Gradient Corrections Research Articles

A comparison of linear consistent correction methods for first-order SPH derivatives

A well-known issue with the widely used Smoothed Particle Hydrodynamics (SPH) method is the neighborhood deficiency. Near the surface, the SPH interpolant fails to accurately capture the underlying fields due to a lack of neighboring particles. These errors may introduce ghost forces or other visual artifacts into the simulation. In this work we investigate three different popular methods to correct the first-order spatial derivative SPH operators up to linear accuracy, namely the Kernel Gradient Correction (KGC), Moving Least Squares (MLS) and Reproducing Kernel Particle Method (RKPM). We provide a thorough, theoretical comparison in which we remark strong resemblance between the aforementioned methods. We support this by an analysis using synthetic test scenarios. Additionally, we apply the correction methods in simulations with boundary handling, viscosity, surface tension, vorticity and elastic solids to showcase the reduction or elimination of common numerical artifacts like ghost forces. Lastly, we show that incorporating the correction algorithms in a state-of-the-art SPH solver only incurs a negligible reduction in computational performance.

Transpiration by sap flow Thermal Dissipation Method: applicability to a hedgerow olive orchard

The climate change requires thrifty use of water resources in agriculture since irrigation is became common also for those crops like olive orchard that were traditionally grown in rainfed conditions. The water requirement is imperative in semi-arid conditions of the Mediterranean basin especially if the olive orchards are cultivated in super high density. For a correct irrigation scheduling, methods to measure transpiration (Tr) at plant level are used. Among the most spread methods to determine Tr, the thermal dissipation method (TDM) has been applied on a hedgerow olive orchard considering: (i) species-specific local calibration, (ii) wound effects, (iii) azimuth correction, and (iv) radial gradient corrections. The performances of the corrected TDM method have been evaluated with respect an independent method, the water balance at weekly scale. If any correction nor specific calibration is carried out, the underestimation of the actual transpiration calculated by TDM was of about -18% with respect to the water balance method.

Molecular dynamics study on the thermal decomposition of 1,3,5-trinitro-1,3,5-triazinane (RDX) catalyzed by aluminum nanoparticles with different contents

The mechanism of thermal decomposition of 1,3,5-trinitro-1,3,5-triazinane (RDX) catalyzed by nano-sized aluminum powder remains unclarified. In the present study, reactive molecular dynamics simulations using the parameterized reactive force field with low gradient correction (ReaxFF-lg) were conducted to study the microscale process of the RDX thermal decomposition catalyzed by different Al contents, and the density functional theory calculations were used to analyze the initial decomposition pathways of RDX on the Al surface. The thermal disintegration and the released energy of RDX are significantly facilitated by an increase in Al concentration at a lower level and the optimal value is around 35 wt%, while a higher concentration of Al will lead to an opposite effect. The dissociation of nitro group is the most probable initial reaction pathway for RDX decomposition on the Al surface. In addition, the evolutions of Al-containing clusters, key intermediates, and final products were analyzed, providing more information about this reaction. The findings suggest that the addition of Al nanoparticles improves the properties of RDX-based explosives, but the optimal amount of Al is critical for achieving the desired effects. The detailed analysis of the reaction mechanism and intermediate products provides valuable insights into the underlying mechanisms of the Al/RDX system.

