TCAS-PINN:Physics-informed neural networks with a novel temporal causality-based adaptive sampling method

Physics-informed neural networks(PINNs)have become an attractive machine learning framework for obtaining solutions to partial differential equations(PDEs).PINNs embed initial,boundary,and PDE constraints into the loss function.The performance of PINNs is generally affected by both training and sampling.Specifically,training methods focus on how to overcome the training difficulties caused by the special PDE residual loss of PINNs,and sampling methods are concerned with the location and distribution of the sampling points upon which evaluations of PDE residual loss are accomplished.However,a common problem among these original PINNs is that they omit special temporal information utilization during the training or sampling stages when dealing with an important PDE category,namely,time-dependent PDEs,where temporal information plays a key role in the algorithms used.There is one method,called Causal PINN,that considers temporal causality at the training level but not special temporal utilization at the sampling level.Incorporating temporal knowledge into sampling remains to be studied.To fill this gap,we propose a novel temporal causality-based adaptive sampling method that dynamically determines the sampling ratio according to both PDE residual and temporal causality.By designing a sampling ratio determined by both residual loss and temporal causality to control the number and location of sampled points in each temporal sub-domain,we provide a practical solution by incorporating temporal information into sampling.Numerical experiments of several nonlinear time-dependent PDEs,including the Cahn–Hilliard,Korteweg–de Vries,Allen–Cahn and wave equations,show that our proposed sampling method can improve the performance.We demonstrate that using such a relatively simple sampling method can improve prediction performance by up to two orders of magnitude compared with the results from other methods,especially when points are limited.

Research on Adaptive Cluster Sampling Method Based on PPS

This paper introduces the principle of PPS-based adaptive cluster sampling method and its modified HH estimator and HT estimator calculation method. It compares PPS-based adaptive cluster sampling method with SRS sampling and SRS-based adaptive group. The difference between the group sampling and the advantages and scope of the PPS adaptive cluster sampling method are analyzed. According to the case analysis, the relevant conclusions are drawn: 1) The adaptive cluster sampling method is more accurate than the SRS sampling;2) SRS adaptive The HT estimator of the cluster sampling is more stable than the HH estimator;3) The two estimators of the PPS adaptive cluster sampling method have little difference in the estimation of the population mean, but the HT estimator variance is smaller and more suitable;4) PPS The HH estimator of adaptive cluster sampling is the same as the HH estimator of SRS adaptive cluster sampling, but the variance is larger and unstable.

Physics-informed neural networks with residual/gradient-based adaptive sampling methods for solving partial differential equations with sharp solutions

We consider solving the forward and inverse partial differential equations(PDEs)which have sharp solutions with physics-informed neural networks(PINNs)in this work.In particular,to better capture the sharpness of the solution,we propose the adaptive sampling methods(ASMs)based on the residual and the gradient of the solution.We first present a residual only-based ASM denoted by ASMⅠ.In this approach,we first train the neural network using a small number of residual points and divide the computational domain into a certain number of sub-domains,then we add new residual points in the sub-domain which has the largest mean absolute value of the residual,and those points which have the largest absolute values of the residual in this sub-domain as new residual points.We further develop a second type of ASM(denoted by ASMⅡ)based on both the residual and the gradient of the solution due to the fact that only the residual may not be able to efficiently capture the sharpness of the solution.The procedure of ASMⅡis almost the same as that of ASMⅠ,and we add new residual points which have not only large residuals but also large gradients.To demonstrate the effectiveness of the present methods,we use both ASMⅠand ASMⅡto solve a number of PDEs,including the Burger equation,the compressible Euler equation,the Poisson equation over an Lshape domain as well as the high-dimensional Poisson equation.It has been shown from the numerical results that the sharp solutions can be well approximated by using either ASMⅠor ASMⅡ,and both methods deliver much more accurate solutions than the original PINNs with the same number of residual points.Moreover,the ASMⅡalgorithm has better performance in terms of accuracy,efficiency,and stability compared with the ASMⅠalgorithm.This means that the gradient of the solution improves the stability and efficiency of the adaptive sampling procedure as well as the accuracy of the solution.Furthermore,we also employ the similar adaptive sampling technique for the data points of boundary conditions(BCs)if the sharpness of the solution is near the boundary.The result of the L-shape Poisson problem indicates that the present method can significantly improve the efficiency,stability,and accuracy.

