this framework, we derive a novel hybrid model and present results from numerical experiments which demonstrate that the hybrid model allows for an accurate approximation of the full particle-based model in realistic scenarios., Comment: 16 pages + 2 pages appendix, 5 figures. Submitted to Mathematical Biosciences

High-dimensional metastable molecular system can often be characterised by a few features of the system, i.e. collective variables (CVs). Thanks to the rapid advance in the area of machine learning and deep learning, various deep learning-based CV identification techniques have been developed in recent years, allowing accurate modelling and efficient simulation of complex molecular systems. In this paper, we look at two different categories of deep learning-based approaches for finding CVs, either by computing leading eigenfunctions of infinitesimal generator or transfer operator associated to the underlying dynamics, or by learning an autoencoder via minimisation of reconstruction error. We present a concise overview of the mathematics behind these two approaches and conduct a comparative numerical study of these two approaches on illustrative examples., Comment: revised version, 14 pages; This is an extended version of the paper submitted to Proceedings in Applied Mathematics and Mechanics (PAMM) 2023

Agent-based models (ABMs) provide an intuitive and powerful framework for studying social dynamics by modeling the interactions of individuals from the perspective of each individual. In addition to simulating and forecasting the dynamics of ABMs, the demand to solve optimization problems to support, for example, decision-making processes naturally arises. Most ABMs, however, are non-deterministic, high-dimensional dynamical systems, so objectives defined in terms of their behavior are computationally expensive. In particular, if the number of agents is large, evaluating the objective functions often becomes prohibitively time-consuming. We consider data-driven reduced models based on the Koopman generator to enable the efficient solution of multi-objective optimization problems involving ABMs. In a first step, we show how to obtain data-driven reduced models of non-deterministic dynamical systems (such as ABMs) that depend potentially nonlinearly on control inputs. We then use them in the second step as surrogate models to solve multi-objective optimal control problems. We first illustrate our approach using the example of a voter model, where we compute optimal controls to steer the agents to a predetermined majority, and then using the example of an epidemic ABM, where we compute optimal containment strategies in a prototypical situation. We demonstrate that the surrogate models effectively approximate the Pareto-optimal points of the ABM dynamics by comparing the surrogate-based results with test points, where the objectives are evaluated using the ABM. Our results show that when objectives are defined by the dynamic behavior of ABMs, data-driven surrogate models support or even enable the solution of multi-objective optimization problems.

The ability to perform attosecond-pump attosecond-probe spectroscopy (APAPS) is a longstanding goal in ultrafast science. While first pioneering experiments demonstrated the feasibility of APAPS, the low repetition rates (10-120 Hz) and the large footprints of existing setups have so far hindered the widespread exploitation of APAPS. Here we demonstrate two-color APAPS using a commercial laser system at 1 kHz, straightforward post-compression in a hollow-core fiber and a compact high-harmonic generation (HHG) setup. The latter enables the generation of intense extreme-ultraviolet (XUV) pulses by using an out-of-focus HHG geometry and by exploiting a transient blueshift of the driving laser in the HHG medium. Near-isolated attosecond pulses are generated, as demonstrated by one-color and two-color XUV-pump XUV-probe experiments. Our concept allows selective pumping and probing on extremely short timescales and permits investigations of fundamental processes that are not accessible by other pump-probe techniques., Comment: 8 pages, 5 figures

The most widely used method for obtaining high-quality two-dimensional materials is through mechanical exfoliation of bulk crystals. Manual identification of suitable flakes from the resulting random distribution of crystal thicknesses and sizes on a substrate is a time-consuming, tedious task. Here, we present a platform for fully automated scanning, detection, and classification of two-dimensional materials, the source code of which we make openly available. Our platform is designed to be accurate, reliable, fast, and versatile in integrating new materials, making it suitable for everyday laboratory work. The implementation allows fully automated scanning and analysis of wafers with an average inference time of 100 ms for images of 2.3 Mpixels. The developed detection algorithm is based on a combination of the flakes' optical contrast toward the substrate and their geometric shape. We demonstrate that it is able to detect the majority of exfoliated flakes of various materials, with an average recall (AR50) between 67% and 89%. We also show that the algorithm can be trained with as few as five flakes of a given material, which we demonstrate for the examples of few-layer graphene, WSe$_2$, MoSe$_2$, CrI$_3$, 1T-TaS$_2$ and hexagonal BN. Our platform has been tested over a two-year period, during which more than $10^6$ images of multiple different materials were acquired by over 30 individual researchers.

A direct detection of black hole formation in neutron star mergers would provide invaluable information about matter in neutron star cores and finite temperature effects on the nuclear equation of state. We study black hole formation in neutron star mergers using a set of 190 numerical relativity simulations consisting of long-lived and black-hole-forming remnants. The postmerger gravitational-wave spectrum of a long-lived remnant has greatly reduced power at a frequency $f$ greater than $f_{\rm peak}$, for $f \gtrsim 4\,\rm kHz$, with $f_{\rm peak} \in [2.5, 4]\,\rm kHz$. On the other hand, black-hole-forming remnants exhibit excess power in the same large $f$ region and manifest exponential damping in the time domain characteristic of a quasinormal mode. We demonstrate that the gravitational-wave signal from a collapsed remnant is indeed a quasinormal ringing. We report on the opportunity for direct detections of black hole formation with next-generation gravitational-wave detectors such as Cosmic Explorer and Einstein Telescope and set forth the tantalizing prospect of such observations up to a distance of 100 Mpc for an optimally oriented and located source with an SNR of 4.

Optical micro-spectroscopy is an invaluable tool for studying and characterizing samples ranging from classical semiconductors to low-dimensional materials and heterostructures. To date, most implementations are based on point-scanning techniques, which are flexible and reliable, but slow. Here, we describe a setup for highly parallel acquisition of hyperspectral reflection and photoluminescence microscope images using a push-broom technique. Spatial as well as spectral distortions are characterized and their digital corrections are presented. We demonstrate close-to diffraction-limited spatial imaging performance and a spectral resolution limited by the spectrograph. The capabilities of the setup are demonstrated by recording a hyperspectral photoluminescence map of a CVD-grown MoSe$_2$-WSe$_2$ lateral heterostructure, from which we extract the luminescence energies, intensities and peak widths across the interface.

In optical nano metrology numerical models are used widely for parameter reconstructions. Using the Bayesian target vector optimization method we fit a finite element numerical model to a Grazing Incidence X-Ray fluorescence data set in order to obtain the geometrical parameters of a nano structured line grating. Gaussian process, stochastic machine learning surrogate models, were trained during the reconstruction and afterwards sampled with a Markov chain Monte Carlo sampler to determine the distribution of the reconstructed model parameters. The numerical discretization parameters of the used finite element model impact the numerical discretization error of the forward model. We investigated the impact of the polynomial order of the finite element ansatz functions on the reconstructed parameters as well as on the model parameter distributions. We showed that such a convergence study allows to determine numerical parameters which allows for efficient and accurate reconstruction results., Comment: Submitted to Metrologia Focus Issue on MATHMET 2023 conference