Adaptive Sampling Scheme Research Articles

Learning Gravity Fields of Small Bodies: Self-adaptive Physics-informed Neural Networks

The reconstruction of the gravity field within the surface region of small bodies is crucial for the surface proximity operations of a probe. However, the irregular shape, uneven mass distribution, and sparse gravitational data of small bodies pose challenges in the reconstruction. We propose a self-adaptive physics-informed neural network (PINN) for the reconstruction of the gravity field within the surface region of irregular and heterogeneous small bodies. First, we introduce an auxiliary-point-based data augmentation strategy to reduce the model’s dependency on the quantity of data. Second, we incorporate a residual-based adaptive sampling strategy to enhance the prediction accuracy of the model in regions with significant variations in small-body density. Finally, we introduce an adaptive weight module based on gradient ascent to mitigate the balancing issue of loss terms in the PINN. Experiments indicate that our algorithm achieves improved accuracy for reconstructing the gravity field within the surface region of small bodies. This work is expected to contribute to the enhancement of safety in surface proximity operations around the surfaces of small bodies.

Simulation model calibration with dynamic stratification and adaptive sampling

ABSTRACT Calibrating simulation models that take large quantities of multi-dimensional data as input is a hard simulation optimization problem. Existing adaptive sampling strategies offer a methodological solution. However, they may not sufficiently reduce the computational cost for estimation and solution algorithm’s progress within a limited budget due to extreme noise levels and heteroscedasticity of system responses. We propose integrating stratification with adaptive sampling for the purpose of efficiency in optimization. Stratification can exploit local dependence in the simulation inputs and outputs. Yet, the state-of-the-art does not provide a full capability to adaptively stratify the data as different solution alternatives are evaluated. We devise two procedures for data-driven calibration problems that involve a large dataset with multiple covariates to calibrate models within a fixed overall simulation budget. The first approach dynamically stratifies the input data using binary trees, while the second approach uses closed-form solutions based on linearity assumptions between the objective function and concomitant variables. We find that dynamical adjustment of stratification structure accelerates optimization and reduces run-to-run variability in generated solutions. Our case study for calibrating a wind power simulation model, widely used in the wind industry, using the proposed stratified adaptive sampling, shows better-calibrated parameters under a limited budget.

Committor Guided Estimates of Molecular Transition Rates.

The probability that a configuration of a physical system reacts, or transitions from one metastable state to another, is quantified by the committor function. This function contains richly detailed mechanistic information about transition pathways, but a full parametrization of the committor requires the construction of a high-dimensional function, a generically challenging task. Recent efforts to leverage neural networks as a means to solve high-dimensional partial differential equations, often called "physics-informed" machine learning, have brought the committor into computational reach. Here, we build on the semigroup approach to learning the committor and assess its utility for predicting dynamical quantities such as transition rates. We show that a careful reframing of the objective function and improved adaptive sampling strategies provide highly accurate representations of the committor. Furthermore, by directly applying the Hill relation, we show that these committors provide accurate transition rates for molecular systems.

Physics-informed neural networks for V-notch stress intensity factor calculation

This paper proposes a physics-informed neural networks (PINNs) based approach for elastic structures with a V-notch, by which the displacement field, stress field as well as the V-notch stress intensity factor (NSIF) can be obtained through artificial neural networks. A PINN model is established for V-notch structures, integrating physical information into a deep neural network to ensure adherence to physical laws while fitting observational data. Subsequently, an adaptive local sampling strategy for V-notch structures is adopted, generating locally dense Gaussian points sampling around regions of stress concentration. Based on this, a sequential PINNs approach for V-notch structures is then established to calculate the NSIF for V-notch structures with arbitrary notch angles. Finally, the effectiveness of the proposed method is validated through three numerical examples. The results demonstrate the method can accurately predict the NSIFs for V-notch structures across a spectrum of opening angles. Compared to the traditional data-driven method, the proposed method is able to more effectively compute the NSIF of V-notch structures due to the integration of physical information and observational data.

Adaptive sampling with tensor leverage scores for exact low-rank third-order tensor completion

Tensor completion aims at estimating the missing entries from the incomplete observation. Under the tensor singular value decomposition framework, the exact recovery of a low-tubal-rank third-order tensor could be achieved via convex optimization with high probability if the tensor satisfies the tensor incoherence condition. In this work, we show that, when the random selection of entries is made adaptive to a distribution which is dependent on the coherence structure of the tensor, any low-tubal-rank tensor of the size n×n×n with tubal-rank r can be exactly recovered with high probability from as few as O(rn2log2⁡(n)) randomly chosen entries. In practice, tensor leverage scores are not known a priori, and we design a two-phase adaptive sampling strategy to obtain the leverage scores. Numerical experiments on synthetic and real-world third-order tensor data sets are used to validate our theoretical results and illustrate that the tensor recovery performance of the proposed two-phase adaptive sampling scheme is better than that of the other state-of-the-art methods.

