Time Step Research Articles

GWO-ANFIS-RD3PG: A reinforcement learning approach with dynamic adjustment and dual replay mechanism for building energy forecasting

Reliable prediction of building energy consumption is essential for effective and sustainable energy management. Traditional forecasting methods, however, face challenges when dealing with sudden changes in energy consumption. To address the above-mentioned issue, we introduce the GWO-ANFIS-RD3PG prediction model in this paper. This model aims to ensure global forecasting accuracy while minimizing prediction errors at sudden change points. A Grey Wolf Optimization (GWO) algorithm with the Adaptive Neuro-Fuzzy Inference System (ANFIS) is proposed to predict the energy consumption type and its fluctuation magnitude for the next time step. Within the Recurrent Dual Experience Replay Buffer DDPG (RD3PG) prediction module, we employ Long Short-Term Memory (LSTM), as the actor network in the Deep Deterministic Policy Gradient (DDPG), to account for long-term dependencies in time series data. Notably, we introduce an adaptive action modification mechanism that allows the agent to optimize actions based on the output of the aforementioned ANFIS, enabling real-time adjustments during sudden change. To further enhance the model’s performance, we adopt a dual experience replay mechanism to store data samples from sudden change points, capturing insight information during these anomalies. Experimental results on two real-world datasets demonstrate that this method reduces MAE by 5.81% and 13.47%, and RMSE by 5.69% and 15.21% compared to the state-of-art models, showing the significance of the proposed method for energy efficiency improvement in real-world building operations.

The asymptotic preserving unified gas kinetic scheme for the multi-scale kinetic SIR epidemic model

In this paper, we present an asymptotic preserving scheme for the two-dimensional space-dependent and multi-scale kinetic SIR epidemic model which is widely used to model the spread of infectious diseases in populations. The scheme combines a discrete ordinate method for the velocity variables and finite volume method for the spatial and time variables. The idea of unified gas kinetic scheme (UGKS) is used to construct the numerical boundary fluxes which needs the formal integral solutions of the model. Due to the coupling of the three transfer equations in the SIR model, it is difficult to obtain these integral solutions dependently. We decouple the system by constructing the fluxes in a separate way. Then following the framework of UGKS we can obtain the macro auxiliary quantities which is needed in the scheme. Thus the SIR model can be solved in the sequential way. In addition, we can show numerically that the scheme is second-order accurate both in space and time. Moreover, it can not only capture the solution of the diffusion limit equations without requiring the cell size and time step being related to the smallness of the scaling parameters, but also resolve the solution in hyperbolic regime in a natural way. Furthermore, the positive property of the UGKS is analyzed in detail, and through adding time step constraint conditions and applying nodal limiters together, the positive UGKS, called PPUGKS2−order, is obtained. Moreover, in order release the time step constraints in the diffusion regime, a temporal first-order accuracy positive preserving UGKS, called PPUGKS1−order, is proposed. Finally, several numerical tests are included to validate the performance of the proposed schemes.

Expressive 3D Facial Animation Generation Based on Local-to-Global Latent Diffusion.

3D Facial animations, crucial to augmented and mixed reality digital media, have evolved from mere aesthetic elements to potent storytelling media. Despite considerable progress in facial animation of neutral emotions, existing methods still struggle to capture the authenticity of emotions. This paper introduces a novel approach to capture fine facial expressions and generate facial animations using audio synchronization. Our method consists of two key components: First, the Local-to-global Latent Diffusion Model (LG-LDM) tailored for authentic facial expressions, which can integrate audio, time step, facial expressions, and other conditions towards possible encoding of emotionally rich yet latent features in response to possibly noisy raw audio signals. The core of LG-LDM is our carefully designed Facial Denoiser Model (FDM) for aligning the local-to-global animation feature with audio. Second, we redesign an Emotion-centric Vector Quantized-Variational AutoEncoder framework (EVQ-VAE) to finely decode the subtle differences under different emotions and reconstruct the final 3D facial geometry. Our work significantly contributes to the key challenges of emotionally realistic 3D facial animation for audio synchronization and enhances the immersive experience and emotional depth in augmented and mixed reality applications. We provide a reproducibility kit including our code, dataset, and detailed instructions for running the experiments. This kit is available at https://github.com/wangxuanx/Face-Diffusion-Model.

