Discrete Space Research Articles

Efficient Pump Scheduling for Large‐Scale Multiproduct Pipelines Using Deep Reinforcement Learning

ABSTRACTOptimizing pump scheduling in multiproduct pipelines can significantly reduce energy consumption and carbon emissions. For pump scheduling in multiproduct pipelines, to describe hydraulic losses more accurately, the model needs to adopt shorter discrete time intervals, which will lead to longer decision‐making time. It combined with the large solution space of large‐scale pipelines, will lead to low solution efficiency with dynamic programming methods and poor solution quality with heuristic optimization algorithms. Given that, this article develops a multiproduct refined oil transmission simulation system and employs the enhanced Proximal Policy Optimization (PPO) algorithm with action space shaping trick to optimize pump scheduling for large‐scale multiproduct pipelines. The method of converting discrete action space to multi‐discrete action space through action shaping can address PPO's low convergence efficiency issue resulting from the large discrete action space challenge common in large‐scale multiproduct pipelines. The experimental results indicate that the proposed method, that is, PPO algorithm with multidiscrete action space exhibits significant advantages in terms of efficiency and robustness in large‐scale pipelines compared to mainstream methods for pump scheduling such as dynamic programming (DP), genetic algorithms (GA), and ant colony optimization (ACO). Furthermore, we demonstrate the effectiveness of action space shaping in large‐scale pipelines from the perspectives of exploration and exploitation.

The distribution amplitude of the ηc-meson at leading twist from lattice QCD

Distribution amplitudes are functions of non-perturbative matrix elements describing the hadronization of quarks and gluons. Thanks to factorization theorems, they can be used to compute the scattering amplitude of high-energy processes. Recently, new ideas have allowed their computation using lattice QCD, which should provide us with a general, fully relativistic determination. We present the first lattice calculation of the ηc-meson distribution amplitude at leading twist. Starting from the relevant matrix element in discrete Euclidean space on a set of Nf = 2 CLS ensembles, we explain the method to connect to continuum Minkowski spacetime. After addressing several sources of systematic uncertainty, we compare to Dyson-Schwinger and non-relativistic QCD determinations of this quantity. We find significant deviations between the latter and our result even at small Ioffe times.

Optimizing Energy Harvesting in Wireless Body Area Networks: A Deep Reinforcement Learning Approach to Dynamic Sampling

In energy-harvesting wireless body area networks (EH-WBAN), the self-sustainability of body sensor nodes without compromising the service quality criteria is very important. In remote vital signs monitoring applications, the sampling rate of body nodes in each period should be determined to achieve this goal. There are two fundamental challenges in determining the sampling rate: 1) In EH-WBAN, the rate of the harvestable energy is time-dependent and unpredictable. 2) The vital signs of the patient have different change rates relevant to the time. Therefore, a technique is required that can learn the changes of the harvestable energy and the change rates of vital signs simultaneously and specify the proper sampling rate for BNs. The reinforcement learning algorithms are among the efficient solutions for this problem because they are capable of learning environmental uncertainties. Previous RL-based methods for determining the BN's sampling rate have three fundamental problems: 1) focus on the optimization of the transmission energy and ignore the sensing energy, 2) only affect one of the two aspects of energy or sensed data in determining the sampling rate and 3) discretization of the problem space does not ensure the determination of the optimal sampling rate. Therefore, this paper proposes a method named “deep reinforcement learning-based dynamic sampling” (DRDS) which first formulates the sampling rate determination problem as a Markov decision process (MDP) and proposes a deep deterministic policy gradient algorithm (DDPG) to solve it. The proposed method considers both energy and data variability aspects in determining the sampling rate. Two parameters, the super-capacitor’s voltage level, and ambient light intensity, are considered for the energy aspect; for the data variability aspect, the long short-term memory (LSTM) algorithm is developed to predict the change rate of data in the next round. Simulations indicate that by preserving the data integrity, the proposed method can decrease the sampling rate and unnecessary data transmission by about 49.95% and 89.7%, respectively, compared with state-of-the-art methods, and allow the sensor to achieve self-sustainability.