Integrating small data and shape prior knowledge with gradient-enhanced Kriging through adaptive knowledge sampling

Integrating prior knowledge into surrogate models constitutes an advanced approach to tackling the challenges posed by small data. The existing gradient-enhanced Kriging (GEK) method can enhance accuracy by incorporating gradient points of shape prior knowledge. Nonetheless, our findings indicate that the strategy employed for setting gradient points significantly impacts accuracy, even when the number of gradient points remains constant. To enhance the efficient utilization of gradient information, we propose a novel Adaptive Knowledge Sampling (AKS) strategy with an innovative acquisition function that balances local exploitation and global exploration, effectively extracting gradient points from shape prior knowledge. The acquisition function consists of three parts: (1) The Local Information Filling Criterion (LIFC), designed to mitigate model error; (2) The Global Information Filling Criterion (GIFC), aimed at reducing model uncertainty in data-sparse areas; and (3) The Minimum Distance Constraint (MDC), implemented to prevent excessive clustering of gradient points. To strike a balance between model accuracy and computational cost, an adaptive stopping condition is introduced to regulate the number of gradient points sampled. The impact of hyperparameters in the AKS strategy was analyzed in detail, and the method’s performance was compared to existing approaches using six benchmark functions and a missile aerodynamic prediction case. The results demonstrate that AKS-GEK offers higher prediction accuracy and robustness when integrating small data with shape prior knowledge.

A graphics processing unit accelerated sparse direct solver and preconditioner with block low rank compression

We present the GPU implementation efforts and challenges of the sparse solver package STRUMPACK. The code is made publicly available on github with a permissive BSD license. STRUMPACK implements an approximate multifrontal solver, a sparse LU factorization which makes use of compression methods to accelerate time to solution and reduce memory usage. Multiple compression schemes based on rank-structured and hierarchical matrix approximations are supported, including hierarchically semi-separable, hierarchically off-diagonal butterfly, and block low rank. In this paper, we present the GPU implementation of the block low rank (BLR) compression method within a multifrontal solver. Our GPU implementation relies on highly optimized vendor libraries such as cuBLAS and cuSOLVER for NVIDIA GPUs, rocBLAS and rocSOLVER for AMD GPUs and the Intel oneAPI Math Kernel Library (oneMKL) for Intel GPUs. Additionally, we rely on external open source libraries such as SLATE (Software for Linear Algebra Targeting Exascale), MAGMA (Matrix Algebra on GPU and Multi-core Architectures), and KBLAS (KAUST BLAS). SLATE is used as a GPU-capable ScaLAPACK replacement. From MAGMA we use variable sized batched dense linear algebra operations such as GEMM, TRSM and LU with partial pivoting. KBLAS provides efficient (batched) low rank matrix compression for NVIDIA GPUs using an adaptive randomized sampling scheme. The resulting sparse solver and preconditioner runs on NVIDIA, AMD and Intel GPUs. Interfaces are available from PETSc, Trilinos and MFEM, or the solver can be used directly in user code. We report results for a range of benchmark applications, using the Perlmutter system from NERSC, Frontier from ORNL, and Aurora from ALCF. For a high frequency wave equation on a regular mesh, using 32 Perlmutter compute nodes, the factorization phase of the exact GPU solver is about 6.5× faster compared to the CPU-only solver. The BLR-enabled GPU solver is about 13.8× faster than the CPU exact solver. For a collection of SuiteSparse matrices, the STRUMPACK exact factorization on a single GPU is on average 1.9× faster than NVIDIA’s cuDSS solver.

