Generalizing to new calorimeter geometries with Geometry-Aware Autoregressive Models (GAAMs) for fast calorimeter simulation

Generation of simulated detector response to collision products is crucial to data analysis in particle physics, but computationally very expensive. One subdetector, the calorimeter, dominates the computational time due to the high granularity of its cells and complexity of the interaction. Generative models can provide more rapid sample production, but currently require significant effort to optimize performance for specific detector geometries, often requiring many networks to describe the varying cell sizes and arrangements, which do not generalize to other geometries. We develop a {\it geometry-aware} autoregressive model, which learns how the calorimeter response varies with geometry, and is capable of generating simulated responses to unseen geometries without additional training. The geometry-aware model outperforms a baseline, unaware model by 50\% in metrics such as the Wasserstein distance between generated and true distributions of key quantities which summarize the simulated response. A single geometry-aware model could replace the hundreds of generative models currently designed for calorimeter simulation by physicists analyzing data collected at the Large Hadron Collider. For the study of future detectors, such a foundational model will be a crucial tool, dramatically reducing the large upfront investment usually needed to develop generative calorimeter models.

Generalized signals on simplicial complexes

Topological signal processing (TSP) over simplicial complexes typically assumes observations associated with the simplicial complexes are real scalars. In this paper, we develop TSP theories for the case where observations belong to abelian groups more general than real numbers, including function spaces that are commonly used to represent time-varying signals. Our approach generalizes the Hodge decomposition and allows for signal processing tasks to be performed on these more complex observations. We propose a unified and flexible framework for TSP that expands its applicability to a wider range of signal processing applications. Numerical results demonstrate the effectiveness of this approach and provide a foundation for future research in this area.

HINT: Hierarchical Mixture Networks For Coherent Probabilistic Forecasting

We present the Hierarchical Mixture Networks (HINT), a model family for efficient and accurate coherent forecasting. We specialize the networks on the task via a multivariate mixture optimized with composite likelihood and made coherent via bootstrap reconciliation. Additionally, we robustify the networks to stark time series scale variations, incorporating normalized feature extraction and recomposition of output scales within their architecture. We demonstrate 8% sCRPS improved accuracy across five datasets compared to the existing state-of-the-art. We conduct ablation studies on our model's components and extensively investigate the theoretical properties of the multivariate mixture. HINT's code is available at this https://github.com/Nixtla/neuralforecast.

A two stages Deep Learning Architecture for Model Reduction of Parametric Time-Dependent Problems

Parametric time-dependent systems are of a crucial importance in modeling real phenomena, often characterized by non-linear behaviors too. Those solutions are typically difficult to generalize in a sufficiently wide parameter space while counting on limited computational resources available. As such, we present a general two-stages deep learning framework able to perform that generalization with low computational effort in time. It consists in a separated training of two pipe-lined predictive models. At first, a certain number of independent neural networks are trained with data-sets taken from different subsets of the parameter space. Successively, a second predictive model is specialized to properly combine the first-stage guesses and compute the right predictions. Promising results are obtained applying the framework to incompressible Navier-Stokes equations in a cavity (Rayleigh-Bernard cavity), obtaining a 97% reduction in the computational time comparing with its numerical resolution for a new value of the Grashof number.

Continuous-Time Functional Diffusion Processes

We introduce functional diffusion processes (FDPs), which generalize traditional score-based diffusion models to infinite-dimensional function spaces. FDPs require a new mathematical framework to describe the forward and backward dynamics, and several extensions to derive practical training objectives. These include infinite-dimensional versions of the Girsanov theorem, in order to be able to compute an ELBO, and of the sampling theorem, in order to guarantee that functional evaluations in a countable set of points are equivalent to infinite-dimensional functions. We use FDPs to build a new breed of generative models in function spaces, which do not require specialized network architectures, and that can work with any kind of continuous data. Our results on synthetic and real data illustrate the advantages of FDPs in simplifying the design requirements of diffusion models.

Uncertainty in Real-Time Semantic Segmentation on Embedded Systems

Application for semantic segmentation models in areas such as autonomous vehicles and human computer interaction require real-time predictive capabilities. The challenges of addressing real-time application is amplified by the need to operate on resource constrained hardware. Whilst development of real-time methods for these platforms has increased, these models are unable to sufficiently reason about uncertainty present. This paper addresses this by combining deep feature extraction from pre-trained models with Bayesian regression and moment propagation for uncertainty aware predictions. We demonstrate how the proposed method can yield meaningful uncertainty on embedded hardware in real-time whilst maintaining predictive performance.