Robust adaptive radar beamforming based on iterative training sample selection using kurtosis of generalized inner product statistics

In engineering application,there is only one adaptive weights estimated by most of traditional early warning radars for adaptive interference suppression in a pulse reputation interval(PRI).Therefore,if the training samples used to calculate the weight vector does not contain the jamming,then the jamming cannot be removed by adaptive spatial filtering.If the weight vector is constantly updated in the range dimension,the training data may contain target echo signals,resulting in signal cancellation effect.To cope with the situation that the training samples are contaminated by target signal,an iterative training sample selection method based on non-homogeneous detector(NHD)is proposed in this paper for updating the weight vector in entire range dimension.The principle is presented,and the validity is proven by simulation results.

Active Kriging-Based Adaptive Importance Sampling for Reliability and Sensitivity Analyses of Stator Blade Regulator

The reliability and sensitivity analyses of stator blade regulator usually involve complex characteristics like highnonlinearity,multi-failure regions,and small failure probability,which brings in unacceptable computing efficiency and accuracy of the current analysismethods.In this case,by fitting the implicit limit state function(LSF)with active Kriging(AK)model and reducing candidate sample poolwith adaptive importance sampling(AIS),a novel AK-AIS method is proposed.Herein,theAKmodel andMarkov chainMonte Carlo(MCMC)are first established to identify the most probable failure region(s)(MPFRs),and the adaptive kernel density estimation(AKDE)importance sampling function is constructed to select the candidate samples.With the best samples sequentially attained in the reduced candidate samples and employed to update the Kriging-fitted LSF,the failure probability and sensitivity indices are acquired at a lower cost.The proposed method is verified by twomulti-failure numerical examples,and then applied to the reliability and sensitivity analyses of a typical stator blade regulator.Withmethods comparison,the proposed AK-AIS is proven to hold the computing advantages on accuracy and efficiency in complex reliability and sensitivity analysis problems.

Knowledge Transfer Learning via Dual Density Sampling for Resource-Limited Domain Adaptation

Most existing domain adaptation(DA) methods aim to explore favorable performance under complicated environments by sampling.However,there are three unsolved problems that limit their efficiencies:ⅰ) they adopt global sampling but neglect to exploit global and local sampling simultaneously;ⅱ)they either transfer knowledge from a global perspective or a local perspective,while overlooking transmission of confident knowledge from both perspectives;and ⅲ) they apply repeated sampling during iteration,which takes a lot of time.To address these problems,knowledge transfer learning via dual density sampling(KTL-DDS) is proposed in this study,which consists of three parts:ⅰ) Dual density sampling(DDS) that jointly leverages two sampling methods associated with different views,i.e.,global density sampling that extracts representative samples with the most common features and local density sampling that selects representative samples with critical boundary information;ⅱ)Consistent maximum mean discrepancy(CMMD) that reduces intra-and cross-domain risks and guarantees high consistency of knowledge by shortening the distances of every two subsets among the four subsets collected by DDS;and ⅲ) Knowledge dissemination(KD) that transmits confident and consistent knowledge from the representative target samples with global and local properties to the whole target domain by preserving the neighboring relationships of the target domain.Mathematical analyses show that DDS avoids repeated sampling during the iteration.With the above three actions,confident knowledge with both global and local properties is transferred,and the memory and running time are greatly reduced.In addition,a general framework named dual density sampling approximation(DDSA) is extended,which can be easily applied to other DA algorithms.Extensive experiments on five datasets in clean,label corruption(LC),feature missing(FM),and LC&FM environments demonstrate the encouraging performance of KTL-DDS.

