Flexible robots may overcome some of the industry's major challenges, such as enabling intrinsically safe human-robot collaboration and achieving a higher load-to-mass ratio. However, controlling flexible robots is complicated due to their complex dynamics, which include oscillatory behavior and a high-dimensional state space. NMPC offers an effective means to control such robots, but its extensive computational demands often limit its application in real-time scenarios. To enable fast control of flexible robots, we propose a framework for a safe approximation of NMPC using imitation learning and a predictive safety filter. Our framework significantly reduces computation time while incurring a slight loss in performance. Compared to NMPC, our framework shows more than a eightfold improvement in computation time when controlling a three-dimensional flexible robot arm in simulation, all while guaranteeing safety constraints. Notably, our approach outperforms conventional reinforcement learning methods. The development of fast and safe approximate NMPC holds the potential to accelerate the adoption of flexible robots in industry.

Accurately predicting the prices of financial time series is essential and challenging for the financial sector. Owing to recent advancements in deep learning techniques, deep learning models are gradually replacing traditional statistical and machine learning models as the first choice for price forecasting tasks. This shift in model selection has led to a notable rise in research related to applying deep learning models to price forecasting, resulting in a rapid accumulation of new knowledge. Therefore, we conducted a literature review of relevant studies over the past three years with a view to aiding researchers and practitioners in the field. This review delves deeply into deep learning-based forecasting models, presenting information on model architectures, practical applications, and their respective advantages and disadvantages. In particular, detailed information is provided on advanced models for price forecasting, such as Transformers, generative adversarial networks (GANs), graph neural networks (GNNs), and deep quantum neural networks (DQNNs). The present contribution also includes potential directions for future research, such as examining the effectiveness of deep learning models with complex structures for price forecasting, extending from point prediction to interval prediction using deep learning models, scrutinising the reliability and validity of decomposition ensembles, and exploring the influence of data volume on model performance.

In the present study, we delineate a strategy focused on non-parametric quantum circuits for the generation of Gaussian random variables (GRVs). This quantum-centric approach serves as a substitute for conventional pseudorandom number generators (PRNGs), such as the \textbf{torch.rand} function in PyTorch. The principal theme of our research is the incorporation of Quantum Random Number Generators (QRNGs) into classical models of diffusion. Notably, our Quantum Gaussian Random Variable Generator fulfills dual roles, facilitating simulations in both Stable Diffusion (SD) and Brownian Motion (BM). This diverges markedly from prevailing methods that utilize parametric quantum circuits (PQCs), often in conjunction with variational quantum eigensolvers (VQEs). Although conventional techniques can accurately approximate ground states in complex systems or model elaborate probability distributions, they require a computationally demanding optimization process to tune parameters. Our non-parametric strategy obviates this necessity. To facilitate assimilating our methodology into existing computational frameworks, we put forward QonFusion, a Python library congruent with both PyTorch and PennyLane, functioning as a bridge between classical and quantum computational paradigms. We validate QonFusion through extensive statistical testing, including tests which confirm the statistical equivalence of the Gaussian samples from our quantum approach to classical counterparts within defined significance limits. QonFusion is available at \url{https://boltzmannentropy.github.io/qonfusion.github.io/} to reproduce all findings here.

Turbulence in fluids, gases, and plasmas remains an open problem of both practical and fundamental importance. Its irreducible complexity usually cannot be tackled computationally in a brute-force style. Here, we combine Large Eddy Simulation (LES) techniques with Machine Learning (ML) to retain only the largest dynamics explicitly, while small-scale dynamics are described by an ML-based sub-grid-scale model. Applying this novel approach to self-driven plasma turbulence allows us to remove large parts of the inertial range, reducing the computational effort by about three orders of magnitude, while retaining the statistical physical properties of the turbulent system.

Crowd navigation has received increasing attention from researchers over the last few decades, resulting in the emergence of numerous approaches aimed at addressing this problem to date. Our proposed approach couples agent motion prediction and planning to avoid the freezing robot problem while simultaneously capturing multi-agent social interactions by utilizing a state-of-the-art trajectory prediction model i.e., social long short-term memory model (Social-LSTM). Leveraging the output of Social-LSTM for the prediction of future trajectories of pedestrians at each time-step given the robot's possible actions, our framework computes the optimal control action using Model Predictive Control (MPC) for the robot to navigate among pedestrians. We demonstrate the effectiveness of our proposed approach in multiple scenarios of simulated crowd navigation and compare it against several state-of-the-art reinforcement learning-based methods.

