Conventional Numerical Approaches Research Articles

Physics-informed convolutional neural network for microgrid economic dispatch

The variability of renewable energy generation and the unpredictability of electricity demand create a need for real-time economic dispatch (ED) of assets in microgrids. However, solving numerical optimization problems in real-time can be incredibly challenging. This study proposes using a convolutional neural network (CNN) based on deep learning to address these challenges. Compared to traditional methods, CNN is more efficient, delivers more dependable results, and has a shorter response time when dealing with uncertainties. While CNN has shown promising results, it does not extract explainable knowledge from the data. To address this limitation, a physics-inspired CNN model is developed by incorporating constraints of the ED problem into the CNN training to ensure that the model follows physical laws while fitting the data. The proposed method can significantly accelerate real-time economic dispatch of microgrids without compromising the accuracy of numerical optimization techniques. The effectiveness of the proposed data-driven approach for optimal allocation of microgrid resources in real-time is verified through a comprehensive comparison with conventional numerical optimization approaches.

Estimating equivalent elastic properties of frozen clay soils using an XFEM-based computational homogenization

This study addresses the challenge of estimating the elastic properties of heterogeneous frozen clay soils by introducing a comprehensive approach that combines analytical and numerical models. The frozen clay soil is treated as a mixture composed of frozen clay-water composites and nonclay mineral inclusions. An inversion algorithm is employed to deduce the elastic properties of the matrix (clay-water composites) of two artificially frozen sandy clay samples with known temperature-dependent elastic properties. Subsequently, a two-dimensional numerical simulation using the eXtended Finite Element Method (XFEM) is conducted to carry out numerical homogenization by considering the imperfect bond among frozen clay-water composites and nonclay minerals. The numerical homogenization model offers insights into the temperature-dependent behavior of the interface stiffness parameter. The numerical homogenization results are compared with conventional numerical homogenization approaches like the FEM, which rigidly defines the bonding between inclusions and the matrix. The comparison indicates that the neglect of imperfect bonds among clay-water composites and nonclay minerals will lead to unrealistic outcomes in cases with a high fraction of inclusions. This integrated approach advances the understanding and prediction of elastic properties of frozen clay soils by considering their heterogeneous nature.

Dynamic optimal energy flow of integrated electricity and gas systems in continuous space

The intrinsic flexibility of integrated electricity and gas systems (IEGSs) hinges on the gas flow dynamics dictated by partial differential equations (PDEs). However, conventional numerical approaches for PDEs grapple with inefficiencies and inaccuracies for operational analysis, chiefly due to the discretization of PDE invoked. For the first time, this study pioneers an analytical methodology for IEGS's analysis, effectively eliminating the pitfalls of discretization in solving gas flow dynamics. Based on this, the dynamic optimal energy flow problem in IEGS is reformulated in continuous space, significantly simplifying complex models while bolstering analytical precision. Case studies affirm the remarkable advantages of the proposed analytical approach. Under comparable scenarios, the proposed method improves computational efficiency dozens of times and exhibits concurrently heightened levels of accuracy.

Utilizing lagging-phase analysis to identify topological phase transitions in 1D chains

The Zak phase serves as a reliable index for pinpointing topological phase transitions within one-dimensional chains, typically ascertained through numerical methods in complex situations. Nonetheless, in proximity to the transition threshold, the numerical Zak phase may become ambiguous. This ambiguity arises from the discrete nature of numerical approaches and the nonlinear relationship between the wave function's phase and the wave vector (k). In response, this paper presents an innovative method aimed at accurately determining the winding number, thereby facilitating the identification of topological phase transitions. Our approach hinges on analyzing the evolution of the phase difference between the projections of the Bloch wave function onto two distinct sublattices. We demonstrate the efficacy of this method through three illustrative examples: the Su–Schrieffer–Heeger model, a magnetic vortex chain, and a trimer lattice chain. The results indicate that our proposed numerical lagging-phase examination method achieves superior precision in identifying topological phase transitions, particularly at critical junctures, compared to the conventional numerical Zak phase approach.

