Local Model Research Articles

Collaborative Training of Data-Driven Remaining Useful Life Prediction Models Using Federated Learning

Remaining useful life prediction models are a central aspect of developing modern and capable prognostics and health management systems. Recently, such models are increasingly data-driven and based on various machine learning techniques, in particular deep neural networks. Such models are notoriously “data hungry”, i.e., to get adequate performance of such models, a substantial amount of diverse training data is needed. However, in several domains in which one would like to deploy data-driven remaining useful life models, there is a lack of data or data are distributed among several actors. Often these actors, for various reasons, cannot share data among themselves. In this paper a method for collaborative training of remaining useful life models based on federated learning is presented. In this setting, actors do not need to share locally held secret data, only model updates. Model updates are aggregated by a central server, and subsequently sent back to each of the clients, until convergence. There are numerous strategies for aggregating clients’ model updates and in this paper two strategies will be explored: 1) federated averaging and 2) federated learning with personalization layers. Federated averaging is the common baseline federated learning strategy where the clients’ models are averaged by the central server to update the global model. Federated averaging has been shown to have a limited ability to deal with non-identically and independently distributed data. To mitigate this problem, federated learning with personalization layers, a strategy similar to federated averaging but where each client is allowed to append custom layers to their local model, is explored. The two federated learning strategies will be evaluated on two datasets: 1) run-to-failure trajectories from power cycling of silicon-carbide metal-oxide semiconductor field-effect transistors, and 2) C-MAPSS, a well-known simulated dataset of turbofan jet engines. Two neural network model architectures commonly used in remaining useful life prediction, long short-term memory with multi-layer perceptron feature extractors, and convolutional gated recurrent unit, will be used for the evaluation. It is shown that similar or better performance is achieved when using federated learning compared to when the model is only trained on local data.

Experimental validation of an hybrid analytical-numerical technique to estimate the directivity of ultrasonic piezoelectric actuators

The generation of guided waves is a common approach for structural health monitoring. The optimization of the excitation strategies very much benefits from the availability of efficient simulation tools. On the one hand, the application of finite elements (FEs) for the analysis of wave propagation problems leads to large models which tend to be computationally costly for optimization studies. On the other hand, semi-analytical approaches provide useful analytical expressions for parametric studies, but may lead to inaccurate estimations of tuning frequencies and directionality, especially at high frequencies. This is mostly because of the simplifying assumptions regarding the stress field at the interface between the actuator patches and the plate. An interesting methodology couples the analytical far-field solution of the plate response with a local FE model of the interface stresses between plate and patches. This method allows the analysis of complex actuation configurations for various purposes, such as directivity steering. In this contribution, we experimentally validate such hybrid FE-analytical technique. A Scanning Laser Doppler velocimeter is employed to retrieve both temporal and spatial Fourier Transforms on a polycarbonate plate, excited by piezoelectric patches, and the directivity patterns of the first symmetric and antisymmetric modes are compared to the numerical predictions.

Study on the influence mechanism of elastic appendage on the longitudinal stability of high-speed planing craft

Aiming at the problem of porpoising during high-speed navigation of planing crafts, this study designed a localized elastic appendage installed in the high-pressure area of the boat bottom, which can improve the longitudinal stability of the planing craft through its passive deformation. The ship model towing test and numerical simulation of rigid model (RM) and local elastic model (LEM) are carried out under still water conditions. The flow field calculation of RM based on CFD and the two-way fluid-structure interaction simulation of LEM based on CFD-FEM are all in good agreement with the experimental data. The test and numerical results indicate that in the speed range of 1–11 m/s, the maximum deformation of the LEM elastic appendage can approach 4 mm. There is an obvious improvement in longitudinal stability following deformation. The stable speed range is increased by 1.2 times and the trim angle of LEM is reduced by a maximum of 15% when compared to RM at the same speed. In terms of resistance, RM and LEM exhibit almost identical characteristics. Based on the details of flow field and the pressure distribution obtained by the numerical simulation, the mechanical properties of the planing craft after the deformation of the local elastic appendage have been analyzed, which provides a new design idea for the planing craft to improve the longitudinal stability.