Influence of the stratification parameters on the wake field of an underwater vehicle in a two-layer stratified flow

Because the ocean exhibits different stratification states in different seasons and regions, the effect of different stratification parameters on a submarine wake must be studied. In particular, to investigate such effect in a two-layer stratified flow, this study established a computational fluid dynamics (CFD) model based on the URANS equations, shear-stress transport (SST) k-ω turbulence model, and Eulerian multiphase flow model. The volume of fluid (VOF) method was adopted to implement the free-surface capture method. The working conditions of the SUBOFF model under an infinite diving depth and near the free surface were compared with those of the experiments, and the convergence of the time step and grid number under stratified flow conditions was verified. These validation steps proved the feasibility of the CFD method. Finally, the effects of the stratification parameters on the free surface waves, internal waves, and turbulent kinetic energy behind the vehicle were observed by varying the stratification parameters to achieve different working conditions. The results show that when an underwater vehicle sails in a two-layer stratified flow, the interstratified density ratio and depth of the internal wave surface affect its wake field. When the underwater vehicle sails in the water layer, with an increase in the interstratified density ratio, the free-surface roughness increases and the turbulent kinetic energy decreases. When the underwater vehicle sails in the salt water layer, the result is just the opposite.

Two novel linearized energy-conserving finite element schemes for nonlinear regularized long wave equation

In this paper, two linearized second-order energy-conserving schemes for the nonlinear regularized long wave (RLW) equation are introduced, the unconditional superclose and superconvergence results are presented by using the conforming finite element method (FEM). Initially, through a skillful decomposition of the nonlinear term, two linearized second-order fully discrete schemes are developed. Compared to the previous nonlinear approaches, these schemes significantly reduce the number of iterations and improve computational efficiency; moreover, they conserve energy, and ensure the boundedness of the numerical solution in the H1-norm directly, which represents an advancement over the L∞-norm boundedness reported in prior studies. Secondly, based on the boundedness of the FE solution, the Ritz projection operator and high-precision results of the linear triangular element, the error estimates for superclose and superconvergence are derived without any restrictions on the ratio between time step size Δt and spatial mesh size h. Finally, four numerical examples are provided to confirm the accuracy of the theoretical analysis and the effectiveness of the method.

Challenges of high-fidelity air quality modeling in urban environments – PALM sensitivity study during stable conditions

Abstract. Urban air quality is an important part of human well-being, and its detailed and precise modeling is important for efficient urban planning. In this study the potential sources of errors in large eddy simulation (LES) runs of the PALM model in stable conditions for a high-traffic residential area in Prague, Czech Republic, with a focus on street canyon ventilation, are investigated. The evaluation of the PALM model simulations against observations obtained during a dedicated campaign revealed unrealistically high concentrations of modeled air pollutants for a short period during a winter inversion episode. To identify potential reasons, the sensitivities of the model to changes in meteorological boundary conditions and adjustments of model parameters were tested. The model adaptations included adding the anthropogenic heat from cars, setting a bottom limit of the subgrid-scale turbulent kinetic energy (TKE), adjusting the profiles of parameters of the synthetic turbulence generator in PALM, and limiting the model time step. The study confirmed the crucial role of the correct meteorological boundary conditions for realistic air quality modeling during stable conditions. Besides this, the studied adjustments of the model parameters proved to have a significant impact in these stable conditions, resulting in a decrease in concentration overestimation in the range 30 %–66 % while exhibiting a negligible influence on model results during the rest of the episode. This suggested that the inclusion or improvement of these processes in PALM is desirable despite their negligible impact in most other conditions. Moreover, the time step limitation test revealed numerical inaccuracies caused by discretization errors which occurred during such extremely stable conditions.