Efficient computational hybrid method for the solution of 2D multi-term fractional order advection-diffusion equation

Abstract Multi-term time-fractional advection diffusion equations are vital for simulating a wide range of physical phenomena, including fluid dynamics and environmental transport processes. However, due to their natural complexity, these equations pose challenges for conventional numerical approaches. In this article, we develop a high order accurate method to solve the multi-term time-fractional advection diffusion equations. We combine the Laplace transform (LT) to integrate the considered equations in time, with Chebyshev spectral method (CSM) for spatial terms The proposed method produces highly accurate solutions with remarkably low computational cost as compared to finite difference method. The propose numerical scheme first employs the LT which reduces the considered problem into a finite set of elliptic equations which may be solved in parallel. Then, the CSM is employed for the disctrezation of spatial operators, which makes it possibly to accurately represent the solution chebyshev grid. Finally, numerical inversion of LT is used to convert the obtain solution from the Laplace domain into the real domain. This work utilizes the modified Talbot’s method and Stehfest’s method for numerical inversion of the LT. To measure the performance, efficiency, and accuracy of the suggested approach, numerical approximations of three models are acquired and verified against the exact solution. The outcomes presented in tables and figures demonstrate that the modified Talbot’s method performed better as compared to Stehfest’s method.

Leveraging artificial intelligence for simplified adiabatic compression heating prediction: Comparing the use of artificial neural networks with conventional numerical approach

This study presents a comprehensive evaluation of artificial neural networks (ANNs) for predicting adiabatic compression heating in high-pressure processing (HPP) and high-pressure thermal processing (HPTP). The ANNs were thoroughly compared with experimental data, as well as data predicted by a previously developed approach. This previous approach used numerical methods to extract relevant material properties from experimental data, which was then used for compression heating predictions by solving an ordinary differential equation. The new work showcases the efficacy of ANNs in accurately predicting compression heating effects. The results indicate that ANNs offer a robust, flexible, and efficient approach for modelling adiabatic heating, with significant implications for the design and optimisation of HPTP treatments. The study underscores the transformative potential of AI in advancing food preservation technologies.

Application of Physics-Informed Neural Networks to River Silting Simulation

Water resource pollution, particularly in river channels, presents a grave environmental challenge that necessitates a comprehensive and systematic approach encompassing assessment, forecasting, and effective management. This article provides a comprehensive exploration of the methodology and modeling tools employed to scrutinize the process of river channel pollution due to silting, rooted in the fundamental principles of hydrodynamics and pollutant transport dynamics. The study’s methodology seamlessly integrates numerical simulations with state-of-the-art neural network techniques, with a specific focus on the physics-informed neural network (PINN) method. This innovative approach represents a groundbreaking fusion of artificial neural networks (ANNs) and physical equations, offering a more efficient and precise means of modeling a wide array of complex processes and phenomena. The proposed mathematical model, grounded in the Euler equation, has been meticulously implemented using the Ansys Fluent software package, ensuring accuracy and reliability in the computations. In a pivotal phase of the research, a thorough comparative analysis was conducted between the results derived using the PINN method and those obtained using conventional numerical approaches with the Ansys Fluent software package. The outcomes of this analysis revealed the superior performance of the PINN method, characterized by the generation of smoother pressure fluctuation profiles and a significantly reduced computation time, underscoring its potential as a transformative modeling tool. The calculated data originating from this study assume paramount significance in the ongoing battle against river sedimentation. Beyond this immediate application, these findings also serve as a valuable resource for creating predictive materials pertaining to river channel silting, thereby empowering decision-makers and environmental stakeholders with essential information. The utilization of modeling techniques to address pollution concerns in river channels holds the potential to revolutionize risk management and safeguard the integrity of our vital water resources. However, it is imperative to underscore that the effectiveness of such models hinges on ongoing monitoring and frequent data updates, ensuring that they remain aligned with real-world conditions. This research not only contributes to the enhanced understanding and proactive management of river channel pollution due to silting but also underscores the pivotal role of advanced modeling methodologies in the preservation of our invaluable water resources for present and future generations.

