Mitigating spectral bias for the multiscale operator learning with hierarchical attention

Neural operators have emerged as a powerful tool for learning the mapping between infinite-dimensional parameter and solution spaces of partial differential equations (PDEs). In this work, we focus on multiscale PDEs that have important applications such as reservoir modeling and turbulence prediction. We demonstrate that for such PDEs, the spectral bias towards low-frequency components presents a significant challenge for existing neural operators. To address this challenge, we propose a hierarchical attention neural operator (HANO) inspired by the hierarchical matrix approach. HANO features a scale-adaptive interaction range and self-attentions over a hierarchy of levels, enabling nested feature computation with controllable linear cost and encoding/decoding of multiscale solution space. We also incorporate an empirical $H^1$ loss function to enhance the learning of high-frequency components. Our numerical experiments demonstrate that HANO outperforms state-of-the-art (SOTA) methods for representative multiscale problems

Characterizing aircraft wake vortex position and strength using LiDAR measurements processed with artificial neural networks

The position and strength of wake vortices captured by LiDAR (Light Detection and Ranging) instruments are usually determined by conventional approaches such as the Radial Velocity (RV) method. Promising wake vortex detection results of LiDAR measurements using machine learning and operational drawbacks of the comparatively slow traditional processing methods motivate exploring the suitability of Artificial Neural Networks (ANNs) for quantitatively estimating the position and strength of aircraft wake vortices. The ANNs are trained by a unique data set of wake vortices generated by aircraft during final approach, which are labeled using the RV method. First comparisons reveal the potential of custom Convolutional Neural Networks in comparison to readily available resources as well as traditional LiDAR processing algorithms

Multi-faceted Methodology for Coastal Vegetation Drag Coefficient Calibration: Implications for Wave Height Attenuation

The accurate prediction of wave height attenuation due to vegetation is crucial for designing effective and efficient natural and nature-based solutions for flood mitigation, shoreline protection, and coastal ecosystem preservation. Central to these predictions is the estimation of the vegetation drag coefficient. The present study undertakes a comprehensive evaluation of three distinct methodologies for estimating the drag coefficient: traditional manual calibration, calibration using a novel application of state-of-the-art metaheuristic optimization algorithms, and the integration of an established empirical bulk drag coefficient formula (Tanino and Nepf, 2008) into the XBeach non-hydrostatic wave model. These methodologies were tested using a series of existing laboratory experiments involving nearshore vegetation on a sloping beach. A key innovation of the study is the first application of metaheuristic optimization algorithms for calibrating the drag coefficient, which enables efficient automated searches to identify optimal values aligning with measurements. We found that the optimization algorithms rapidly converge to precise drag coefficients, enhancing accuracy and overcoming limitations in manual calibration which can be laborious and inconsistent. While the integrated empirical formula also demonstrates reasonable performance, the optimization approach exemplifies the potential of computational techniques to transform traditional practices of model calibration. Comparing these strategies provides a framework to determine the most effective methodology based on constraints in determining the vegetation drag coefficient

The Formation of Stars: From Clouds to Cores

High resolution simulations were conducted to investigate different stages of the star formation process, from molecular cloud formation to single protostellar collapse. The simulations were performed using AstroBEAR, a state-of-the-art, multiphysics, adaptive mesh refinement code for astrophysical fluid dynamics. In each of the cases, the fluid dynamical properties of the potentially star forming gas were investigated to reveal the relative roles of gravity, magnetic fields, turbulence, and shocks. The models successfully produce many of the structural characteristics of star forming regions. While the simulations modeled isolated, or semi-isolated, phases of the star formation process, cumulatively they represent over 5 orders of magnitude change in spatial scale. Insights provided from this work will aid the development and interpretation of the next generation of simulations -- those which will model star formation through the phases using self-consistent, hierarchical frameworks

Computational Imaging Approach to Recovery of Target Coordinates Using Orbital Sensor Data

This dissertation addresses the components necessary for simulation of an image-based recovery of the position of a target using orbital image sensors. Each component is considered in detail, focusing on the effect that design choices and system parameters have on the accuracy of the position estimate. Changes in sensor resolution, varying amounts of blur, differences in image noise level, selection of algorithms used for each component, and lag introduced by excessive processing time all contribute to the accuracy of the result regarding recovery of target coordinates using orbital sensor data. Using physical targets and sensors in this scenario would be cost-prohibitive in the exploratory setting posed, therefore a simulated target path is generated using Bezier curves which approximate representative paths followed by the targets of interest. Orbital trajectories for the sensors are designed on an elliptical model representative of the motion of physical orbital sensors. Images from each sensor are simulated based on the position and orientation of the sensor, the position of the target, and the imaging parameters selected for the experiment (resolution, noise level, blur level, etc.). Post-processing of the simulated imagery seeks to reduce noise and blur and increase resolution. The only information available for calculating the target position by a fully implemented system are the sensor position and orientation vectors and the images from each sensor. From these data we develop a reliable method of recovering the target position and analyze the impact on near-realtime processing. We also discuss the influence of adjustments to system components on overall capabilities and address the potential system size, weight, and power requirements from realistic implementation approaches

Reports about 8 selected benchmark cases of model hierarchies : Deliverable number: D5.1 - Version 0.1