Designing Adaptive Multiple Dependent State Sampling Plan for Accelerated Life Tests

A novel adaptive multiple dependent state sampling plan(AMDSSP)was designed to inspect products from a continuous manufacturing process under the accelerated life test(ALT)using both double sampling plan(DSP)and multiple dependent state sampling plan(MDSSP)concepts.Under accelerated conditions,the lifetime of a product follows the Weibull distribution with a known shape parameter,while the scale parameter can be determined using the acceleration factor(AF).The Arrhenius model is used to estimate AF when the damaging process is temperature-sensitive.An economic design of the proposed sampling plan was also considered for the ALT.A genetic algorithm with nonlinear optimization was used to estimate optimal plan parameters to minimize the average sample number(ASN)and total cost of inspection(TC)under both producer’s and consumer’s risks.Numerical results are presented to support the AMDSSP for the ALT,while performance comparisons between the AMDSSP,the MDSSP and a single sampling plan(SSP)for the ALT are discussed.Results indicated that the AMDSSP was more flexible and efficient for ASN and TC than the MDSSP and SSP plans under accelerated conditions.The AMDSSP also had a higher operating characteristic(OC)curve than both the existing sampling plans.Two real datasets of electronic devices for the ALT at high temperatures demonstrated the practicality and usefulness of the proposed sampling plan.

Multiple-target tracking with adaptive sampling intervals for phased-array radar

A novel adaptive sampling interval algorithm for multitarget tracking is presented. This algorithm which is based on interacting multiple models incorporates the grey relational grade （GRG） into the particle swarm optimization （PSO）. Firstly, the desired tracking accuracy is set for each target. Secondly, sampling intervals are selected as particles, and then the advantage of the GRG is taken as the measurement function for resource management. Meanwhile, the fitness value of the PSO is used to measure the difference between desired tracking accuracy and estimated tracking accuracy. Finally, it is suggested that the radar should track the target whose prediction value of the next sampling interval is the smallest. Simulations show that the proposed method improves both the tracking accuracy and tracking efficiency of the phased-array radar.

Adaptive Space Expansion for Fast Motion Planning

The sampling process is very inefficient for sam-pling-based motion planning algorithms that excess random sam-ples are generated in the planning space.In this paper,we pro-pose an adaptive space expansion(ASE)approach which belongs to the informed sampling category to improve the sampling effi-ciency for quickly finding a feasible path.The ASE method enlarges the search space gradually and restrains the sampling process in a sequence of small hyper-ellipsoid ring subsets to avoid exploring the unnecessary space.Specifically,for a con-structed small hyper-ellipsoid ring subset,if the algorithm cannot find a feasible path in it,then the subset is expanded.Thus,the ASE method successively does space exploring and space expan-sion until the final path has been found.Besides,we present a particular construction method of the hyper-ellipsoid ring that uniform random samples can be directly generated in it.At last,we present a feasible motion planner BiASE and an asymptoti-cally optimal motion planner BiASE*using the bidirectional exploring method and the ASE strategy.Simulations demon-strate that the computation speed is much faster than that of the state-of-the-art algorithms.The source codes are available at https://github.com/shshlei/ompl.

Efficiency of the Adaptive Cluster Sampling Designs in Estimation of Rare Populations

Adaptive cluster sampling (ACS) has been a very important tool in estimation of population parameters of rare and clustered population. The fundamental idea behind this sampling plan is to decide on an initial sample from a defined population and to keep on sampling within the vicinity of the units that satisfy the condition that at least one characteristic of interest exists in a unit selected in the initial sample. Despite being an important tool for sampling rare and clustered population, adaptive cluster sampling design is unable to control the final sample size when no prior knowledge of the population is available. Thus adaptive cluster sampling with data-driven stopping rule (ACS’) was proposed to control the final sample size when prior knowledge of population structure is not available. This study examined the behavior of the HT, and HH estimator under the ACS design and ACS’ design using artificial population that is designed to have all the characteristics of a rare and clustered population. The efficiencies of the HT and HH estimator were used to determine the most efficient design in estimation of population mean in rare and clustered population. Results of both the simulated data and the real data show that the adaptive cluster sampling with stopping rule is more efficient for estimation of rare and clustered population than ordinary adaptive cluster sampling.

Distributed model predictive control based on adaptive sampling mechanism

In this work,an adaptive sampling control strategy for distributed predictive control is proposed.According to the proposed method,the sampling rate of each subsystem of the accused object is determined based on the periodic detection of its dynamic behavior and calculations made using a correlation function.Then,the optimal sampling interval within the period is obtained and sent to the corresponding sub-prediction controller,and the sampling interval of the controller is changed accordingly before the next sampling period begins.In the next control period,the adaptive sampling mechanism recalculates the sampling rate of each subsystem’s measurable output variable according to both the abovementioned method and the change in the dynamic behavior of the entire system,and this process is repeated.Such an adaptive sampling interval selection based on an autocorrelation function that measures dynamic behavior can dynamically optimize the selection of sampling rate according to the real-time change in the dynamic behavior of the controlled object.It can also accurately capture dynamic changes,meaning that each sub-prediction controller can more accurately calculate the optimal control quantity at the next moment,significantly improving the performance of distributed model predictive control(DMPC).A comparison demonstrates that the proposed adaptive sampling DMPC algorithm has better tracking performance than the traditional DMPC algorithm.