In-situ shrinkage measurement of alkali-activated materials using focused ion beam combined with environmental scanning electron microscopy

Drying shrinkage of alkali-activated slag (AAS) has gained significant attention since the volumetric instability of this material can generate premature cracking and degrade the long-term durability of concrete structures. The unique shrinkage behavior of AAS originates mainly from the particular characteristics of its main hydrated products. However, few studies have even at-tempted to investigate the shrinkage behavior of hydrated products in AAS materials. This paper presented a new method of investigating drying shrinkage behavior of AAS using focused ion beam (FIB) combined with environmental scanning electron microscopy (ESEM). This innovative experimental method allowed the in-situ measurement of phase-specific shrinkage. The results showed FIB/ESEM technique can be successfully implemented to cementitious material to prepare phase-specific samples. Furthermore, object-oriented finite element method (OOF2) has been utilized to compute the shrinkage behavior of AAS concrete using a proposed multi-scale scheme. The computations can be made at multi-scales which highlight the effect of hydration products on shrinkage behaviors. OOF2 calculation at the micro-length scale predicted an increase in the shrinkage due to the well-dispersed hydration products inside the matrix. At larger scale, the decrease in the overall shrinkage is related to the extremely low shrinkage value by aggregates. The findings reveal OOF2 offers the capability to accurately measure local stress and strain distribution within heterogeneous materials, a feature notably absent in conventional numerical homogenization approaches. The importance of this benefit is highlighted particularly in the context of free-restrained shrinkage prediction, as conventional homogenization methods fail to account for stress.

Development of a behaviour pattern-based testing approach for coupled socioeconomic and environmental models

Understanding the interactions between human and environmental systems is key to sustainable environmental management. Dynamically Coupled Socioeconomic system dynamics models integrated with physically-based Environmental Models (DCSEMs) are promising tools to appropriately capture the non-linear relationships between complex socioeconomic and biophysical systems, thereby supporting sustainable environmental management. However, existing approaches for testing integrated models are commonly based on the point-to-point analysis of model outputs, which is not suitable for DCSEMs that are behaviour pattern oriented. Consequently, the lack of well-defined behaviour pattern-based approaches has limited the adaptability of DCSEMs. To address this gap, this study proposes a novel behaviour pattern-based model testing approach that includes global sensitivity analysis (GSA), auto-calibration algorithms, and evaluation to assess behaviour pattern similarities between model outputs and real-world trends. The proposed approach is demonstrated through a real-world case study, in which an existing DCSEM is calibrated and evaluated to simulate water table depth in the Rechna Doab region of Pakistan. Compared to the conventional numerical point approach, the proposed approach is better suited for DCSEMs, as it replicates observed system behaviour patterns (as opposed to observed point values) over time. Furthermore, the outcomes of the Theil inequality statistical analysis and parameter distribution analysis provide evidence that the suggested approach is effective in testing and improving the performance of the DCSEM by capturing the spatial heterogeneity within the study area. The proposed behaviour-pattern testing procedure is a useful approach for model testing in data-limited, spatially-distributed DCSEMs.

Spatiotemporal graph neural network for multivariate multi-step ahead time-series forecasting of sea temperature

This paper proposes a spatiotemporal graph neural network capable of effective representation learning of the spatiotemporal interrelationships and interdependencies of in-situ observation data from multiple locations for multivariate multi-step ahead time-series forecasting. The propose model is largely composed of graph learning, spatial encoder, and temporal decoder, and ablation studies on variants of the three modules and comparative experiments with state-of-the-art deep neural networks for sequence modeling were also performed extensively. The proposed model showed improved predictability than conventional numerical model-based approaches or state-of-the-art models by applying consecutive multi-step ahead time-series prediction of sea surface temperature at multiple locations along the coast. For more rigorous performance evaluation, not only the overall performance of the test data, but also the performance of extreme cases included in the test data based on historical records were separately assessed. The prediction rationales were also presented through quantified relative contributions between neighbor locations using the trained adjacency matrix obtained through graph learning. The results showed that it is well consistent with the ocean physics and geographical domain knowledge, demonstrating the feasibility and reliability of the proposed method. Therefore, the proposed method shows sufficient potential to be used as a scientific tool for decision-making in extreme events such as marine heat waves or for operational ocean forecasting.