Drug-target interaction prediction with collaborative contrastive learning and adaptive self-paced sampling strategy

BackgroundDrug-target interaction (DTI) prediction plays a pivotal role in drug discovery and drug repositioning, enabling the identification of potential drug candidates. However, most previous approaches often do not fully utilize the complementary relationships among multiple biological networks, which limits their ability to learn more consistent representations. Additionally, the selection strategy of negative samples significantly affects the performance of contrastive learning methods.ResultsIn this study, we propose CCL-ASPS, a novel deep learning model that incorporates Collaborative Contrastive Learning (CCL) and Adaptive Self-Paced Sampling strategy (ASPS) for drug-target interaction prediction. CCL-ASPS leverages multiple networks to learn the fused embeddings of drugs and targets, ensuring their consistent representations from individual networks. Furthermore, ASPS dynamically selects more informative negative sample pairs for contrastive learning. Experiment results on the established dataset demonstrate that CCL-ASPS achieves significant improvements compared to current state-of-the-art methods. Moreover, ablation experiments confirm the contributions of the proposed CCL and ASPS strategies.ConclusionsBy integrating Collaborative Contrastive Learning and Adaptive Self-Paced Sampling, the proposed CCL-ASPS effectively addresses the limitations of previous methods. This study demonstrates that CCL-ASPS achieves notable improvements in DTI predictive performance compared to current state-of-the-art approaches. The case study and cold start experiments further illustrate the capability of CCL-ASPS to effectively predict previously unknown DTI, potentially facilitating the identification of new drug-target interactions.

Using removable sensors in structural health monitoring: A Bayesian methodology for attachment-to-attachment uncertainty quantification

Structural responses are vulnerable to perturbations when subjected to variable environmental and operational conditions, thereby contributing to the slow uptake of Structural Health Monitoring (SHM) beyond academic research. More importantly, SHM systems using removable sensors face additional sensing variability due to the inherent uncertainty in sensor reattachment compared to permanently attached sensors. In this study, a novel probabilistic approach is developed for output-only damage detection utilizing ultrasonic guided waves. Experimental uncertainties and sensor attachment factors are simultaneously considered for the first time in a Bayesian context. The uncertainty introduced by reattached sensors is incorporated into the likelihood function in a comprehensive way. Bayesian model class selection using an adaptive sampling scheme is adopted to evaluate the evidence of discrete damage classes. A reference case to an aluminum plate with progressive notches is utilized to demonstrate the significant effects of attachment uncertainty on guided wave signals. The optimal data normalization model for guided wave processing under different attachment states is evaluated using the Mahalanobis distance. The notch length is identified accurately along with the uncertainty, even though the latent adhesive parameters cannot be estimated directly.

Adaptive Sampling for Signals Associated with the Special Affine Fourier Transform

Adaptive sampling is inspired by the working principle of biological neurons, which converts the amplitude information of the received signal into a time sequence through a time encoding machine (TEM). The article mainly studies uniform sampling and adaptive sampling of non-bandlimited signals in two kinds of function spaces associated with the special affine Fourier transform (SAFT). Firstly, based on the stability characterization of the basis functions, we prove the existence of orthogonal projection operators in function spaces associated with the canonical convolution and the SAFT-convolution, respectively. Secondly, uniform sampling theorems are established for two kinds of signals living in the proposed function spaces. Finally, adaptive sampling schemes based on the crossing TEM and the integrate-and-fire TEM are studied. Moreover, the corresponding iterative reconstruction algorithms with exponential convergence are provided.

Adaptive sampling strategy for Fourier single-pixel imaging

Fourier single-pixel imaging is a technique that utilizes Fourier bases as illumination patterns to capture images. While the use of orthogonal bases enhances the imaging quality compared with other methods of single pixel imaging, the slow imaging speed has hindered its broader application. Acquiring only low-frequency Fourier coefficients enables capturing a significant portion of image information at low sampling ratio, thereby enhancing imaging speed. Nevertheless, truncating frequencies results in a loss of image detail and a decrease in picture quality. To address this challenge, this paper introduces an adaptive sampling strategy for Fourier single-pixel imaging, allowing for customized sampling distributions for each specific object. The sampling distribution is dynamically generated based on the acquired Fourier coefficients during the acquisition process, eliminating the need for prior information. Through extensive simulations and experimental analysis, this approach has demonstrated its ability to capture more complex image details at equivalent sampling ratios.