Near future flash flood prediction in an arid region under climate change

Flash floods represent a significant threat, triggering severe natural disasters and leading to extensive damage to properties and infrastructure, which in turn results in the loss of lives and significant economic damages. In this study, a comprehensive statistical approach was applied to future flood predictions in the coastal basin of North Al-Abatinah, Oman. In this context, the initial step involves analyzing eighteen General Circulation Models (GCMs) to identify the most suitable one. Subsequently, we assessed four CMIP6 scenarios for future rainfall analysis. Next, different Machine Learning (ML) algorithms were employed through H2O-AutoML to identify the best model for downscaling future rainfall predictions. Forty distribution functions were then fitted to the future daily rainfall, and the best-fit model was selected to project future Intensity-Duration-Frequency (IDF) curves. Finally, the Soil and Water Assessment Tool (SWAT) model was utilized with sub-daily time steps to make accurate flash flood predictions in the study area. The findings reveal that IITM-ESM is the most effective among GCM models. Additionally, the application of stacked ensemble ML model proved to be the most reliable in downscaling future rainfall. Furthermore, this study highlighted that floods entering urbanized areas could reach 20.33 and 20.70 m³/s under pessimistic scenarios during rainfall events with 100 and 200-year return periods, respectively. This hierarchical comprehensive approach provides reliable results by utilizing the most effective model at each step, offering in-depth insight into future flash flood prediction.

The CNN-LSTM-attention Model for short term prediction of the Polar Motion

Abstract The accuracy of polar motion prediction significantly impacts the fields of coordinate frame transformation, satellite orbit determination, and deep space exploration. The present study develops two short term forecasting models based on the EOP 14C04 series. One hybrid approach incorporates convolutional neural networks (CNN) and long short-term memory networks (LSTM), augmented with an attention mechanism; whereas another baseline model comprises CNN and LSTM. The first model, in contrast to the second model, incorporates an attention mechanism module for a more comprehensive integration of temporal information at each time step. In the initial short-term forecasting experiment, we conducted 360 repeated predictions, and the findings revealed that the parameters suitable for PMX forecasting may not necessarily be applicable to PMY forecasting. In the second experiment, the two models generated a total of 500 forecasts, each encompassing short-term predictions ranging from 1 to 30 days. The experimental results demonstrate that the first model exhibits mean absolute error (MAE) range of 0 ~ 7.72 mas for PMX and 0 ~ 4.73 mas for PMY, while the second model shows MAE range of 0 ~ 7.88 mas for PMX and 0 ~ 4.78 mas for PMY. After two exploratory experiments, we discovered the following results: the first model exhibits marginally superior predictive accuracy compared to the second model. Furthermore, this study substantiates the robustness of both models in short-term prediction and affirms the significance of assigning distinct weights to past temporal intervals in forecasting, thereby offering a novel perspective for polar motion prediction research.

Decomposition of nonlinear collision operator in quantum lattice Boltzmann algorithm

Abstract We propose a quantum algorithm to tackle the quadratic nonlinearity in the Lattice Boltzmann (LB) collision operator. The key idea is to build the quantum gates based on the particle distribution functions (PDF) within the coherence time for qubits, and upon quantum state evolution, the resulting PDFs will have quadraticity. To this end, we decompose the collision operator for a DmQn lattice model into a product of 2(n+1) operators, where n is the number of lattice velocity directions. After decomposition, the (n+1) operators with constant entries remain unchanged throughout the simulation, whereas the remaining (n+1) will be built based on the statevector of the previous time step. Also, we show that such a decomposition is not unique. Compared to the second-order Carleman-linearized LB, the present approach reduces the circuit width by half and circuit depth by exponential order. The algorithm has been verified through the one-dimensional flow discontinuity and two-dimensional Kolmogrov-like flow test cases.

Adaptive time step selection for spectral deferred correction

AbstractSpectral Deferred Correction (SDC) is an iterative method for the numerical solution of ordinary differential equations. It works by refining the numerical solution for an initial value problem by approximately solving differential equations for the error, and can be interpreted as a preconditioned fixed-point iteration for solving the fully implicit collocation problem. We adopt techniques from embedded Runge-Kutta Methods (RKM) to SDC in order to provide a mechanism for adaptive time step size selection and thus increase computational efficiency of SDC. We propose two SDC-specific estimates of the local error that are generic and do not rely on problem specific quantities. We demonstrate a gain in efficiency over standard SDC with fixed step size and compare efficiency favorably against state-of-the-art adaptive RKM.