SRL‐ProtoNet: Self‐supervised representation learning for few‐shot remote sensing scene classification

AbstractUsing a deep learning method to classify a large amount of labelled remote sensing scene data produces good performance. However, it is challenging for deep learning based methods to generalise to classification tasks with limited data. Few‐shot learning allows neural networks to classify unseen categories when confronted with a handful of labelled data. Currently, episodic tasks based on meta‐learning can effectively complete few‐shot classification, and training an encoder that can conduct representation learning has become an important component of few‐shot learning. An end‐to‐end few‐shot remote sensing scene classification model based on ProtoNet and self‐supervised learning is proposed. The authors design the Pre‐prototype for a more discrete feature space and better integration with self‐supervised learning, and also propose the ProtoMixer for higher quality prototypes with a global receptive field. The authors’ method outperforms the existing state‐of‐the‐art self‐supervised based methods on three widely used benchmark datasets: UC‐Merced, NWPU‐RESISC45, and AID. Compare with previous state‐of‐the‐art performance. For the one‐shot setting, this method improves by 1.21%, 2.36%, and 0.84% in AID, UC‐Merced, and NWPU‐RESISC45, respectively. For the five‐shot setting, this method surpasses by 0.85%, 2.79%, and 0.74% in the AID, UC‐Merced, and NWPU‐RESISC45, respectively.

Discretisation of the Hough parameter space for fitting and recognising geometric primitives in 3D point clouds

Research in recognising and fitting simple geometric shapes has been ongoing since the 1970s, with various approaches proposed, including stochastic methods, parameter methods, primitive-based registration techniques, and more recently, deep learning. The Hough transform is a method of interest due to its demonstrated robustness to noise and outliers, ability to handle missing data, and support for multiple model instances. Unfortunately, one of the main limitations of the Hough transform is how to properly discretise its parameter space, as increasing their number or decreasing the sampling frequency can make it computationally expensive.The relationship between the approximation accuracy and the parameter space’s discretisation is investigated to address this. We present two distinct discretisations to illustrate how the fitting and recognition quality can be improved by selecting an appropriate parameter discretisation. Our parameter-driven space discretisation is shown to significantly improve the parameter recognition quality over the classical method and reduce computational time and space by decreasing the discretisation’s dimension, as demonstrated by an extensive validation on a benchmark of geometric primitives. Preliminary experiments are also presented on segmenting datasets from urban buildings and CAD objects.

Fast generation of spectrally shaped disorder.

Media with correlated disorder display unexpected transport properties, but it is still a challenge to design structures with desired spectral features at scale. In this work, we introduce an optimal formulation of this inverse problem by means of the nonuniform fast Fourier transform, thus arriving at an algorithm capable of generating systems with arbitrary spectral properties, with a computational cost that scales O(NlogN) with system size. The method is extended to accommodate arbitrary real-space interactions, such as short-range repulsion, to simultaneously control short- and long-range correlations. We thus generate the largest-ever stealthy hyperuniform configurations in 2d (N=10^{9}) and 3d (N>10^{7}) and demonstrate the flexibility of the approach by generating structures with designed spectral features at scale. By an Ewald sphere construction we link the spectral and optical properties at the single-scattering level and show that stealthy hyperuniform structures generically display transmission gaps, providing a concrete example of fine-tuning of a physical property. We also show that large 3d power-law hyperuniformity in particle packings leads to single-scattering properties nearly identical to those of simple hard spheres. Finally, we demonstrate generalizations of the approach to impose features in either continuous or discrete real space, using constraints in either continuous or discrete reciprocal space. In particular, enforcing large spectral power at peaks with the right symmetry leads to the nondeterministic generation of quasicrystalline structures in 2d and 3d. This technique should become an essential tool to embed, and understand the role of, long-range correlations in disordered metamaterials.

A Novel Set-Based Discrete Particle Swarm Optimization for Wastewater Treatment Process Effluent Scheduling.