Enhancing Unmanned Aerial Vehicle Task Assignment with the Adaptive Sampling-Based Task Rationality Review Algorithm

As the application areas of unmanned aerial vehicles (UAVs) continue to expand, the importance of UAV task allocation becomes increasingly evident. A highly effective and efficient UAV task assignment method can significantly enhance the quality of task completion. However, traditional heuristic algorithms often perform poorly in complex and dynamic environments, and existing auction-based algorithms typically fail to ensure optimal assignment results. Therefore, this paper proposes a more rigorous and comprehensive mathematical model for UAV task assignment. By introducing task path decision variables, we achieve a mathematical description of UAV task paths and propose collaborative action constraints. To balance the benefits and efficiency of task assignment, we introduce a novel method: the Adaptive Sampling-Based Task Rationality Review Algorithm (ASTRRA). In the ASTRRA, to address the issue of high-value tasks being easily overlooked when the sampling probability decreases, we propose an adaptive sampling strategy. This strategy increases the sampling probability of high-value targets, ensuring a balance between computational efficiency and maximizing task value. To handle the coherence issues in UAV task paths, we propose a task review and classification method. This method involves reviewing issues in UAV task paths and conducting classified independent auctions, thereby improving the overall task assignment value. Additionally, to resolve the crossover problems between UAV task paths, we introduce a crossover path exchange strategy, further optimizing the task assignment scheme and enhancing the overall value. Experimental results demonstrate that the ASTRRA exhibits excellent performance across various task scales and dynamic scenarios, showing strong robustness and effectively improving task assignment outcomes.

Adaptive sampling in ecology: Key challenges and future opportunities

Abstract Traditional ecological monitoring employs fixed designs, which do not vary over the survey duration. Adaptive sampling, whereby the data already collected informs a sampling design which changes over the course of the study, can provide a more optimal and flexible survey design but is little used in ecology. We aim to provide an introduction to adaptive sampling for ecologists. We review previous literature and highlight examples of both empirical adaptive approaches, such as adaptive cluster sampling, and more novel model‐based adaptive methods. To conceptualise the process of adaptive sampling we identify four key stages: choice of data, definition of a criterion, selection of new sampling occasions and sampling activity. We discuss each stage in turn and focus on the decisions ecologists need to consider in order to successfully implement an adaptive sampling strategy. We include a full walkthrough of an adaptive sampling example with code provided to demonstrate each step. Adaptive sampling has potential advantages to ecologists but so far has had limited uptake. We review key challenges and barriers to uptake and suggest potential ways forward. We hope our paper will both increase awareness of adaptive sampling methods and provide a useful resource for ecologists considering an adaptive survey design.

Efficient Rational Approximation of Optical Response Functions with the AAA Algorithm

AbstractA theoretical framework for the rational approximation of optical response functions in resonant photonic systems is introduced. The framework is based on the AAA algorithm and further allows to solve the underlying nonlinear eigenproblems and to efficiently model sensitivities. An adaptive sampling strategy exploits the predominance of resonances in the physical response. A chiral metasurface is investigated and it is shown that the chiroptical response on parameter variations can be accurately modeled in the vicinity of the relevant resonance frequencies.

LUCMT: Learnable under-sampling and reconstructed network with cross multi-head attention transformer for accelerating MR image reconstruction

Background and ObjectiveAs a widely used technique for Magnetic Resonance Image (MRI) acceleration, compressed sensing MRI involves two main issues: designing an effective sampling strategy and reconstructing the image from significantly under-sampled K-space data. In this paper, an innovative approach is proposed to address these two challenges simultaneously. MethodsA novel MRI reconstruction method, termed as LUCMT, is implemented by integrating a learnable under-sampling strategy with a reconstruction network based on the Cross Multi-head Attention Transformer. In contrast to conventional static sampling methods, the proposed adaptive sampling scheme is processed optimally by learning the optimal sampling technique, which involves binarizing the sampling pattern by a sigmoid function and computing gradients by backpropagation. And the reconstruction network is designed by using CS-MRI depth unfolding network that incorporates a Cross Multi-head Attention (CMA) module with inertial and gradient descent terms. ResultsT1 brain MR images from the FastMRI dataset are used to validate the performance of the proposed method. A series of experiments are conducted to validate the superior performance of our proposed network in terms of quantitative metrics and visual quality. Compared with other state-of-the-art reconstruction methods, LUCMT achieves better reconstruction performances with more accurate details. Specifically, LUCMT achieves PSNR and SSIM results of 41.87/0.9749, 46.64/0.9868, 50.41/0.9924, and 53.51/0.9955 at sampling rates of 10 %, 20 %, 30 %, and 40 %, respectively. ConclusionsThe proposed LUCMT method can provide a promising way for generating optimal under-sampling mask and accelerating MRI reconstruction accurately.