Effects of wall vibrations on channel flows

The effect of surface vibrations on the pressure-gradient-driven flows in channels has been studied. The analysis considered monochromatic waves and laminar flows. The effectiveness of the vibrations was gauged by determining the pressure gradient correction required to maintain the same flow rate as without vibrations. Waves propagating upstream always increase pressure losses. Flow response to waves propagating downstream is more complex and changes as a function of the flow Reynolds number. Such waves reduce losses if the Reynolds number $Re <\ \sim\!\!100$ , but these waves must be sufficiently fast to reduce pressure losses for larger Re values. In general, the supercritical waves, i.e. waves faster than the reference flow, reduce pressure losses with the magnitude of reduction increasing monotonically with the wave phase speed and wavenumber. The need for an external pressure gradient is eliminated if sufficiently short and fast waves are used. Generally, the subcritical waves, i.e. waves with velocities similar to the reference flow, increase pressure losses. This increase changes somewhat irregularly as a function of the wave phase speed and wavenumber forming local maxima and minima. These waves can reduce pressure losses only if the Reynolds number becomes large enough. It is shown that subcritical waves with very small amplitudes but matching the natural flow frequencies produce significant pressure losses.

Directional modifier adaptation based on input selection for real-time optimization

Modifier adaptation (MA) is commonly used for economic optimization of systems under model uncertainty. In MA, gradient correction terms require estimation through perturbations, thus delaying the optimization procedure. A directional modifier adaptation method is proposed whereby a subset of available gradient corrections are made. An algorithm that evaluates possible adaptation strategies and chooses those with the largest economic effect is proposed, thereby allowing economical operation with less delay. The proposed scheme, named dMAIS, is deployed on the Williams-Otto process where it is found to outperform MA if not inhibited by filtering. Systems can also suffer from constraint violation if uncertainty is present, hampering safety and profitability. An adjustment step is proposed as part of dMAIS, whereby gradients are used to drive the plant to constraint satisfaction. The adjustments are studied in an evaporator case with a product quality constraint whereby dMAIS is shown to result in infrequent violations leading to higher throughput. The proposed approach was also compared to standard directional MA in the evaporator case study, where it was found to be economically beneficial. The benefits of dMAIS are observed most saliently for systems with increasing disturbance frequency.

Nonrelativistic limit of first-order relativistic viscous fluids

Out-of-equilibrium effects may play an important role in the dynamics of neutron star mergers and in heavy-ion collisions. Bemfica, Disconzi, Noronha and Kovtun (BDNK) recently derived a causal, locally well posed, and modally stable relativistic fluid model that incorporates the effects of viscosity and heat diffusion. We study the nonrelativistic limit of this fluid model and show that causality for relativistic motion restricts the transport coefficients in the nonrelativistic limit. This restriction provides an upper bound on the ratio of the shear viscosity to the entropy density for fluids that can be described as relativistic within the BDNK model and can be exactly modeled using the Navier-Stokes equation in the nonrelativistic limit. Furthermore, we show that the Fourier law of heat conduction must be modified by higher gradient corrections for such fluids. We also show that the nonrelativistic limit of the BDNK equations of motion are never hyperbolic, in contrast to the nonrelativistic limit of extended variable models, whose nonrelativistic equations of motion can be hyperbolic or not depending on the scaling of the transport coefficients present in the auxiliary equations for viscous degrees of freedom.

Research and application of nodal stress correction at stiffness mutation position for fatigue life evaluation

This paper proposes a two-level stress correction method to overcome the limitations of the element stress average method that is typically used to calculate the nodal stress in finite element analyses and increase the fatigue life evaluation accuracy at the stiffness mutation positions of large-scale structure. In the first stage, a standard-deviation-weighted stress smoothing method is used to address the high element stress dispersion at the stiffness mutation point. The second stage involves a stress gradient correction method established based on the theory that the nodal stress is affected by other nodal stresses on the stress gradient path. The nodal stresses of the key points of an 80-ton gondola car body are extracted using the two-level stress correction method, and the fatigue life of the key points is evaluated considering the load spectrum of the Daqin coal line. The fatigue lives corresponding to the measured stress spectrum at the key points are compared with the simulated values. Compared with that obtained by the traditional method, the fatigue life of the key joints obtained by the proposed method is closer to the actual fatigue life. Additionally, the nodal stress at the stiffness mutation position obtained by the proposed method is more accurate. Therefore, the two-level stress correction method is a promising platform for the fatigue life evaluation of large-scale structures.