Childhood stunting in Indonesia: assessing the performance of Bayesian spatial conditional autoregressive models.

Stunting continues to be a significant health issue, particularly in developing nations, with Indonesia ranking third in prevalence in Southeast Asia. This research examined the risk of stunting and influencing factors in Indonesia by implementing various Bayesian spatial conditional autoregressive (CAR) models that include covariates. A total of 750 models were run, including five different Bayesian spatial CAR models (Besag-York-Mollie (BYM), CAR Leroux and three forms of localised CAR), with 30 covariate combinations and five different hyperprior combinations for each model. The Poisson distribution was employed to model the counts of stunting cases. After a comprehensive evaluation of all model selection criteria utilized, the Bayesian localised CAR model with three covariates were preferred, either allowing up to 2 clusters with a variance hyperprior of inverse-gamma (1, 0.1) or allowing 3 clusters with a variance hyperprior of inverse-gamma (1, 0.01). Poverty and recent low birth weight (LBW) births are significantly associated with an increased risk of stunting, whereas child diet diversity is inversely related to the risk of stunting. Model results indicated that Sulawesi Barat Province has the highest risk of stunting, with DKI Jakarta Province the lowest. These areas with high stunting require interventions to reduce poverty, LBW births and increase child diet diversity.

Research on The local clothing thermal insulation prediction model with different dress state of indoor occupants

In a dynamic and non-uniform thermal environment, adjusting personal dress states is an effective method for achieving thermal comfort. During this process, clothing thermal insulation, as a key parameter in human thermoregulation models, is not uniformly distributed across the body. However, current thermal comfort standards do not provide a direct method for obtaining local clothing thermal insulation. Based on field surveys, this study summarized typical year-round clothing ensembles and common dress states, and tested the local thermal insulation of 40 clothing ensembles and 60 individual garments using a thermal manikin. Subsequently, a prediction model for the local thermal insulation of clothing ensembles was developed based on the overall thermal insulation of individual garments. Meanwhile, it was found that changes in dress state significantly alter the thermal insulation of body parts such as the arms and chest. Simulations conducted using the JOS-3 and UCB models revealed that the lower the ambient temperature, the greater the impact of changes in local clothing thermal insulation on human skin temperature and thermal sensation. Finally, a correction model for different dress states was developed, and comparison with existing models showed the lower root mean square error (RMSE) between the predicted and measured values. This study provides a more accurate and convenient method for determining local thermal insulation, offering a data foundation for improving indoor environmental control and enhancing energy efficiency.

Reconciliation of weak pairwise spike-train correlations and highly coherent local field potentials across space.

Multi-electrode arrays covering several square millimeters of neural tissue provide simultaneous access to population signals such as extracellular potentials and spiking activity of one hundred or more individual neurons. The interpretation of the recorded data calls for multiscale computational models with corresponding spatial dimensions and signal predictions. Multi-layer spiking neuron network models of local cortical circuits covering about $1\,{\text{mm}^{2}}$ have been developed, integrating experimentally obtained neuron-type-specific connectivity data and reproducing features of observed in-vivo spiking statistics. Local field potentials can be computed from the simulated spiking activity. We here extend a local network and local field potential model to an area of $4\times 4\,{\text{mm}^{2}}$, preserving the neuron density and introducing distance-dependent connection probabilities and conduction delays. We find that the upscaling procedure preserves the overall spiking statistics of the original model and reproduces asynchronous irregular spiking across populations and weak pairwise spike-train correlations in agreement with experimental recordings from sensory cortex. Also compatible with experimental observations, the correlation of local field potential signals is strong and decays over a distance of several hundred micrometers. Enhanced spatial coherence in the low-gamma band around $50\,\text{Hz}$ may explain the recent report of an apparent band-pass filter effect in the spatial reach of the local field potential.