With the escalating severity of environmental pollution caused by effluent, the wastewater treatment process (WWTP) has gained significant attention. The wastewater treatment efficiency and effluent quality are significantly impacted by effluent scheduling that adjusts the hydraulic retention time. However, the sequential batch and continuous nature of the effluent pose challenges, resulting in complex scheduling models with strong constraints that are difficult to tackle using existing scheduling methods. To optimize maximum completion time and effluent quality simultaneously, this article proposes a restructured set-based discrete particle swarm optimization (RS-DPSO) algorithm to address the WWTP effluent scheduling problem (WWTP-ESP). First, an effective encoding and decoding method is designed to effectively map solutions to feasible schedules using temporal and spatial information. Second, a restructured set-based discrete particle swarm algorithm is introduced to enhance the searching ability in discrete solution space via restructuring the solution set. Third, a constraint handling strategy based on violation degree ranking is designed to reduce the waste of computational resources. Fourth, a Sobel filter based local search is proposed to guide particle search direction to enhance search efficiency ability. The RS-DPSO provides a novel method for solving WWTP-ESP problems with complex discrete solution space. The comparative experiments indicate that the novel designs are effective and the proposed algorithm has superior performance over existing algorithms in solving the WWTP-ESP.

Comparative Assessment of U-Net-Based Deep Learning Models for Segmenting Microfractures and Pore Spaces in Digital Rocks

Summary Segmentation of high-resolution X-ray microcomputed tomography (µCT) images is crucial in digital rock physics (DRP), affecting the characterization and analysis of microscale phenomena in the porous media. The complexity of geological structures and nonideal scanning conditions pose significant challenges to conventional image segmentation approaches. Motivated by the recent increasing popularity of deep learning (DL) techniques in image processing, this work undertakes a comparative study of DL models, specifically U-Net and its variants, for segmenting multiple targets with distinguished features in digital rocks, including discrete fracture networks (DFNs), pore spaces, and solid rock. Particularly, DFNs have a smaller volumetric fraction over others, bringing in a substantial challenge of imbalanced segmentation. The primary focus is to evaluate the architecture and feature enhancement strategies of various DL models, including U-Net, attention U-Net, residual U-Net, U-Net++, and residual U-Net++. The models were designed as 2.5D, utilizing a central 2D image and its two adjacent upper and lower 2D images as input to provide a pseudo-3D context. In addition, because the ground truth of segmentation was unknown for real-world digital rocks, we created a benchmark data set following the inverse operations of segmentation. The data synthesis started from the label images (i.e., solid rock, pore spaces, and DFNs), followed by simulating partial volume blurring, adding random background noise, and introducing ring artifacts to mimic real raw X-ray µCT images. The data set, which included various rock types (i.e., sandstone and artificial data), scanning resolution, and magnitudes of noise and artifacts, was divided into training and testing data sets with a 90% and 10% ratio, respectively. Moreover, in addition to the conventional pixel-wise evaluation metrics, the physics-based metric of the lattice-Boltzmann method (LBM) simulated permeability provided more comprehensive assessments. The results demonstrated that the residual connections, nested architectures, and redesigned skip connections contribute to the model performance and give the residual U-Net++ the highest accuracy. The improvements were mainly on the boundaries and small targets, especially the DFNs, which dominate the interconnectivity and therefore affect the permeability greatly. This study also rigorously evaluated the efficiency and generalization of each model, demonstrating that the sophisticated architectures achieved excellent practicability and maintained robust performance on completely unseen data, ensuring their suitability for diverse and challenging DRP applications.

Targeted nano-energetic material exploration through active learning algorithm implementation

This paper presents an active learning-based method designed to guide experiments towards user-defined specific regions, termed ”regions of interest,” within vast and multi-dimensional thermite design spaces. Thermites composed of metallic reactant coupled to an inorganic oxidizer are non-explosive energetic materials which stay inert and stable until subjected to a sufficiently strong thermal stimulus, after which they undergo fast burning with release of high amount of chemical energy (up to 16 kJ.cm−3). They represent an interesting class of nano-engineered energetic material because of their high adiabatic flame temperature (> 2600 °C) and customizable combustion properties. We introduced a new acquisition function combining linearly two factors with the usual standard deviation of a Gaussian Process Regression algorithm. A first factor guides the sampling towards the defined zone of interest, and a second, is an incentive function that encourages the exploration of under-sampled regions of the design space. We found that our algorithm effectively provides up to several tens of nanothermites that achieve specific desired properties well-distributed within the design space, after only 200 samplings, whereas, Latin Hypercube Sampling procedure samples less than 10 points of interest. Our framework is tailored for typical discrete search spaces involving multiple measured physical properties and when only a small dataset is available, as it is the case in thermite materials. But more generally, this research represents a significant advancement for large-scale problems in energetic materials science and engineering, where predicting the effect of feature modification is desired but limited simulations or experiments can be afforded due to their high cost.