Boosting the transferability of adversarial attacks with adaptive points selecting in temporal neighborhood

Deep neural networks are highly susceptible to imperceptible noise, even to the human eye. While high attack success rate has been achieved in white-box setting, the attack performance tends to decline in black-box environments. To address this challenge, this study introduces a novel adaptive points selecting iterative fast gradient sign method, named AI-FGSM, which leverages temporal neighborhoods to enhance transferability performance in black-box environments. AI-FGSM is unique in that it extracts gradients from additional points in the temporal neighborhood and adjusts the current gradient using previous gradients to maintain the updated trend's stability. This gradient correction enables faster optimization and restricts falling into local optima. Experimental results on the ImageNet dataset show that AI-FGSM outperforms advanced gradient-based attack methods such as MI-FGSM and NI-FGSM in terms of attack success rate and transferability. Moreover, in black-box environments, AI-FGSM achieves an average attack performance improvement of 44.2% for some models with adversarial training and 32.9% for several models without adversarial training. These results confirm the performance and effectiveness of AI-FGSM, underscoring its potential as a powerful tool for improving the transferability of adversarial attacks.

Coherent backscattering in the topological Hall effect

The mutual interplay between electron transport and magnetism has attracted considerable attention in recent years, primarily motivated by strategies to manipulate magnetic degrees of freedom electrically, such as spin–orbit torques and domain wall motion. Within this field the topological Hall effect, which originates from scalar spin chirality, is an example of inter-band quantum coherence induced by real-space inhomogeneous magnetic textures, and its magnitude depends on the winding number and chiral spin features that establish the total topological charge of the system. Remarkably, in the two decades since its discovery, there has been no research on the quantum correction to the topological Hall effect. Here we will show that, unlike the ordinary Hall effect, the inhomogeneous magnetization arising from the spin texture will give additional scattering terms in the kinetic equation, which result in a quantum correction to the topological Hall resistivity. We focus on two-dimensional systems, where weak localization is strongest, and determine the complicated gradient corrections to the Cooperon and kinetic equation. Whereas the weak localization correction to the topological Hall effect is not large in currently known materials, we show that it is experimentally observable in dilute magnetic semiconductors. Our theoretical results will stimulate experiments on the topological Hall effect and fill the theoretical knowledge gap on weak localization corrections to transverse transport.

New Gradient Correction Scheme for Electronically Nonadiabatic Dynamics Involving Multiple Spin States

It has been recommended that the best representation to use for trajectory surface hopping (TSH) calculations is the fully adiabatic basis in which the Hamiltonian is diagonal. Simulations of intersystem crossing processes with conventional TSH methods require an explicit computation of nonadiabatic coupling vectors (NACs) in the molecular-Coulomb-Hamiltonian (MCH) basis, also called the spin-orbit-free basis, in order to compute the gradient in the fully adiabatic basis (also called the diagonal representation). This explicit requirement destroys some of the advantages of the overlap-based algorithms and curvature-driven algorithms that can be used for the most efficient TSH calculations. Therefore, although these algorithms allow one to perform NAC-free simulations for internal conversion processes, one still requires NACs for intersystem crossing. Here, we show that how the NAC requirement is circumvented by a new computation scheme called the time-derivative-matrix scheme.

Accurate computation of geoid-quasigeoid separation in mountainous region – A case study in Colorado with full extension to the experimental geoid region