Using the Discrete Wavelet Transform for Lossy On‐the‐Fly Compression of GPU Fluid Simulations

ABSTRACTHigh‐performance computing in fluid dynamics frequently confronts substantial memory demands, especially in large‐scale applications. Data compression techniques can alleviate these memory constraints, but introduce new challenges. This paper introduces an innovative on‐the‐fly low‐overhead lossy compression technique tailored for GPU‐based fluid simulations, utilizing the discrete wavelet transform (DWT). The technique is applicable to any numerical scheme where the data is stored on a regular grid and the time step is computed using a stencil. Our approach significantly diminishes memory requirements, achieving up to a 10‐fold long‐term reduction on a D3Q27 simulation, while minimally impacting the simulation accuracy. The methodology is built around careful design choices to achieve a satisfactory compression ratio/speed trade‐off. It effectively maintains mass conservation and accurately preserves essential discontinuities in simulations. Extensive testing with a D3Q27 Lattice‐Boltzmann method (LBM) simulation on a single GPU has shown that large‐scale grids can be processed with minimal impact on the simulation accuracy and acceptable compression times. This compression technique demonstrates a robust capability to handle memory limitations in fluid simulations, opening the door to more complex and larger‐scale simulations.

Evaluating the performance of water distribution network deterioration using customer-oriented performance indices

ABSTRACT Water distribution networks (WDNs) are an essential urban infrastructure, with their performance directly influencing societal well-being. Our study applied to a real network model that employs a 24-h simulation with 1-h time steps and evaluates the impact of leaks and loss in the pipe cross-sectional area on WDN hydraulic performance as experienced by end users. Adhering to a UK utility's 20-m head pressure requirement as the water main benchmark, we present two new customer-oriented performance indices (CPIs) centred on network reliability and pressure deficit severity. The new CPIs adeptly quantify network performance degradation due to pipe deterioration. This degradation translates directly to a poor customer experience, highlighting the potential for these CPIs to pinpoint areas of the network where performance levels are compromised. Furthermore, the CPIs identify individual pipes within the network where defects would severely impact network performance and the sets of pipes which, when simultaneously experiencing defects, would lead to a more severe loss in network performance. Results show that the CPIs capture relatively small performance declines and identify sensitive pipes impacting network performance, providing insights for optimised inspection and maintenance intervention to provide better customer service.

Transforming chaotic and stiff systems to improve numerical accuracy

AbstractSystems of differential equations can exhibit chaotic or stiff behavior under specific conditions, posing challenges for time-stepping numerical methods. For explicit methods, the required time step resolution significantly exceeds the resolution associated with the smoothness of the exact solution for specified accuracy. In order to improve efficiency, the question arises whether transformation to asymptotically stable solutions can be performed, for which neighbouring solutions converge towards each other at a controlled rate. Employing the concept of local Lyapunov exponents, it is shown that chaotic differential equations can indeed be transformed to obtain high accuracy, whereas stiff equations cannot. For instance, the accuracy of explicit fourth order Runge–Kutta solution of the Lorenz chaotic equations can be increased by several orders of magnitude. Alternatively, the time step can be significantly extended with retained accuracy. The transform method applies broadly to chaotic systems, including weather prediction and turbulence.

Graph-driven multi-vessel long-term trajectories prediction for route planning under complex waters

Current collision avoidance algorithms used in autonomous navigation vessels are hindered by limited long-term visibility of dynamic obstacles, resulting in overly cautious and frequent avoidance maneuvers that can actually increase the risk of collisions in complex waterways. Therefore, this paper proposed a novel graph-driven multi-vessel long-term trajectory prediction method (termed GMLTP), which extends the length of real-time and accurate prediction of other vessel trajectories. GMLTP can enhance collision avoidance algorithms by enabling more anticipatory trajectory prediction, ultimately supporting real-time route planning in creating safer, more efficient, and optimized routes. Specifically, GMLTP consists of a multi-graph spatial convolution (MGSC) layer and a probability sparse (ProbSparse) self-attention Transformer. MGSC is a finer spatial interactions extractor, which supports the modeling of spatial dependency evolution on longer sequences and thus improves the perception of long-term trends, while ProbSparse self-attention Transformer is used to reduce the computation of learning long-term global time dependencies and thus extending the predictable length. Extensive experimental results indicate that GMLTP exhibits better accuracy and generalization in prediction tasks beyond 48-timesteps (each time step is 10 s), which can provide better assistance to current real-time route planning tasks.