Influence of Different Altitudes on the Solid Rocket Contrail Formation in the Near Field

Detecting the infrared characteristics of the contrails is a reasonable approach to tracing the rocket, and the particle properties of the contrails are the basis of the infrared analysis. The conventional numerical approach to obtaining the particle properties is a Euler/Lagrange method or a simple Euler/Euler method, difficultly obtaining more accurate results because it ignores the particle size distribution in parcels or cells. A modified Euler/Euler method is applied to simulate the contrail formation in the near field of a solid rocket motor at different altitudes, which considers the size distribution by adding the first- to second-order particle radius moments based on the simple Euler/Euler method. The simulation results show that the crystals are generated at altitudes from 10 km to 20 km and that the contrails are visible at altitudes from 10 km to 15 km, where the radii of the crystals are from 0.1 μm to 0.3 μm. The visible contrails indicate that aviation vehicles are cruising at altitudes from 10 km to 15 km, and the smaller crystals indicate that the contrails are generated by rockets, not aircraft. Our work can provide important insight for the follow-up infrared analysis of the contrails based on the obtained particle radii.

Hydro-structural response of complex elevated pile cap substructures to strom surge impact by smoothed particle hydrodynamics: Part 2: Model results

Extreme waves, i.e., tsunamis and storm surges, can generate tremendous hydraulic bores capable of inflicting considerable damage to near-shore bridge infrastructure, often leading to structural failure. The conventional numerical approach to studying hydrodynamic impact is based on Eulerian grid-based, e.g., finite volume or diffused element algorithms. These perform well with perfectly defined simulation domains. However, in case of severe surface deformation, these grids must be continually reconstructed, which is time-intensive and introduces cumulative system errors. As Smoothed Particle Hydrodynamic (SPH) integrates the hydrodynamic equations of motion on each particle in Lagrangian formalism, it can handle complex wave non-linearity without mesh constraints. In this study opensource DualSPHysics model is applied to study the hydrodynamic response and group effect of elevated pile cap substructures to impulsive surge impact. Two conventional grids (2 × 2, 2 × 3 array-layout) and a hexagonal pile arrangement under three submersion levels are considered in studying the pile group effect on hydrodynamic forcing mechanism, flow characteristics, and factors governing pressure variability. The uplift thrust on the pile cap was found to be dependent on the surge fluid mass, incident velocity, and vertical distance between the surge breaking point and cap bottom. At impulsive impact, gridded pile arrangement offered greater resistance to incident surge flow. In reference to free flow condition, hexagonal layout can reduce the average flow velocity by 8.22–19.76%, while for a gridded system, it is between 14.00% and 23.52% depending on the submersion level. However, in a quasi-steady state, the flow resistance of the hexagonal system was greater. The study also compared the numerical results to accepted offshore design standards, which were found to underestimate the pile's group effect, specifically for complex hexagonal layouts. Later, it proposes rationalized force diagrams to be applied in design of complex elevated structures. The paper's finding is expected to contribute to formulating new guidelines for resilient hydraulic design of coastal and deep-water elevated structures.

Multilayer Perceptron-Based Stress Evolution Analysis Under DC Current Stressing for Multisegment Wires

Electromigration (EM) is one of the major concerns in the reliability analysis of very large-scale integration (VLSI) systems due to the continuous technology scaling. Accurately predicting the time-to-failure of integrated circuits (ICs) becomes increasingly important for modern IC design. However, traditional methods are often not sufficiently accurate, leading to undesirable over-design especially in advanced technology nodes. In this article, we propose an approach using multilayer perceptrons (MLPs) to compute stress evolution in the interconnect trees during the void nucleation phase. The availability of a customized trial function for neural network training holds the promise of finding dynamic mesh-free stress evolution on complex interconnect trees under time-varying temperatures. Specifically, we formulate a new objective function considering the EM-induced coupled partial differential equations (PDEs), boundary conditions (BCs), and initial conditions to enforce the physics-based constraints in the spatial–temporal domain. The proposed model avoids meshing and reduces temporal iterations compared with conventional numerical approaches like finite element method. Numerical results confirm its advantages on accuracy and computational performance.