Inspecting petrochemical pipelines is challenging due to hazardous materials, narrow diameters, and inaccessible locations. Mobile robots are promising for autonomous pipeline inspection and mapping. This project aimed to simulate and implement a robot capable of simultaneous localization and mapping (SLAM) in an indoor maze-like environment representing simplified pipelines. The approach involved simulating a differential drive robot in Gazebo/ROS, equipping it with sensors, implementing SLAM using mapping, and path planning with move_base. A physical robot was then built and tested by manually driving it in a constructed maze while collecting sensor data and mapping. Sensor fusion of wheel encoders, Kinect camera, and inertial measurement unit (IMU) data was explored to improve odometry and mapping accuracy without encoders. The final map had reasonable correspondence to the true maze despite lacking wheel encoders. In summary, results show the feasibility of using ROS-based SLAM for pipeline inspection if accounting for real-world complexities.

Uncertainty is prevalent in engineering design, statistical learning, and decision making broadly. Due to inherent risk-averseness and ambiguity about assumptions, it is common to address uncertainty by formulating and solving conservative optimization models expressed using measures of risk and related concepts. We survey the rapid development of risk measures over the last quarter century. From their beginning in financial engineering, we recount the spread to nearly all areas of engineering and applied mathematics. Solidly rooted in convex analysis, risk measures furnish a general framework for handling uncertainty with significant computational and theoretical advantages. We describe the key facts, list several concrete algorithms, and provide an extensive list of references for further reading. The survey recalls connections with utility theory and distributionally robust optimization, points to emerging applications areas such as fair machine learning, and defines measures of reliability.

Many real-world processes have complex tail dependence structures that cannot be characterized using classical Gaussian processes. More flexible spatial extremes models exhibit appealing extremal dependence properties but are often exceedingly prohibitive to fit and simulate from in high dimensions. In this paper, we develop a new spatial extremes model that has flexible and non-stationary dependence properties, and we integrate it in the encoding-decoding structure of a variational autoencoder (XVAE), whose parameters are estimated via variational Bayes combined with deep learning. The XVAE can be used as a spatio-temporal emulator that characterizes the distribution of potential mechanistic model output states and produces outputs that have the same statistical properties as the inputs, especially in the tail. As an aside, our approach also provides a novel way of making fast inference with complex extreme-value processes. Through extensive simulation studies, we show that our XVAE is substantially more time-efficient than traditional Bayesian inference while also outperforming many spatial extremes models with a stationary dependence structure. To further demonstrate the computational power of the XVAE, we analyze a high-resolution satellite-derived dataset of sea surface temperature in the Red Sea, which includes 30 years of daily measurements at 16703 grid cells. We find that the extremal dependence strength is weaker in the interior of Red Sea and it has decreased slightly over time.

The spatial prediction (interpolation) problem arises in various fields of science and engineering that study spatially distributed variables. In the case of scattered data, filling gaps facilitates understanding of the spatial features, visualization of the observed process, and it is also necessary to obtain fully populated grids of spatially dependent parameters used in partial differential equations. Spatial prediction is highly relevant to many disciplines, such as environmental mapping, risk assessment(Christakos, 2012) and environmental health studies (Christakos and Hristopulos, 2013), subsurface hydrology (Kitanidis, 1997; Rubin, 2003), mining (Goovaerts, 1997), and oil reserves estimation (Hohn, 1988; Hamzehpour and Sahimi, 2006). In addition, remote sensing images often include gaps with missing data (e.g., clouds, snow, heavy precipitation, ground vegetation coverage, etc.) that need to be filled (Rossi et al, 1994). Spatial prediction is also useful in image analysis (Winkler, 2003; Gui and Wei, 2004) and signal processing (Unser and Blu, 2005; Ramani and Unser, 2006) including medical applications (Parrott et al, 1993; Cao and Worsley, 2001).

Orbital-free density functional theory (OFDFT) is a quantum chemistry formulation that has a lower cost scaling than the prevailing Kohn-Sham DFT, which is increasingly desired for contemporary molecular research. However, its accuracy is limited by the kinetic energy density functional, which is notoriously hard to approximate for non-periodic molecular systems. In this work, we propose M-OFDFT, an OFDFT approach capable of solving molecular systems using a deep-learning functional model. We build the essential nonlocality into the model, which is made affordable by the concise density representation as expansion coefficients under an atomic basis. With techniques to address unconventional learning challenges therein, M-OFDFT achieves a comparable accuracy with Kohn-Sham DFT on a wide range of molecules untouched by OFDFT before. More attractively, M-OFDFT extrapolates well to molecules much larger than those in training, which unleashes the appealing scaling for studying large molecules including proteins, representing an advancement of the accuracy-efficiency trade-off frontier in quantum chemistry.