How Super Is Supertrack? Expediting Care of Fast-track Patients through a Pediatric Emergency Department.

Fast-track models decrease patient crowding in emergency departments (EDs) by redirecting low-acuity patients to an expedited care pathway. In 2016, this institution's pediatric ED created a fast-track pathway for patients evaluated in a rapid assessment triage area who needed further management in the primary ED. This "Supertrack" designation was intended for patients requiring up to 1 hour of additional care, though means of ensuring these patients were discharged within their anticipated timeframe were lacking. We aimed to increase the percentage of Supertrack patients discharged within 1 hour of their ED bed assignment from 17% to 50%. Interventions included the creation of objective Supertrack criteria, departmental-wide progress reports, personalized reminders, intake huddles, and documentation prompts. We visualized data from Plan, Do, Study, Act (PDSA) cycles with statistical process control charts to determine special cause variation. The percentage of Supertrack patients discharged within their anticipated timeframe increased from 17% to 27% without an increase in return ED visits. The average time Supertrack patients spent in the ED decreased from 121 to 103 minutes. Personalized reminders demonstrated a significant but short-lived improvement. We improved the flow of Supertrack patients by decreasing their length of stay and increasing how many were discharged within their anticipated timeframe. Limitations included an unexpected surge in patients with respiratory complaints and staffing and structural constraints preventing the designation of a discrete Supertrack assessment space with dedicated providers. These findings are helpful for institutions seeking to develop an effective fast-track model with limited space and resources.

A Novel Model Predictive Current Control With Reduced Computational Burden Based on Discrete Space Vector Modulation for PMSM Drives

A Novel Model Predictive Current Control With Reduced Computational Burden Based on Discrete Space Vector Modulation for PMSM Drives

A Transformative Topological Representation for Link Modeling, Prediction and Cross-Domain Network Analysis.

Many complex social, biological, or physical systems are characterized as networks, and recovering the missing links of a network could shed important lights on its structure and dynamics. A good topological representation is crucial to accurate link modeling and prediction, yet how to account for the kaleidoscopic changes in link formation patterns remains a challenge, especially for analysis in cross-domain studies. We propose a new link representation scheme by projecting the local environment of a link into a "dipole plane", where neighboring nodes of the link are positioned via their relative proximity to the two anchors of the link, like a dipole. By doing this, complex and discrete topology arising from link formation is turned to differentiable point-cloud distribution, opening up new possibilities for topological feature-engineering with desired expressiveness, interpretability and generalization. Our approach has comparable or even superior results against state-of-the-art GNNs, meanwhile with a model up to hundreds of times smaller and running much faster. Furthermore, it provides a universal platform to systematically profile, study, and compare link-patterns from miscellaneous real-world networks. This allows building a global link-pattern atlas, based on which we have uncovered interesting common patterns of link formation, i.e., the bridge-style, the radiation-style, and the community-style across a wide collection of networks with highly different nature.

A novel Gauss–Jacobi quadrature for multiscale Boltzmann solvers

In this paper, we introduce a novel Gauss–Jacobi quadrature rule designed for infinite intervals, which is specifically applied to the velocity discretization in multi-scale Boltzmann solvers. Our method utilizes a newly formulated bell-shaped weight function for numerical integration. We establish the relationship between this new quadrature and the classical Gauss–Jacobi, as well as the Gauss–Hermite quadrature rules, and we compare the resulting discrete velocity distributions with several commonly used methods. Additionally, we validate the performance of our method through numerical simulations of flows with various Knudsen numbers. The proposed quadrature provides fresh insights into velocity space discretization.