Laplacian Convolutional Representation for Traffic Time Series Imputation

Spatiotemporal traffic data imputation is of great significance in intelligent transportation systems and data-driven decision-making processes. To make an accurate reconstruction from partially observed traffic data, we assert the importance of characterizing both global and local trends in traffic time series. In the literature, substantial prior works have demonstrated the effectiveness of utilizing low-rankness property of traffic data by matrix/tensor completion models. In this study, we first introduce a Laplacian kernel to temporal regularization for characterizing local trends in traffic time series, which can be formulated in the form of circular convolution. Then, we develop a low-rank Laplacian convolutional representation (LCR) model by putting the nuclear norm of a circulant matrix and the Laplacian temporal regularization together, which is proved to meet a unified framework that takes a fast Fourier transform (FFT) solution in a relatively low time complexity. Through extensive experiments on some traffic datasets, we demonstrate the superiority of LCR for imputing traffic time series of various time series behaviors (e.g., data noises and strong/weak periodicity). The proposed LCR model is an efficient and effective solution to large-scale traffic data imputation over the existing baseline models. Despite the LCR's application to time series data, the key modeling idea lies in bridging the low-rank models and the Laplacian regularization through FFT, which is also applicable to image inpainting. The adapted datasets and Python implementation are publicly available at https://github.com/xinychen/transdim.

Local Gaussian Modifiers (LGMs): UAV dynamic trajectory generation for onboard computation

Agile autonomous drones are becoming increasingly popular in research due to the challenges they represent in fields like control, state estimation, or perception at high speeds. When all algorithms are computed onboard the uav, the computational limitations make the task of agile and robust flight even more difficult. One of the most computationally expensive tasks in agile flight is the generation of optimal trajectories that tackles the problem of planning a minimum time trajectory for a quadrotor over a sequence of specified waypoints. When these trajectories must be updated online due to changes in the environment or uncertainties, this high computational cost can leverage to not reach the desired waypoints or even crash in cluttered environments. In this paper, a fast lightweight dynamic trajectory modification approach is presented to allow modifying computational heavy trajectories using Local Gaussian Modifiers (LGMs), when recalculating a trajectory is not possible due to the time of computation. Our approach was validated in simulation, being able to pass through a race circuit with dynamic gates with top speeds up to 16.0 m/s, and was also validated in real flight reaching speeds up to 4.0 m/s in a fully autonomous onboard computing condition.

Dynamic DH-MBIR for Phase-Error Estimation from Streaming Digital-Holography Data

Directed energy applications require the estimation of digital-holographic (DH) phase errors due to atmospheric turbulence in order to accurately focus the outgoing beam. These phase error estimates must be computed with very low latency to keep pace with changing atmospheric parameters, which requires that phase errors be estimated in a single shot of DH data. The digital holography model-based iterative reconstruction (DH-MBIR) algorithm is capable of accurately estimating phase errors in a single shot using the expectation maximization (EM) algorithm. However, existing implementations of DH-MBIR require hundreds of iterations, which is not practical for real-time applications. In this paper, we present the Dynamic DH-MBIR (DDH-MBIR) algorithm for estimating isoplanatic phase errors from streaming single-shot data with extremely low latency. The Dynamic DH-MBIR algorithm reduces the computation and latency by orders of magnitude relative to conventional DH-MBIR, making real-time throughput and latency feasible in applications. Using simulated data that models frozen flow of atmospheric turbulence, we show that our algorithm can achieve a consistently high Strehl ratio with realistic simulation parameters using only 1 iteration per timestep.

A Range-Null Space Decomposition Approach for Fast and Flexible Spectral Compressive Imaging

We present RND-SCI, a novel framework for compressive hyperspectral image (HSI) reconstruction. Our framework decomposes the reconstructed object into range-space and null-space components, where the range-space part ensures the solution conforms to the compression process, and the null-space term introduces a deep HSI prior to constraining the output to have satisfactory properties. RND-SCI is not only simple in design with strong interpretability but also can be easily adapted to various HSI reconstruction networks, improving the quality of HSIs with minimal computational overhead. RND-SCI significantly boosts the performance of HSI reconstruction networks in retraining, fine-tuning or plugging into a pre-trained off-the-shelf model. Based on the framework and SAUNet, we design an extremely fast HSI reconstruction network, RND-SAUNet, which achieves an astounding 91 frames per second while maintaining superior reconstruction accuracy compared to other less time-consuming methods. Code and models are available at https://github.com/hustvl/RND-SCI.