Assessing the accuracy of global digital elevation models for hydrological analysis: the cases of Syria and Russia

Digital elevation models provide valuable information about the surface topography. The resolution and accuracy of the data used to create the models are critical for the results of hydrological analysis. Available global digital elevation models obtain high potential in terms of data sources; however, their performance requires meticulous evaluation for different terrain characteristics and applications. Aim. To determine the accuracy and resolution of data provided by current and old global models, namely SRTM 1, SRTM GL1, V3 ASTER, GMTED2010, PALSAR ALOS, and GTOPO 30, using the example of two terrains. The study considers the areas in Syria (Syrian coast) and Russia (Chernoyarsky and Akhtubinsky districts in the Astrakhan region) represented by different elevation models. A matching degree between model and real elevations measured by GPS was determined to carry out the hydrological analysis of the land surface. For this purpose, three statistical measures, including range, standard deviation and correlation were defined by means of BaseCamp, ARCGIS PRO & SAGA_GIS software. Data resolution indicates the degree of detail represented in the DEM dataset, which is established by the spatial sampling interval or the size of the grid cell used to represent the land surface. Data accuracy refers to the matching degree between the elevation values derived from the DEM and the actual data obtained on the surface. Results. In terms of correlation coefficient and standard deviation, the GMTED 2010 and ASTER V3 model for the Syrian region and the ALOS PALSAR and SRTM GL 1 model for the Russian region prove to be the most effective for hydrological analysis in the absence of accurate local models.

Federated Diverse Self-ensembling Learning Approach for Data Heterogenity in Drive Vision

Federated learning (FL) has developed as an efficient framework that can be used to train models across isolated data sources while also protecting the privacy of the data. In FL a common method is to construct local and global models together, with the global model (server) informing the local models and the local models (clients) updating the global model. Most present works assume clients have labeled datasets and the server has no data for supervised learning (SL) problems. In reality, clients lack the competence and drive to identify their data, while the server may host a tiny amount. How to reasonably use serverlabeled and client-unlabeled data is crucial in semi-supervised learning (SSL) and Cclientdata heterogeneity is widespread in FL. However, inadequate high-quality labels and non-IID client data, especially in autonomous driving, decrease model performance across domains and interact negatively. To solve this Semi-Supervised Federated Learning (SSFL) problem, we come up with a new FL algorithm called FedDSL in this work. We use self-ensemble learning and complementary negative learning in our method to make clients’ unsupervised learning on unlabeled data more accurate and efficient. It also coordinates the model training on both the server side and the clients’ side. In an important distinction to earlier research that kept some subset of labels at each client, our method is the first to implement SSFL for clients with 0% labeled non-IID data. Our contributions include the effectiveness of self-ensemble learning by using confidence score vector for calculating only for the current model performing data filtering and initiated negative learning by showing the data filtering performance in the beginning rounds. Our approach has been rigorously validated on two significant autonomous driving datasets, BDD100K and Cityscapes, proving to be highly effective. We have achieved state-of-the-art results and the metric that is utilized to evaluate the effectiveness of each detection task is mean average precision (mAP@0.5). Astonishingly FedDSL performs nearly as well as fully-supervised centralized training approaches, despite the fact that it only uses 25% of the labels in the Global model.

Accuracy assessment of recent global ocean tide models in coastal waters of the European North West Shelf