Adaptive sampling for mesh spectrum editing

A mesh editing framework is presented in this paper, which integrates Free-Form Deformation (FFD) and geometry signal processing. By using simplified model from original mesh, the editing task can be accomplished with a few operations. We take the deformation of the proxy and the position coordinates of the mesh models as geometry signal. Wavelet analysis is em- ployed to separate local detail information gracefully. The crucial innovation of this paper is a new adaptive regular sampling approach for our signal analysis based editing framework. In our approach, an original mesh is resampled and then refined itera- tively which reflects optimization of our proposed spectrum preserving energy. As an extension of our spectrum editing scheme, the editing principle is applied to geometry details transferring, which brings satisfying results.

A New Estimator Using Auxiliary Information in Stratified Adaptive Cluster Sampling

In this paper, we study the estimators of the population mean in stratified adaptive cluster sampling by using the information of the auxiliary variable. Simulations showed that if the variable of interest (y) and the auxiliary variables (x,z) have high positive correlation then the estimate of the mean square error of the ratio estimators is less than the estimate of the mean square error of the product estimator. The estimators which use only one auxiliary variable were better than the estimators which use two auxiliary variables.

Adaptive Sampling for Near Space Hypersonic Gliding Target Tracking

For modern phased array radar systems,the adaptive control of the target revisiting time is important for efficient radar resource allocation,especially in maneuvering target tracking applications.This paper presents a novel interactive multiple model(IMM)algorithm optimized for tracking maneuvering near space hypersonic gliding vehicles(NSHGV)with a fast adaptive sam-pling control logic.The algorithm utilizes the model probabilities to dynamically adjust the revisit time corresponding to NSHGV maneuvers,thus achieving a balance between tracking accuracy and resource consumption.Simulation results on typical NSHGV targets show that the proposed algo-rithm improves tracking accuracy and resource allocation efficiency compared to other conventional multiple model algorithms.

Adaptive Radial Based Sampling for Reliability and Reliability Sensitivity Analysis Involving Truncated Correlated Normal Variables

The reliability and reliability sensitivity （ RS ） models are presented for the engineering problem involving truncated correlated normal variables （CNV）, and in the case an adaptive radial based sampling is used to analyze the reliability and the RS. In the presented models, the truncated CNV is transformed to general CNV, and the value domains of the truncated CNV are treated as multiple failure modes, then the reliability and the RS with the truncated CNV are transformed to the general cases, on which an e^cient radial based sampling is used to analyze the trans- formed reliability and RS. An adaptive strategy is employed to search for the optimal radial in the sampling, by which the robustness of the method is improved. After the model concepts and the detailed implementation are given, several examples are presented to demonstrate the feasibility of the model and the efficiency of the solutions.

Knowledge Graph Embedding Based on Adaptive Negative Sampling

Knowledge graph embedding aims at embedding entities and relations in a knowledge graph into a continuous, dense, low-dimensional and realvalued vector space. Among various embedding models appeared in recent years, translation-based models such as TransE, TransH and TransR achieve state-of-the-art performance. However, in these models, negative triples used for training phase are generated by replacing each positive entity in positive triples with negative entities from the entity set with the same probability;as a result, a large number of invalid negative triples will be generated and used in the training process. In this paper, a method named adaptive negative sampling (ANS) is proposed to generate valid negative triples. In this method, it first divided all the entities into a number of groups which consist of similar entities by some clustering algorithms such as K-Means. Then, corresponding to each positive triple, the head entity was replaced by a negative entity from the cluster in which the head entity was located and the tail entity was replaced in a similar approach. As a result, it generated a set of high-quality negative triples which benefit for improving the effectiveness of embedding models. The ANS method was combined with the TransE model and the resulted model was named as TransE-ANS. Experimental results show that TransE-ANS achieves significant improvement in the link prediction task.