Flexible Dual Multi-Modal Hashing for Incomplete Multi-Modal Retrieval

Multimodal hashing aims to efficiently integrate multi-source data into a unified discrete Hamming space, facilitating fast similarity searches with minimal query and storage overhead. Traditional multimodal hashing assumes that data from different sources are fully observed, an assumption that fails in real-world scenarios involving large-scale multimodal data, thereby compromising conventional methods. To address these limitations during both training and retrieval, our approach manages dual-stage data missing, occurring in both phases. In this paper, we introduce a novel framework called Flexible Dual Multimodal Hashing (FDMH), which recovers missing data at both stages by jointly leveraging low-dimensional data relations and semantic graph structural relationships in multi-source data, achieving promising performance in incomplete multimodal retrieval. We transform the original features into anchor graphs and use existing modalities to reconstruct the anchor graphs of missing modalities. Based on these anchor graphs, we perform weight-adaptive fusion in the semantic space, supervised by original semantic labels, and apply a tensor nuclear norm to enforce consistency constraints on the projection matrices across different modalities. Furthermore, our method flexibly fuses existing and recovered modalities during retrieval. We validate the effectiveness of our approach through extensive experiments on four large-scale multimodal datasets, demonstrating its robust performance in real-world dual-missing retrieval scenarios.

Information based explanation methods for deep learning agents—with applications on large open-source chess models

With large chess-playing neural network models like AlphaZero contesting the state of the art within the world of computerised chess, two challenges present themselves: the question of how to explain the domain knowledge internalised by such models, and the problem that such models are not made openly available. This work presents the re-implementation of the concept detection methodology applied to AlphaZero, by using large, open-source chess models with comparable performance. We obtain results similar to those achieved when applying this methodology to AlphaZero, while relying solely on open-source resources. We also present a novel explainable AI (XAI) method, which is guaranteed to highlight exhaustively and exclusively the information used by the explained model. This method generates visual explanations tailored to domains characterised by discrete input spaces, as is the case for chess. Our presented method has the desirable property of controlling the information flow between any input vector and the given model, which in turn provides strict guarantees regarding what information is used by the trained model during inference. We demonstrate the viability of our method by applying it to standard 8×8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$8 \ imes 8$$\\end{document} chess, using large open-source chess models.

Crossing and dismantling boundaries: recognising the value of professional staff within higher education

In this article, we use the concept of the third space to explore how professional staff within UK universities experience boundaries. We focus on professional staff working in three areas of higher education that have been conceptualised differently as third spaces to date: widening participation, technical staff and academic administration. We draw on empirical research from three distinct, but related, qualitative research projects that explored contemporary issues, institutional change, professional identities, relationships and expertise within these under-researched professional contexts. We show how boundaries are experienced, crossed and sometimes dismantled. We highlight where increased collaboration has a positive effect on achieving institutional goals through improved relationships between academic and professional staff, and the recognition of diverse forms of knowledge within the university workforce. We argue for a conception of the third space that is not a discrete or distinct space, which professionals work within or outside of, but instead conceived of as a way of working, which all higher education professionals may engage in, to greater or lesser extents. Doing so provides new insights into the existence of third space working among new professional groups and highlights the potential for all professional staff to engage in third space working to the benefit of their institutions.

Psychometric evaluation of high-resolution electrotactile interface for conveying 3D spatial information

This study presents a detailed psychometric evaluation of a novel high-resolution electrotactile interface, which is developed to provide users with 3D spatial information and facilitate enhanced interaction with a Supernumerary Robotic Limb (SRL). The research introduces a novel electrotactile system that employs a multi-pad electrode configuration on the thigh, aimed at delivering intuitive feedback to users about the position of the SRL in a three-dimensional space. The interface's effectiveness was assessed through a series of psychometric tests, including static spatial discrimination, target-reaching with spatial feedback, frequency discrimination, and combined spatial/frequency modulation. The key findings demonstrate that participants could differentiate between 30 electrode pads with an average success rate of 62.7% when they were activated statically, while in the dynamic target-reaching task, the success rate increased to 88.1%. Frequency discrimination tests further revealed that four frequency levels could be distinguished with 86.0% success rate in single-pad feedback while the performance decreased to 74.3% in multi-pad distributed feedback. Finaly, in the closed-loop test with mixed spatial and frequency modulation, participants achieved an overall success rate of 78.8% in target reaching across 10 × 4 discrete 2D space. These results highlight the interface’s capability to transmit high-resolution spatial information through electrotactile feedback, offering a foundation for future applications in tactile-based navigation and control systems.