Abstract The geoid-quasigeoid separation (GQS) traditionally uses the Bouguer anomalies to approximate the difference between the mean gravity and normal gravity along the plumb line. This approximation is adequate in flat and low elevation areas, but not in high and rugged mountains. To increase the accuracy, higher order terms of the corrections (potential and gravity gradient) to the approximation were computed in Colorado where the 1 cm geoid computation experiment was conducted. Over an area of 730 km by 560 km where the elevation ranges between 932 and 4,385 m, the potential correction (Pot. Corr.) reaches −0.190 m and its root mean square (RMS) is 0.019 m. The gravity gradient correction is small but has high variation: the RMS of the correction is merely 0.003 m but varies from −0.025 to 0.020 m. In addition, the difference between the Bouguer gravity anomaly and gravity disturbance causes about a 0.01 m bias and a maximum correction of 0.02 m. The total corrections range from −0.135 to 0.180 m, with an RMS value of 0.019 m for the region. The magnitude of the corrections is large enough and is not negligible considering today’s cm-geoid requirement. After the test in Colorado, the complete GQS term is computed in 1′ × 1′ grids for the experimental geoid 2020 (xGEOID20), which covers a region bordered by latitude 0–85° north, longitude 180–350° east. Over the land areas, the RMS of the GQS is 0.119 m and the maximum reaches 1.3 m. The RMS of the GQS increases with respect to the height until 4,000 m, then decreases unexpectedly. At the highest peaks (5,500–6,000 m) of Denali and Mount Logan, the RMS of the GQS ranges between 0.08 and 0.189 m. The small GQS at these high peaks are caused by steep slopes around the peaks that produce large Pot. Corr. caused by the topography. In addition, the higher order correction terms reach half of a meter in those peaks.

Demonstration of RANS models with wall functions in the spectral element code Nek5000

The spectral element based computational fluid dynamics (CFD) code Nek5000 has been traditionally used for high-fidelity applications, such as direct numerical simulation (DNS) and large eddy simulation (LES). These techniques require very fine numerical resolution to accurately capture turbulent fluctuations which can be prohibitively expensive for users without access to leadership class computing facilities. For broader application and adoption, significant effort has been invested to develop Reynolds-averaged Navier–Stokes (RANS) capabilities in Nek5000.This work presents details of the implementation and demonstration of the standard wall functions for the k – τ model in Nek5000. Results using the wall-modeled approach are compared to a wall-resolved approach for cases with negligible pressure gradient, viz., channel flow, pipe flow and flow in a reactor subchannel. Results show reasonably good agreement between the two approaches for friction factor and Nusselt number. Some expected differences are identified near the wall. These cases demonstrate the potential for significant computational savings by using much coarser meshes for the wall-modeled approach, with only minor differences between the predicted result. Additionally, several Reynolds numbers up to 1,000,000 are demonstrated for pipe flow and predicted friction factors and Nusselt numbers compared well to available correlations, with the worst below 10%. As the Reynolds number is increased, better agreement is observed between the correlations and the wall-modeled approach. In addition, flow in a molten salt fast reactor (MSFR) core is considered which features an adverse pressure gradient and flow separation. It showcases the inability of standard wall functions to accurately predict flows with adverse pressure gradients. The results, however, match reasonably well in trend in regions of the flow where the boundary layer is attached. Ongoing research is dedicated to include a pressure gradient correction to wall functions to improve the accuracy of flows with separation or reattachment and adverse or favorable pressure gradients.

Bone suppression of lateral chest x-rays with imperfect and limited dual-energy subtraction images.

Bone suppression is to suppress the superimposed bone components over the soft tissues within the lung area of Chest X-ray (CXR), which is potentially useful for the subsequent lung disease diagnosis for radiologists, as well as computer-aided systems. Despite bone suppression methods for frontal CXRs being well studied, it remains challenging for lateral CXRs due to the limited and imperfect DES dataset containing paired lateral CXR and soft-tissue/bone images and more complex anatomical structures in the lateral view. In this work, we propose a bone suppression method for lateral CXRs by leveraging a two-stage distillation learning strategy and a specific data correction method. Specifically, a primary model is first trained on a real DES dataset with limited samples. The bone-suppressed results on a relatively large lateral CXR dataset produced by the primary model are improved by a designed gradient correction method. Secondly, the corrected results serve as training samples to train the distillated model. By automatically learning knowledge from both the primary model and the extra correction procedure, our distillated model is expected to promote the performance of the primary model while omitting the tedious correction procedure. We adopt an ensemble model named MsDd-MAP for the primary and distillated models, which learns the complementary information of Multi-scale and Dual-domain (i.e., intensity and gradient) and fuses them in a maximum-a-posteriori (MAP) framework. Our method is evaluated on a two-exposure lateral DES dataset consisting of 46 subjects and a lateral CXR dataset consisting of 240 subjects. The experimental results suggest that our method is superior to other competing methods regarding the quantitative evaluation metrics. Furthermore, the subjective evaluation by three experienced radiologists also indicates that the distillated model can produce more visually appealing soft-tissue images than the primary model, even comparable to real DES imaging for lateral CXRs.