The accuracy of global ocean tide models is assessed in coastal waters of the European North West Shelf to ascertain where higher resolution local (forecast) models are most needed for geophysical and navigational applications, and which global models are most suitable for providing boundary conditions for regional and local tide models. Five recent global ocean tide models (FES2014b, EOT20, TPXO9-atlas-v5, GOT4.10c, and DTU16) are considered, with the models first compared by interpolating them onto common grids and computing the mean absolute deviation at each grid point. Coastline tide gauge and offshore bottom pressure sensor data were collated from several sources to give a total of 279 observation sites for evaluating model accuracy, including observational values from 137 locations that have not previously been released and have therefore not been assimilated into any of the global models tested. The residual errors between each model’s predicted phasor and the corresponding observed phasor were calculated at each observation location, and quantified using the root mean square (RMS) and median absolute residual (MAR) for the eight tidal constituents M2, S2, N2, O1, K1, K2, P1, and Q1. To avoid RMS values being biased by observation point density, a Voronoi-weighted RMS based on the water area of the Voronoi polygon about each observation location was also developed and used. Four zones were defined based on ocean depth to gauge model performance, and model inaccuracy is again demonstrated in near-shore regions. Seven further zones were defined based on geographical areas, which reveals inhomogeneity among the global models. The smallest overall root sum square (RSS) RMS error across all eight constituents arises with FES2014b, although TPXO9-atlas-v5 has the best performance when using the MAR and Voronoi-weighted RMS metrics. Using only the 137 observation sites that have not been assimilated by any model and therefore provide an independent accuracy assessment, FES2014b exhibits the smallest errors at the coastline, with an RSS RMS of 24.46 cm. All models exhibit larger errors with the 137 independent observation sites than with all 279 observation sites, with an average overall increase in RSS RMS error of 12%, and an increase of 30% for coastline tide gauges, highlighting the need for local model development in these areas.

Experimental evaluations of Berkeley thermal sensation and comfort models in electric vehicle cabin under cold outdoor conditions

As the automobile industry is transitioning toward electric vehicles, manufacturers have started implementing local warmers alongside cabin heating, ventilation, and air conditioning (HVAC) systems for effective thermal comfort management. However, optimal operating strategies need to be developed for integrating local warmers with HVAC systems. Although the Berkeley models comprising local/overall thermal sensation and comfort models offer insights in this regard, they lack follow-up assessments for occupants transitioning from very cold states. In this study, Berkeley models were evaluated using two sets of experimental data collected in a transient vehicle cabin under cold outdoor conditions: test (A) with cabin HVAC alone and test (B) with both HVAC and local warmers. The findings confirm the satisfactory performances of the Berkeley models for predicting overall sensation and comfort, with a maximum root mean-squared error (RMSE) of 0.15. The local comfort model performed poorly with the original coefficients across both datasets (maximum RMSE of 1.96). Therefore, the model coefficients were regressed for the dataset from test A and validated against the dataset from test B to achieve a maximum RMSE of 0.49. With these regressed coefficients, it was observed that moving toward a neutral overall state diminished the potential to maximize local comfort. Conversely, the local sensation model showed poor agreement (maximum RMSE of 1.9); we confirmed that accurate adaptive setpoint temperatures are a prerequisite for ensuring good predictions from the model. These findings are expected to contribute toward future efforts in using Berkeley models to formulate effective local warmer–HVAC operational strategies in electric vehicles.

Adaptive compressed learning boosts both efficiency and utility of differentially private federated learning

In the federated learning (FL) research field, current research is confronted with several pivotal challenges, e.g., data privacy, model utility and communication efficiency. Furthermore, these challenges are further amplified by statistical data heterogeneous in the FL system. Thus, a novel Communication-efficient and Utility-assured Gaussian differential privacy-based Personalized Federated Adaptive Compressed Learning method, called CUG-PFACL, is proposed. Specifically, an end-to-end local adaptive compressed learning strategy is designed, including three crucial modules, namely the measurement matrix, the personalized compressed data transformation and the local model. Especially, jointly training the measurement matrix module and the personalized compressed data transformation module can mitigate the inherent statistical heterogeneity while preserving all important characteristics of the compressed private data of each local client, and alleviate the additional heterogeneity induced by Gaussian differential privacy in each global communication round. Numerous experimental simulation and comparisons demonstrate that CUG-PFACL has three notable advantages: data privacy guarantee, enhanced personalized model utility and high-efficient communication.