Throughput fairness trade-offs for downlink non-orthogonal multiple access systems in 5G networks

In this work, user pairing and power allocation are proposed as a hybrid scheme to maximise throughput and achieve system fairness in the non-orthogonal multiple access (NOMA) system in 5G networks. The proposed approach is designed to improve the throughput and fairness performance of the downlink NOMA system in 5G networks. User pairing and power allocation schemes are separated to reduce resource allocation complexity. Integer linear programming is applied to perform user pairing, and particle swarm optimisation is used for power allocation. Moreover, the optimisation problem is formulated by converting multi-objective functions into a single function using the scalarisation of multi-objective optimisation problems, and the penalty function is used to prevent optimisation from violating the power, fairness, and data rate constraints. Simulation results show that the proposed model outperforms the conventional numerical approach by at least 9% of throughput maximisation and achieves an acceptable fairness rate.

A hybrid numerical/machine learning model development to improve the bimetal performance in the electric circuit breakers

Bimetals are widely used as a thermal tripping mechanism inside the miniature circuit breakers (MCBs) products when an overload current passes through the circuit for a certain period. Experimental, numerical, and, recently artificial intelligence methods are widely used in designing electric components. However, developing the bimetal for MCB products somewhat differs from developing other conductor items since they are strongly related to the electrical, mechanical, and thermal performance of the MCB. The conventional experimental and numerical approaches are time-consuming processes that cannot be easily utilized in optimizing the product's performance within the development lead time. In this study, a simple, fast, robust, and accurate novel methodology has been introduced to predict the temperature rise of the bimetal and other related performance characteristics. The numerical model has been built on the time-based finite difference method to frame the theoretical thermal model of the bimetal. Then, the numerical model has been consolidated by the machine learning (ML) model to take advantage of the experiments to provide an accurate, fast and reliable model finally. The novel model agrees well with the experimental tests, where the maximum error does not exceed 8%. The model has been used to redesign the bimetal of a 32 A MCB product and significantly reduce the maximum temperature by 24 °C. The novel model is promising since it considerably reduces the required design time, provides accurate predictions, and helps to optimize the performance of the circuit breaker products.

An adaptive time-stepping method for the phase-field molecular beam epitaxial growth model on evolving surfaces

In this paper, a stable and efficient numerical method is presented to simulate the phase-field molecular beam epitaxial growth model on evolving surfaces. The energy dissipation law of the phase-field molecular beam epitaxial growth model on evolving surfaces does not hold for the arbitrary surface velocity which can be considered as a result of external force of the system. However, the stiffness caused by the model’s small interfacial parameter makes conventional numerical approach unstable. Hence, a stabilized semi-implicit method combined with the evolving surface finite element method is proposed and analyzed for the space-time discretization. Moreover, to improve the computational efficiency, an adaptive time-stepping technique which takes account of the energy evolution and surface velocity is also provided. Numerical examples are given to verify the effectiveness of the proposed strategy. Several numerical simulations are performed to explore the beam epitaxial growth on evolving surfaces.

Machine-Learning-Based Near-Surface Ozone Forecasting Model with Planetary Boundary Layer Information.

Surface ozone is one of six air pollutants designated as harmful by National Ambient Air Quality Standards because it can adversely impact human health and the environment. Thus, ozone forecasting is a critical task that can help people avoid dangerously high ozone concentrations. Conventional numerical approaches, as well as data-driven forecasting approaches, have been studied for ozone forecasting. Data-driven forecasting models, in particular, have gained momentum with the introduction of machine learning advancements. We consider planetary boundary layer (PBL) height as a new input feature for data-driven ozone forecasting models. PBL has been shown to impact ozone concentrations, making it an important factor in ozone forecasts. In this paper, we investigate the effectiveness of utilization of PBL height on the performance of surface ozone forecasts. We present both surface ozone forecasting models, based on multilayer perceptron (MLP) and bidirectional long short-term memory (LSTM) models. These two models forecast hourly ozone concentrations for an upcoming 24-h period using two types of input data, such as measurement data and PBL height. We consider the predicted values of PBL height obtained from the weather research and forecasting (WRF) model, since it is difficult to gather actual PBL measurements. We evaluate two ozone forecasting models in terms of index of agreement (IOA), mean absolute error (MAE), and root mean square error (RMSE). Results showed that the MLP-based and bidirectional LSTM-based models yielded lower MAE and RMSE when considering forecasted PBL height, but there was no significant changes in IOA when compared with models in which no forecasted PBL data were used. This result suggests that utilizing forecasted PBL height can improve the forecasting performance of data-driven prediction models for surface ozone concentrations.