A novel liquid fraction iteration methodology for addressing oscillatory issues in the total enthalpy method

The total enthalpy method (TEM) has been proposed and employed for several decades to address both isothermal and gradual phase change problems. However, recent investigations into isothermal phase changes have revealed that the phase interface predicted by the TEM oscillates with variations in spatial and temporal discretizations, due to the inconsistency between liquid fraction and enthalpy. To address this issue, and drawing inspiration from the liquid fraction iteration methodology used in the widely adopted heat source method (HSM) to ensure consistency between liquid fraction and temperature, this paper introduces a novel liquid fraction iteration methodology specifically tailored for the TEM, referred to as the iterative TEM (ITEM). This approach is validated against an experimental benchmark involving the melting of a pure substance. Grid and time-step dependence studies confirm that the ITEM effectively eliminates oscillations and exhibits convergence with respect to both grid size and time step. Moreover, the ITEM achieves accuracy comparable to that of the HSM. Finally, the computational costs associated with the ITEM are examined, revealing that costs increase rapidly once the grid Fourier number (Fo) exceeds one. Maintaining the grid Fo number below approximately 0.5 and ensuring the ratio of the relaxation factor to the grid Fo number to approach one significantly improve computational efficiency. The relaxation factor is a crucial parameter within the liquid fraction iteration scheme.

Drainage gradient versus seasonal cycles: Differential response of microbial community composition to variations in soil moisture

AbstractThe variation in the soil microbial community composition over time was assessed at monthly time steps for 1 year in three neighboring Mollisols spanning a drainage gradient. This was done to distinguish between natural oscillations in the community composition versus lasting adaptations to environmental factors such as soil water availability. To isolate soil water availability as a controlling factor, we selected three soils sharing the same soil order (fine‐silty, superactive Argixerolls/Argialbolls); slope (0%–1%); temperature regime (mesic); moisture regime (xeric); and land use history (continuous grassland for the past 10 years) but differing in drainage class (well‐drained vs. moderately well‐drained vs. poorly drained). Changes in microbial diversity were quantified by monitoring the bacterial community at monthly intervals for 1 year. Within individual soils, α‐diversity varied little with season and drainage classes. Despite the three soils experiencing the same climate regime and vegetation/land use, they exhibited distinct community composition and turnover, which we attribute to differences in moisture availability across drainage and seasons. We posit that a seasonal recurring drop in soil redox potential induced by seasonal water saturation in the poorly drained soil is the most probable cause setting the microbial community of that soil apart from those in the better drained soils. Our investigation suggests that not all indicators of microbial diversity share the same sensitivity to seasonal and drainage‐related soil moisture variations.

Impact of the frequency error of direct digital synthesizers on the evaluation of two-photon light shift in atom gravimeters

One major systematic error for free-fall atom gravimeters is the effect of two-photon light shift (LS2). In the process of evaluating LS2, the results can be affected by the residual frequency error of direct digital synthesizers due to necessary experimental parameter changes. In this paper, the impact of the coupling effect between the frequency error and LS2 has been investigated and analyzed, along with the related physical mechanisms. The parameters of the frequency error sequence, such as the time step of δt and the time delay of Δt, significantly affect the bias and uncertainty of LS2. Notably, when these parameters are significantly altered or misaligned, the impact can reach several tens of µGal. Conversely, when they remain within the optimal ranges, the impact can be minimal. Specifically, when δt is less than or equal to 10 µs, the impact on the LS2 bias is less than 0.3 µGal, with the contribution to the total uncertainty of the gravity value being approximately 0.1 µGal. Furthermore, after correcting the phase shift introduced by the frequency error, the evaluation results have a similar improvement effect on the whole. Compared to the LS2 theoretical value, the residual is generally on the order of µGal. Through the comprehensive analysis and optimization, as well as related experiments, this cross-effect is managed and decoupled, leading to accurate LS2 evaluation results. This improvement ensures a better accuracy in the obtained absolute gravity values. The analysis methods discussed can provide an effective strategy for enhancing the performance of atom gravimeters.