FLAV: Federated Learning for Autonomous Vehicle privacy protection

Autonomous Vehicle Systems are committed to safer, more efficient and more convenient transportation on the roads of the future. However, concerns about vehicle data privacy and security remain significant. Federated Learning, as a decentralized machine learning approach, allows multiple devices or data sources to collaboratively train models without sharing raw data, providing essential privacy protection. In this paper, we propose a privacy-preserving framework for autonomous vehicles, named FLAV. First, we use a multi-chain parallel aggregation strategy to transmit model parameters and design a model parameter filtering mechanism, which reduces communication overhead by filtering out the local model parameters of certain vehicles, thereby alleviating bandwidth pressure. Second, we introduce a dynamic adjustment mechanism that automatically adjusts the regularization strength in the loss function by comparing the differences between each vehicle’s local model parameters and the cumulative parameters from the preceding vehicles in the chain. This mechanism effectively balances local model training with global model consistency, ensuring the model’s adaptability to local data while enhancing the coordination of models between vehicles in the chain. Experimental results demonstrate that our proposed method reduces communication costs while improving model accuracy and privacy protection, effectively ensuring the security of autonomous driving data.

MemberShield: A framework for federated learning with membership privacy

Federated Learning (FL) allows multiple data owners to build high-quality deep learning models collaboratively, by sharing only model updates and keeping data on their premises. Even though FL offers privacy-by-design, it is vulnerable to membership inference attacks (MIA), where an adversary tries to determine whether a sample was included in the training data. Existing defenses against MIA cannot offer meaningful privacy protection without significantly hampering the model’s utility and causing a non-negligible training overhead. In this paper we analyze the underlying causes of the differences in the model behavior for member and non-member samples, which arise from model overfitting and facilitate MIAs. Accordingly, we propose MemberShield, a generalization-based defense method for MIAs that consists of: (i) one-time preprocessing of each client’s training data labels that transforms one-hot encoded labels to soft labels and eventually exploits them in local training, and (ii) early stopping the training when the local model’s validation accuracy does not improve on that of the global model for a number of epochs. Extensive empirical evaluations on three widely used datasets and four model architectures demonstrate that MemberShield outperforms state-of-the-art defense methods by delivering substantially better practical privacy protection against all forms of MIAs, while better preserving the target model utility. On top of that, our proposal significantly reduces training time and is straightforward to implement, by just tuning a single hyperparameter.

DT-Block: Adaptive vertical federated reinforcement learning scheme for secure and efficient communication in 6G

The necessities of security and data sharing have focused on federated learning because of using decentralized data sources. The existing works used federated learning for security, however, it still faces many challenges such as poor security and privacy, computational complexity, etc. In this research, we propose adaptive vertical federated learning using a reinforcement learning approach and blockchain. The proposed work includes three phases: user registration and authentication, machine learning-based client selection, and adaptive secure federated learning. Initially, all the users register their credentials to the cognitive agent, which generates a private key, public key, and random number using a Chaotic Isogenic Post Quantum Cryptography (CIPQC) algorithm. Second, optimal clients are selected for participating in federated learning which improves learning rate and reduces complexity. Here, optimal clients are selected by the Enhanced Multilayer Feed Forward Neural Network (EMFFN) algorithm by considering CSI, RSSI, bandwidth, energy, communication efficiency, and statistical efficiency. Finally, adaptive secure federated learning is performed by the Distributed Distributional Deep Deterministic Policy Gradient (D4PG) algorithm, where the local models are adaptively used by the private strategy based on its sensitivity. The aggregated global models are stored in DT-block (dendrimer tree-based blockchain) which stores the data in a dendrimer tree structure for increasing scalability and reducing search time during data retrieval. The simulation of this research is conducted by NS-3.26 network simulator and the performance of the proposed DT-Block model is estimated based on various performance metrics such as accuracy, delay, loss, f1-score, and security strength this demonstrated that the suggested effort produced better results both in terms of quantitative and qualitative aspects.