一种基于Multiple Sampling的高精度相位差测量算法研究

阐述了一种相位差测量算法。首先介绍了Multiple Sampling算法的理论根据,并且进行了算法仿真实验和误差分析,然后在此基础上进行了谐波及噪声分析,提出了针对可变频信号的算法仿真方案,结果表明在增大白噪声幅度的情况下,初相最坏误差仍控制在高精度工程标准内。

Adaptive sampling for corrugated plate digitization using a laser displacement sensor

The surface quality of a corrugated plate directly determines the heat transfer property of the thermal power mechanical apparatus.Traditional detection methods are impractical for real-world production,being slow and destructive.In contrast,the point laser displacement sensor,employing the optical triangle method,emerges as a promising device for assessing parts with variable curvature and highly reflective surfaces.Despite its benefits,high-density sampling by an innate frequency introduces challenges such as data redundancy and a poor signal-to-noise ratio,potentially affecting the efficiency and precision of subsequent data processing.To address these challenges,adjustable frequency data sampling has been developed for this sensor,allowing adaptive sampling for corrugated plate digitization.The process begins with surface digitization to extract discrete points,which are transformed into intersection curves using the B-spline fitting technique.Subsequently,dominant points are identified,considering multigeometric constraints for curvature and arch height.Finally,the sampling signal is adjusted based on the distribution information of dominant points.Comparative results indicate that the proposed method effectively minimizes redundant sampling without compromising the accurate capture of essential geometric features.

Cross-classes domain inference with network sampling for natural resource inventory

There are two distinct types of domains,design-and cross-classes domains,with the former extensively studied under the topic of small-area estimation.In natural resource inventory,however,most classes listed in the condition tables of national inventory programs are characterized as cross-classes domains,such as vegetation type,productivity class,and age class.To date,challenges remain active for inventorying cross-classes domains because these domains are usually of unknown sampling frame and spatial distribution with the result that inference relies on population-level as opposed to domain-level sampling.Multiple challenges are noteworthy:(1)efficient sampling strategies are difficult to develop because of little priori information about the target domain;(2)domain inference relies on a sample designed for the population,so within-domain sample sizes could be too small to support a precise estimation;and(3)increasing sample size for the population does not ensure an increase to the domain,so actual sample size for a target domain remains highly uncertain,particularly for small domains.In this paper,we introduce a design-based generalized systematic adaptive cluster sampling(GSACS)for inventorying cross-classes domains.Design-unbiased Hansen-Hurwitz and Horvitz-Thompson estimators are derived for domain totals and compared within GSACS and with systematic sampling(SYS).Comprehensive Monte Carlo simulations show that(1)GSACS Hansen-Hurwitz and Horvitz-Thompson estimators are unbiased and equally efficient,whereas thelatter outperforms the former for supporting a sample of size one;(2)SYS is a special case of GSACS while the latter outperforms the former in terms of increased efficiency and reduced intensity;(3)GSACS Horvitz-Thompson variance estimator is design-unbiased for a single SYS sample;and(4)rules-ofthumb summarized with respect to sampling design and spatial effect improve precision.Because inventorying a mini domain is analogous to inventorying a rare variable,alternative network sampling procedures are also readily available for inventorying cross-classes domains.

A Novel Multiple Dependent State Sampling Plan Based on Time Truncated Life Tests Using Mean Lifetime

The design of a new adaptive version of the multiple dependent state(AMDS)sampling plan is presented based on the time truncated life test under the Weibull distribution.We achieved the proposed sampling plan by applying the concept of the double sampling plan and existing multiple dependent state sampling plans.A warning sign for acceptance number was proposed to increase the probability of current lot acceptance.The optimal plan parameters were determined simultaneously with nonlinear optimization problems under the producer’s risk and consumer’s risk.A simulation study was presented to support the proposed sampling plan.A comparison between the proposed and existing sampling plans,namely multiple dependent state(MDS)sampling plans and a modified multiple dependent state(MMDS)sampling plan,was considered under the average sampling number and operating characteristic curve values.In addition,the use of two real datasets demonstrated the practicality and usefulness of the proposed sampling plan.The results indicated that the proposed plan is more flexible and efficient in terms of the average sample number compared to the existing MDS and MMDS sampling plans.