A fully-coupled algorithm with implicit surface tension treatment for interfacial flows with large density ratios

The stability of most surface-tension-driven interfacial flow simulations is governed by the capillary time-step constraint. This concerns particularly small-scale flows and, more generally, highly-resolved liquid-gas simulations with moderate inertia. To date, the majority of interfacial-flow simulations are performed using an explicit surface-tension treatment, which restrains the performance of such simulations. Recently, an implicit treatment of surface tension able to breach the capillary time-step constraint using the volume-of-fluid (VOF) method was proposed, based on a fully-coupled pressure-based finite-volume algorithm. To this end, the interface-advection equation is incorporated implicitly into the linear flow solver, resulting in a tight coupling between all implicit solution variables (colour function, pressure, velocity). However, this algorithm is limited to uniform density and viscosity fields. Here, we present a fully-coupled algorithm for interfacial flows with implicit surface tension applicable to interfacial flows with large density and viscosity ratios. This is achieved by solving the continuity and momentum equations in conservative form, whereby the density is treated implicitly with respect to the colour function, and the advection term of the interface-advection equation is discretised using the THINC/QQ algebraic VOF scheme, yielding a consistent discretisation of the advective terms. This new algorithm is tested by considering representative surface-tension-dominated interfacial flows, including the Laplace equilibrium of a stationary droplet and the three-dimensional Rayleigh-Plateau instability of a liquid filament. The presented results demonstrate that interfacial flows with large density and viscosity ratios can be simulated and energy conservation is ensured, even with a time step larger than the capillary time-step constraint, provided that other time-step restrictions are satisfied.

On the Definition of Velocity in Discrete-Time, Stochastic Langevin Simulations

We systematically develop beneficial and practical velocity measures for accurate and efficient statistical simulations of the Langevin equation with direct applications to computational statistical mechanics and molecular dynamics sampling. Recognizing that the existing velocity measures for the most statistically accurate discrete-time Verlet-type algorithms are inconsistent with the simulated configurational coordinate, we seek to create and analyze new velocity companions that both improve existing methods as well as offer practical options for implementation in existing computer codes. The work is based on the set of GJ methods that, of all methods, for any time step within the stability criteria correctly reproduces the most basic statistical features of a Langevin system; namely correct Boltzmann distribution for harmonic potentials and correct transport in the form of drift and diffusion for linear potentials. Several new and improved velocities exhibiting correct drift are identified, and we expand on an earlier conclusion that, generally, only half-step velocities can exhibit correct, time-step independent Maxwell–Boltzmann distributions. Specific practical and efficient algorithms are given in familiar forms, and these are used to numerically validate the analytically derived expectations. One especially simple algorithm is highlighted, and the ability of one of the new on-site velocities to produce statistically correct averages for a particular damping value is specified.

Synthesis of novel green nanocomposites by considering enhanced oil recovery and asphaltene adsorption effectiveness in calcite and dolomite formations

Asphaltene deposition is known as the main issues in reservoirs, which causes formation damage in reservoir. This research investigated the effects of a newly introduced green nanocomposites, namely eucalyptus/CuO/Fe3O4/xanthan nanocomposites (EC-NCs), on the inhibition of asphaltene precipitation in calcite and dolomite formations. First, at two time steps of 48 and 96 h, asphaltene adsorption on EC-NCs surfaces was examined through scanning electron microscope (SEM) tests in both calcite and formation tests. Moreover, asphaltene adsorption on the surface of EC-NCs was confirmed through isotherm models including Langmuir and Freundlich and the interfacial tension between CO2 and oil. Finally, a series of static and dynamic tests were performed at the highest adsorption pressure points, including 4200, 3950, and 3700 psi, and at the highest adsorption time step, i.e., 96 h, and the effects of asphaltene adsorption were seen on permeability reduction and asphaltene precipitation. EC-NCs exhibited superior efficacy in both asphaltene adsorption and precipitation inhibition. Two separate pressure changes were observed, and the ratios of the interfacial tension slope in the 2nd to the 1st regions [1st: 200–2700 psi, 2nd:2700–4200 psi] were changed from 19.44 % to 25.00 % and 29.74 % in 48 and 96 h, respectively, and this confirms that asphaltene had indeed adhered to the surface of the EC-NCs. Moreover, at 48, and 96 h, the size reductions of particles in SEM for calcite and dolomite were (29.27 %, 56.81 %), and (59.09 %, 62.25 %), respectively, which shows asphaltene adsorption was more efficient in dolomite formation, and in 96 h.