Quantum partonic transport in QCD matter

We study gradient corrections to the transport equation for energetic light partons in dense QCD environments. In the diffusion limit, the transport dynamics is solely controlled by small-angle elastic scatterings, leading to transverse momentum broadening with respect to the parton's initial direction. Such a parton propagation is usually considered in the limit of transversely homogeneous matter. The transport processes admit a classical description and the transverse spatial dependence of the medium properties emerges only through the jet quenching parameter. In this work, we show that a gradient expansion of the all-order evolution equation for the partonic Wigner function leads to an evolution equation in the Boltzmann-diffusion form only up to the leading order in transverse gradients. At the second order in gradients, the quantum corrections associated with nonlocal interactions give rise to a novel transport that can be implemented in Monte Carlo simulations. In addition, using our results, we compute the gradient corrections to the jet quenching parameter in inhomogeneous matter.

Notch Fatigue Life Prediction Model Considering Stress Gradient Influence Depth and Weight Function

Notch characteristics significantly affect the fatigue performance of engineered components, for which the stress gradient effect is worth careful consideration. The traditional stress gradient analysis method based on the Coffin–Manson equation does not take into account the stress gradient influence range regarding the definition of the stress gradient correction factor, nor the high-stress gradient region, which has a greater influence on fatigue life. To address the aforementioned problems, a new notch fatigue life model is proposed in this paper. First, the stress–strain field at the root of the notch is analyzed to define the depth of stress gradient influence, following which the influence of the low-stress gradient region is reduced by a weighting function in the calculation of the stress gradient correction factor. Finally, to validate the method, three sets of experimental data, including TC4, GH4169, and EN8B, were used and compared with three other models. The results demonstrate that the predicted lifetimes of the new model are all within a 2-fold dispersion band, and the prediction ability is better than that of the other three models.

An improved multiphase SPH algorithm with kernel gradient correction for modelling fuel–coolant interaction

Fuel–coolant interaction (FCI) has a pivotal role in the development of core disruptive accident in a sodium-cooled fast reactor. The drastic deformation of multiphase interface in the FCI is hard to deal with in the traditional grid method. In this paper, an improved multiphase smoothed particle hydrodynamics (SPH) algorithm corrected with the kernel gradient correction (KGC) technique is presented for multiphase flow with a large density ratio and complex interfacial behaviors. The density discontinuity across the multiphase interface is described with the use of special volume, which only depends on the position information of adjacent particles. This multiphase SPH algorithm, which is troubled by an unstable and mixed-interface problem under a large density ratio, is significantly improved with the KGC technique. The accuracy and robustness of the improved method are demonstrated in the numerical simulations of the deformation of a square droplet, Rayleigh–Taylor instability, and bubble rising in water. The verified corrected multiphase SPH is applied to simulate the hydrodynamic behaviors of the general FCI and the interaction between fuels coated with stainless steel film and coolant. Boundary layer stripping, Rayleigh–Taylor instability, and Kelvin–Helmholtz instability are observed as important mechanisms of hydraulic fracturing. The fragments’ distribution and the influence of stainless steel film are analyzed. The existence of a stainless steel film has been shown to inhibit breakage.