A generalization of the Exner law for sediment nonlocal transport at bedform scale

Recent researches have highlighted the significance of nonlocal processes in understanding the morphodynamics and sediment transport across landscapes. Nonlocal processes in sediment transport refer to the influence of landscape properties beyond the immediate vicinity of a given point on the sediment flux. Existing nonlocal models, employing fractional operators, aim to capture global correlated nonlocality using a global convolution operator. Nevertheless, such models tend to disregard nonlocal phenomena occurring at regional scales, potentially resulting in substantial inaccuracies due to an inadequate representation of sediment transport processes at these scales. This study presents a novel and more comprehensive mathematical formulation of the nonlocal Exner law, leveraging the peridynamic differential operator (PDDO). The proposed regional nonlocal model incorporates nonlocal sediment transport processes by utilizing a pre-defined weight function and interaction domain within the framework of the PDDO. The novel regional nonlocal model effectively bridges the gap between local and global models by integrating both short-range and long-range interactions in sediment transport. Application reveals that that the regional nonlocal model provides a significantly enhanced accuracy in depicting profiles at the bedform scale compared to the local and the global models.

Heat transfer characteristics of a turbulent swirl jet issuing from a circular nozzle

Experimental and numerical studies on the flow field and cooling performance of a swirling jet, impinging on a flat surface is presented. A new nozzle that resembles the swirl injector of a liquid propellant rocket engine is used. This study considers different parameters including swirl number(S), Reynolds number(Re), normalised orifice to target spacing (Z/D) and confinement. The performance of various RANS and LES turbulence models is assessed using the data obtained from present experimental studies and that reported in literature. RNG k-ϵ turbulent model is successful in predicting heat transfer in non swirling flow. In the case of swirling flow, LES WALEM(Wall Adapting Local Eddy viscosity Model) predicts the heat transfer better than the other models. The performance of Swirling Impinging Jets(SIJ) and Cylindrical Impinging Jets (CIJ) is compared. At higher Z/D, introduction of swirl results in reduction in heat transfer and this is because of the increased spreading of the jet and reduction in velocity of the jet impinging on the target. Better performance is achieved at lower Z/D when a cylindrical jet is introduced with a small amount of swirl. For Z/D = 2 and S = 0.2, the peak Nu increases by 10 % and average Nu in the stagnation region increases by 6 % in comparison to CIJ. The position of the peak Nu moves away from the axis of the jet and there is better uniformity in Nu in the stagnation region. For Z/D = 2 swirling flow creates secondary peak(which usually occurs at high Re)even at low Re. At very low Z/D, top wall confinement causes increase in both peak heat transfer and average heat transfer in the stagnation region.

Modified local Granger causality analysis based on Peter‐Clark algorithm for multivariate time series prediction on IoT data

AbstractClimate data collected through Internet of Things (IoT) devices often contain high‐dimensional, nonlinear, and auto‐correlated characteristics, and general causality analysis methods obtain quantitative causality analysis results between variables based on conditional independence tests or Granger causality, and so forth. However, it is difficult to capture dynamic properties between variables of temporal distribution, which can obtain information that cannot be obtained by the mean detection method. Therefore, this paper proposed a new causality analysis method based on Peter‐Clark (PC) algorithm and modified local Granger causality (MLGC) analysis method, called PC‐MLGC, to reveal the causal relationships between variables and explore the dynamic properties on temporal distribution. First, the PC algorithm is applied to compute the relevant variables of each variable. Then, the results obtained in the previous stage are fed into the modified local Granger causality analysis model to explore causalities between variables. Finally, combined with the quantitative causality analysis results, the dynamic characteristic curves between variables can be obtained, and the accuracy of the causal relationship between variables can be further verified. The effectiveness of the proposed method is further demonstrated by comparing it with standard Granger causality analysis and a two‐stage causal network learning method on one benchmark dataset and two real‐world datasets.