Based on the multitude of industrial applications, benchmarks for model hierarchies will be created that will form a basis for the interdisciplinary research and for the training programme. These will be equipped with publically available data and will be used for training in modelling, model testing, reduced order modelling, error estimation, efficiency optimization in algorithmic approaches, and testing of the generated MSO/MOR software. The present document includes the description about the selection of (at least) eight benchmark cases of model hierarchies.EC/H2020/765374/EU/Reduced Order Modelling, Simulation and Optimization of Coupled Systems/ROMSO

Artificial Intelligence in the Creative Industries: A Review

This paper reviews the current state of the art in Artificial Intelligence (AI) technologies and applications in the context of the creative industries. A brief background of AI, and specifically Machine Learning (ML) algorithms, is provided including Convolutional Neural Network (CNNs), Generative Adversarial Networks (GANs), Recurrent Neural Networks (RNNs) and Deep Reinforcement Learning (DRL). We categorise creative applications into five groups related to how AI technologies are used: i) content creation, ii) information analysis, iii) content enhancement and post production workflows, iv) information extraction and enhancement, and v) data compression. We critically examine the successes and limitations of this rapidly advancing technology in each of these areas. We further differentiate between the use of AI as a creative tool and its potential as a creator in its own right. We foresee that, in the near future, machine learning-based AI will be adopted widely as a tool or collaborative assistant for creativity. In contrast, we observe that the successes of machine learning in domains with fewer constraints, where AI is the `creator', remain modest. The potential of AI (or its developers) to win awards for its original creations in competition with human creatives is also limited, based on contemporary technologies. We therefore conclude that, in the context of creative industries, maximum benefit from AI will be derived where its focus is human centric -- where it is designed to augment, rather than replace, human creativity

Turbulence and wind velocity profiles from adaptive optics telemetry: a general and scalable solution for extremely large telescopes

Advanced Adaptive Optics (AO) instruments on ground-based telescopes require accurate knowledge of the strength and velocity of atmospheric turbulence. Measuring these parameters as a function of altitude assists point spread function reconstruction, AO temporal control techniques, smart scheduling of science cases and is required by wide-field AO systems to optimise the reconstruction of an observed wavefront. The variability of the atmosphere makes it important to have a measure of the turbulence profile in real-time. This measurement can be performed by iteratively fitting an analytically generated covariance matrix to the cross-covariance of Shack–Hartmann Wavefront Sensor (SHWFS) centroids. In this study we explore the benefits of reducing the number of cross-covariance data points and fitting to a covariance map Region of Interest (ROI). Both of these methods are based on the SLOpe Detection And Ranging (SLODAR) technique. A technique for using the covariance map ROI to measure and compensate for SHWFS misalignments is also introduced. We compare the accuracy of covariance matrix and map ROI optical turbulence profiling using simulated data from CANARY, an AO demonstrator on the 4.2 m William Herschel Telescope (WHT), La Palma. It is shown that the covariance map ROI optimises the accuracy of turbulence profiling. In addition, we show that the covariance map ROI reduces the fitting time for an Extremely Large Telescope-scale (ELT-scale) system by a factor of 72. SLODAR spatio-temporal analysis can be used to visualise the wind velocity profile. However, the limited altitude-resolution of current AO systems makes it difficult to disentangle the movement of independent layers. We address this issue and introduce a novel technique that uses SLODAR data analysis for automated wind velocity profiling. Simulated data from CANARY is used to demonstrate the proficiency of the technique. We apply our turbulence and wind velocity profiling techniques on-sky using data from both CANARY and the Adaptive Optics Facility (AOF). The AOF is on the 8.2m Yepun telescope at the Very Large Telescope (VLT), Paranal. On-sky turbulence and wind velocity profiles from CANARY are compared to contemporaneous profiles from Stereo-SCIDAR, a dedicated high-resolution atmospheric profiler. Wind velocity profiles from CANARY and the AOF are compared to the European Centre for Medium-range Weather Forecasts (ECMWF). We also present AOF time sequences that show detailed examples of turbulence and wind velocity profiles at the VLT. The software packages that we developed to collect all of the presented results are open-source. They can be configured to any tomographic AO system

The implications of costly airflows for space-use and movement decisions in birds

The behavioural ecology of flight has largely considered how birds respond to mean flow conditions, but it is the gusty or extreme airflows that are likely to be particularly challenging. This thesis addresses this, examining the strategies birds use to negotiate turbulence over land, and exceedingly strong winds at sea. I first develop a method for sensing turbulence at fine scales using data collected onboard the animals themselves, taking homing pigeons (Columba livia) as model flapping fliers. Fine scale variation in the flight altitude and body displacement emerged as effective proxies of turbulence. I then assess the impact of freestream turbulence on flapping fliers and find that pigeons adapted their wingbeat kinematics (frequency and amplitude) to increase their flight stability in response to turbulence, but did so without a clear increase in flight effort. In my final two chapters I examine the responses of two seabird species to strong winds, first at sea, and then on land. Specifically, I investigate how streaked shearwaters (Calonectris leucomelas) respond to tropical cyclones, and how common guillemots (Uria aalge) select their breeding cliffs in relation to airflow conditions. I find that shearwaters fly towards the eye of the storm. This tendency increases with cyclone intensity and may enable birds to avoid strong onshore winds and reduce the associated risks of forced landings and/ or injury. Finally, computational fluid dynamics models reveal that guillemots select breeding cliffs that are sheltered from wind and storm conditions, rather than from the mean wind alone, or heat stress. This model of habitat selection could also predict habitat use across islands. Overall, this highlights the varied and sometimes surprising capacities of birds to cope with extreme and variable airflows and operate in areas that are, as yet, inaccessible to aircraft