Interface Scattering as a Nonlocal Transport Phenomenon in Semiconductors

Macroscopically non-local effects are common in electron transport in semiconductor devices, occurring whenever the mean free path and/or the deBroglie wavelength are not small compared to geometry/flow length scales. When such effects are important, standard diffusion-drift (DD) theory becomes inaccurate and in need of revision, with the best known example being density-gradient (DG) theory wherein a gradient term is added to the electron gas equation of state to approximate the effect of quantum non-locality. Here we consider a similarly motivated gradient correction to the electron-lattice interaction that accounts for non-locality in the transport physics. Versions of DD and DG theory with this correction are discussed, and then are applied to the analysis of long-channel field-effect transistors where they are found to provide a physics-based approach for modeling and understanding interface scattering.

A Client Selection Method Based on Loss Function Optimization for Federated Learning

Federated learning is a distributed machine learning method that can solve the increasingly serious problem of data islands and user data privacy, as it allows training data to be kept locally and not shared with other users. It trains a global model by aggregating locally-computed models of clients rather than their raw data. However, the divergence of local models caused by data heterogeneity of different clients may lead to slow convergence of the global model. For this problem, we focus on the client selection with federated learning, which can affect the convergence performance of the global model with the selected local models. We propose FedChoice, a client selection method based on loss function optimization, to select appropriate local models to improve the convergence of the global model. It firstly sets selected probability for clients with the value of loss function, and the client with high loss will be set higher selected probability, which can make them more likely to participate in training. Then, it introduces a local control vector and a global control vector to predict the local gradient direction and global gradient direction, respectively, and calculates the gradient correction vector to correct the gradient direction to reduce the cumulative deviation of the local gradient caused by the Non-IID data. We make experiments to verify the validity of FedChoice on CIFAR-10, CINIC-10, MNIST, EMNITS, and FEMNIST datasets, and the results show that the convergence of FedChoice is significantly improved, compared with FedAvg, FedProx, and FedNova.

The CEEMDAN-ps-gcGRU Model On Water Pressure Prediction With Strong Irregularity

As for urban water dispatch, multiple steps of water pressure prediction are necessary. Due to the strong irregularity of water pressure, both machine learning and original deep learning methods can't accurately predict water pressure. In order to predict the water pressure with significant irregularity, this paper has developed a prediction model. The CEEMDAN approach seeks to reduce the noise of the raw water pressure data, which is directly recorded by sensors. The extraction of pump state signals has the ability to introduce extra useful information to the training model. Gradient Correction Methodology is a new strategy for increasing the precision of water pressure prediction in multi-step models. It could alleviate the gradient disappearing issue for long horizon prediction. In general, the designed prediction model on water pressure performs better than other models with long step sizes.

Recursive Estimation of Modifiers for Real-Time Optimization with Gradient Adaptation

Because of the uncertainties during the design phase of processes, the drift of process parameters during the plant lifetime and exogenous factors affecting the supply or demand of materials, the operation of continuous processes needs to be updated to track the economically optimal conditions that maximize the profit. For this reason, the practice of RealTime Optimization (RTO) has been established in the process industry to assist in selecting the setpoints to be used in the process. Real Time Optimization works by updating the setpoints of a plant using a model. To cope with the inevitable inaccuracy of the available models, various techniques have been developed, most notably parameter adaptation and Modifier Adaptation (MA). MA corrects the process model by bias and gradient correction terms for the variables of interest (typically the cost function and constraints), such that the RTO algorithm is guaranteed to reach a true (local) plant optimum upon convergence. The most crucial part in RTO-MA schemes is the estimation of the gradients, which requires the evaluation of the plant response at several points and determines the overall complexity of the RTO-MA problem. The goal of this contribution is to show how a recursive estimator that shares some similarities with the Kalman filter can be used to estimate the modifiers.