Improving a shell-tube latent heat thermal energy storage unit for building hot water demand using metal foam inserts at a constant pumping power

The phase transition heat transfer during the melting and solidification processes of phase change materials (PCMs) was modeled in a shell-tube thermal energy storage unit. For the first time, special attention was dedicated to the heat transfer enhancement on the heat transfer fluid (HTF) side by placing metal foam (MF) inserts in the HTF tube. The MF inserts on the HTF side were placed next to the fin bases to produce the maximum heat transfer enhancement. A two-temperature local thermal non-equilibrium model was applied to accurately model the transient heat transfer in the MF domains. To perform a fair heat transfer analysis and consider the hydrodynamic aspects of heat transfer, the pumping power for driving the HTF fluid was kept fixed. The finite element method with automatic time-step control was used to integrate the model equations. Results show that the insertion of the MF in the HTF tube enhances conduction heat transfer but reduces flow for a constant pump power. Using a small amount of MF provides a good flow rate and a convective heat transfer while using a large amount of MF provides good conduction heat transfer but a poor flow rate and convection. A moderate amount of MF inserts results in poor conduction and a poor flow rate, notably increasing the phase transition time. A 5 % MF insert could provide about a 13 % shorter solidification time compared to a 25 % MF insert. Thus, a well-designed and engineered MF insert configuration on the HTF side can reduce the phase transition time and improve the energy storage power.

Research on the load transfer performance of large-span steel truss cable-stayed bridge structures

Since the wave is accompanied by the transfer of energy in the process of transmission, and the energy density at the node directly affects the bearing capacity and service performance of the steel truss cable-stayed bridge members and joints, this paper quantitatively studies the energy density at the key nodes of the long-span steel truss cable-stayed bridge from the perspective of the wave response of the structure. Firstly, according to the drawings of Xiangshan Bridge, a local finite element model of the steel truss cable-stayed bridge is established, and by changing the angle between the cable and the steel truss girder and the bending stiffness of the cable, the variation law of energy density at the connection node between the cable and the steel truss girder is obtained by changing the angle between the cable and the steel truss girder and the bending stiffness of the cableway. Due to the limitations of finite element wave analysis, from the perspective of theoretical analysis, this paper establishes the local scattering matrix at the node, proves the obtained law to a certain extent, and uses the return wave-light matrix method to analyze and solve the energy density at the connection node between the cable bar and the steel truss girder, and the final analytical solution is in good agreement with the numerical solution, which proves that the law obtained by numerical analysis is correct.

Spatially Local Surrogate Modeling of Subgrid-Scale Effects in Idealized Atmospheric Flows: A Deep Learned Approach Using High-Resolution Simulation Data

Abstract We introduce a machine learned surrogate model from high-resolution simulation data to capture the subgrid-scale effects in dry, stratified atmospheric flows. We use deep neural networks (NNs) to model the spatially local state differences between a coarse-resolution simulation and a high-resolution simulation. The setup enables the capture of both dissipative and antidissipative effects in the state differences. The NN model is able to accurately capture the state differences in offline tests outside the training regime. In online tests intended for production use, the NN-coupled coarse simulation has higher accuracy over a significant period of time compared to the coarse-resolution simulation without any correction. We provide evidence of the capability of the NN model to accurately capture high-gradient regions in the flow field. With the accumulation of the errors, the NN-coupled simulation becomes computationally unstable after approximately 90 coarse simulation time steps. Insights gained from these surrogate models further pave the way for formulating stable, complex, physics-based spatially local NN models which are driven by traditional subgrid-scale turbulence closure models. Significance Statement Flows in the atmosphere are highly chaotic and turbulent, comprising flow structures of broad scales. For effective computational modeling of atmospheric flows, the effects of the small- and large-scale structures need to be captured by the simulations. Capturing the small-scale structures requires fine-resolution simulations. Even with the current state-of-the-art supercomputers, it can be prohibitively expensive to simulate these flows when computed for the entire earth over climate time scales. Thus, it is necessary to focus on the larger-scale structures using a coarse-resolution simulation while capturing the effects of the smaller-scale structures using some parameterization (approximation) scheme and incorporating it into the coarse-resolution simulation. We use machine learning to model the effects of the small-scale structures (subgrid-scale effects) in atmospheric flows. Data from a fine-resolution simulation is used to compute the missing subgrid-scale effects in coarse-resolution simulations. We then use machine learning models to approximate these differences between the coarse- and fine-resolution simulations. We see improved accuracy for the coarse-resolution simulations when corrected using these machine learned models.