Stress-related discrete variable topology optimization with handling non-physical stress concentrations

The accuracy of stress calculation with a fixed mesh significantly affects the stress-based topology optimization, due to potential non-physical stress concentrations in voxel-based topology descriptions. This paper proposes a novel problem-independent machine learning enhanced high-precision stress calculation method (PIML-HPSCM) to address this challenge. As an immersed analysis method, PIML-HPSCM combines the high efficiency of fixed mesh with the accuracy of body-fitted mesh, without complex integration schemes of other immersed methods. PIML-HPSCM utilizes the extended multiscale finite element method to depict the material heterogeneity within high-resolution boundary elements. The accurate stress field can then be calculated conveniently by establishing stress evaluation matrices of high-resolution boundary elements. Moreover, the PIML is independent of problem settings and is applicable for various problems with the same governing equation type. Invoking the offline-trained neural network online can enhance stress calculation efficiency by 10–20 times. The stress-based discrete variable topology optimization, which naturally avoids singular stress phenomenon, is efficiently addressed by the sequential approximate integer programming method with PIML-HPSCM. Results from 2D and 3D examples demonstrate that the stresses calculated by PIML-HPSCM are consistent with those by body-fitted mesh, and optimized designs effectively eliminate stress concentrations of initial designs and have uniform stress distributions.

Convergence of the Two Point Flux Approximation method and the fitted Two Point Flux Approximation method for options pricing with local volatility function

In this paper, we deal with numerical approximations for solving the Black–Scholes Partial Differential Equation (PDE) for European and American options pricing with local volatility. This PDE is well-known to be degenerated. Local volatility model is a model where the volatility depends locally of both stock price and time. In contrast to constant volatility or time-dependent volatility models for which analytical representations of the exact solution is known for European Call options, there is no analytical solution for local volatility. The space discretization is performed using the classical finite volume method with Two-Point Flux Approximation (TPFA) and a novel scheme called Fitted Two-Point Flux Approximation (FTPFA). The Fitted Two-Point Flux Approximation (FTPFA) combines the fitted finite volume method and the standard TPFA method. More precisely the fitted finite volume method is used when the stock price approaches zero with the goal to handle the degeneracy of the PDE while the TPFA method is used on the rest of space domain. This combination yields our fitted TPFA scheme. The Euler method is used for the time discretization. We provide the rigorous convergence proofs of the two fully discretized schemes. Numerical experiments to support theoretical results are provided.

A sequential multi-agent reinforcement learning framework for different action spaces

In many real-world decision-making tasks, multi-agent need to learn collaboration in a high-dimensional complex action space, rather than just a single discrete action space. Recently, value decomposition learning methods such as QMIX have emerged as a promising approaches for collaborative multi-agent tasks. However, most of the value decomposition algorithms can only be used in discrete action space, which would limit their practicability. To address the limitation, we propose a novel algorithm called Multi-Agent Sequential Q-Networks (MASQN), which can be applied to the multi-agent domains with continuous, multidiscrete or hybrid action spaces. The proposed algorithm is based on the structure of centralized training with decentralized execution (CTDE). The decentralized actors ensure adaptability to different action spaces by utilizing action space discretization and sequential models, and the centralized critic utilizes the value decomposition architecture to guide effective updates of the policy parameters for each agent. We also give the convergence of joint policy from the perspective of policy iteration, by combining it with the CTDE structure and the constraint of the Individual Global Max (IGM) condition. Finally, we evaluate the MASQN algorithm on two benchmark environments: MAMuJoCo and Hybrid Predator–Prey. The empirical results show that MASQN out performs the state-of-the-art performance on three different action spaces.