Tracking the explosion characteristics of the hydrogen-air mixture near a concrete barrier wall using CESE IBM FSI solver in LS-DYNA incorporating the reduced chemical kinetic model

Barriers are introduced as an efficient method for the protection of infrastructures and people from overpressure effects owing to accidental gaseous explosions. Therefore, capturing the pressure wave propagation in front of and behind the barrier plays an important role in designing a protective wall and hazard analysis of pipeline explosion accidents. To this end and to track the explosion characteristics of the hydrogen-air mixture near a concrete barrier wall, a new numerical approach in the compressible CESE solver based on the immersed boundary method (IBM) was utilized and coupled with the LS-DYNA® structural FEM solver in which the finite-rate chemistry model was in touch with the fluid-structure interaction (FSI). For the wall, the Concrete Damage Model (MAT_72R3) was employed as the constitutive material model. Existing experimental results were utilized to verify the 3D numerical model. Furthermore, the obtained numerical simulation results were compared with the conventional numerical approach called the TNT equivalent method using the MMALE algorithm in the open literature to show its drawbacks in predicting the pressure wave propagation in front of and particularly behind the wall surface. The results showed that by incorporating the finite-rate chemistry model in the CESE IBM FSI solver, all the explosion characteristics related to the hydrogen-air mixture detonation in front of and behind the wall surface can be accurately predicted since it involves detonation wave/structure interaction, chemical reaction, fluid motion, and structural deformation. Therefore, it is strongly recommended to use the CESE IBM FSI solver in conjunction with appropriate chemical kinetics as an alternative method instead of the conventional method to accurately model the gaseous mixture explosion process in a relatively complex environment and solve more practical applications in explosion and safety industries.

Modelling the thermal–hydro-mechanical behaviour of unsaturated soils with a high degree of saturation using an extended precise integration method

Unsaturated soils with a high degree of saturation (HDS) are commonly encountered in marine and lacustrine sediments. In these soils, the gas phase generally exists in the state of discrete bubbles, which is sensitive to stress and temperature changes and can dramatically change the soil's engineering properties. This paper explores the thermal-induced behaviour of HDS soils using an efficient extended precise integration method (XPIM). Biot poroelasticity theory, extended to include thermal effects and compressibility of gas–water mixture, is employed to analyze the soil behaviour under non-isothermal conditions. Based on the Laplace–Fourier transform and Taylor series expansion, such problems can be solved by XPIM. The robustness of XPIM was confirmed by comparing the present results with analytical solutions and test data. Extensive parametric studies are undertaken to examine both the effects of soil grain thermal expansion and anisotropic permeability on soil behaviour and temperature effects on the degree of saturation ( Sr). The thermal-induced variations in Sr are more pronounced with lower initial values (e.g., 90% compared to 99%). These quantitative results demonstrate the benefits of the proposed method, which proves to be extremely efficient and several orders more precise than conventional numerical approaches, with its precision limited only by the computational effort used.

Prediction of 12 Photonic Crystal Fiber Optical Properties Using MLP in Deep Learning

In this letter, we proposed the use of feed-forward multilayer perceptron in deep learning-based artificial neural network (ANN) to accurately predict 12 optical parameters of silica-based photonic crystal fiber (PCF) within milliseconds using 6 input parameters. The optimized ANN has 3 hidden layers and each layer has 50 neurons. The PCF has several hexagonal-shaped layers with circular air holes, and it uses silica as the cladding and FK51A glass as the core. The PCF parameters that have been successfully predicted include birefringence, chromatic dispersion, effective area, effective refractive index, nonlinear coefficient, numerical aperture, power fraction, relative sensitivity, V-parameter, and loss profiles such as confinement loss, effective material loss, and scattering loss. The prediction has high accuracy with a loss of only 0.00567 and a learning rate of 0.0001. 7-fold validation and batching are used to increase scalability during validation. The proposed ANN is over 99.9% faster than conventional numerical simulation approaches.