An investigation of stochastic trust-region based algorithms for finite-sum minimization

This work elaborates on the TRust-region-ish (TRish) algorithm, a stochastic optimization method for finite-sum minimization problems proposed by Curtis et al. in [F.E. Curtis, K. Scheinberg, and R. Shi, A stochastic trust region algorithm based on careful step normalization, INFORMS. J. Optim. 1(3) (2019), pp. 200–220; F.E. Curtis and R. Shi, A fully stochastic second-order trust region method, Optim. Methods Softw. 37(3) (2022), pp. 844–877]. A theoretical analysis that complements the results in the literature is presented, and the issue of tuning the involved hyper-parameters is investigated. Our study also focuses on a practical version of the method, which computes the stochastic gradient by means of the inner product test and the orthogonality test proposed by Bollapragada et al. in [R. Bollapragada, R. Byrd, and J. Nocedal, Adaptive sampling strategies for stochastic optimization, SIAM. J. Optim. 28(4) (2018), pp. 3312–3343]. It is shown experimentally that this implementation improves the performance of TRish and reduces its sensitivity to the choice of the hyper-parameters.

ADS-VQA: Adaptive sampling model for video quality assessment

No-reference video quality assessment (NR-VQA) for user-generated content (UGC) plays a crucial role in ensuring the quality of video services. Although some works have achieved impressive results, their performance-complexity trade-off is still sub-optimal. On the one hand, overly complex network structures and additional inputs require more computing resources. On the other hand, the simple sampling methods have tended to overlook the temporal characteristics of the videos, resulting in the degradation of local textures and potential distortion of the thematic content, consequently leading to the performance decline of the VQA technologies. Therefore, in this paper, we propose an enhanced NR-VQA model, known as the Adaptive Sampling Strategy for Video Quality Assessment (ADS-VQA). Temporally, we conduct non-uniform sampling on videos utilizing features from the lateral geniculate nucleus (LGN) to capture the temporal characteristics of videos. Spatially, a dual-branch structure is designed to supplement spatial features across different levels. The one branch samples patches at their raw resolution, effectively preserving the local texture detail. The other branch performs a downsampling process guided by saliency cues, attaining global semantic features with a diminished computational expense. Experimental results demonstrate that the proposed approach achieves high performance at a lower computational cost than most state-of-the-art VQA models on four popular VQA databases.

Applying sequential adaptive strategies for sampling animal populations: An empirical study

AbstractTraditional sampling methods may prove inadequate when dealing with spatially clustered populations or when studying rare events or traits that are not easily detectable across the target population. When both scenarios occur simultaneously, adaptive sampling strategies can represent a viable option to enhance the detectability of cases of interest. This paper delves into the application of a novel class of sequential adaptive sampling strategies to animal surveys. These strategies, originally proposed for human population tuberculosis prevalence surveys, allow oversampling of the rare interest variables while managing on‐field constraints. This ensures that the unfixed sample size, typical of adaptive sampling, does not compromise overall cost‐effectiveness. We explore a strategy within this class that integrates an adaptive component into a Poisson sequential selection. The aim is twofold: to intensify the detection of cases by exploiting the spatial clustering and to provide a flexible framework for managing logistics and budget constraints. To illustrate the strengths and weaknesses of this Poisson‐based sequential adaptive sampling strategy compared to traditional sampling methods, a simulation study was conducted on a blue‐winged teal population in Florida, USA. The results showcase the benefits of the proposed strategy and open avenues for future methodological and practical improvements.

Graph reinforcement learning for flexible job shop scheduling under industrial demand response: A production and energy nexus perspective

Amidst the global energy crisis, the industrial sector is facing unparalleled energy conservation challenges as a primary energy consumer. Industrial demand response (IDR) is a promising strategy to enhance the energy efficiency of manufacturing enterprises. This paper introduces a graph reinforcement learning (GRL)-based method for flexible job shop scheduling under IDR from a production and energy nexus perspective. The scheduling problem is initially formulated as a Markov Decision Process (MDP). On this basis, the scheduling state is represented by a unique heterogeneous disjunctive graph incorporating IDR features, and the reward is constructed through a tailored generalized electricity consumption index (GECI). Moreover, a mixed graph neural network scheduler is designed to tackle this MDP, which integrates the heterogeneous attention mechanism and adaptive greedy sampling strategy. Furthermore, a proximal policy optimization algorithm is employed for training to obtain optimal scheduling schemes. Empirical case studies indicate that the proposed method can reduce GECI by up to 14.44% and 2.22%, respectively, outperforming existing well-known dispatching rules and another scheduling method based on GRL.

Automated path planning for functionally graded materials considering phase stability and solidification behavior: Application to the Mo-Nb-Ta-Ti system

Functionally graded materials have the potential to improve upon monolithic parts by locally tailoring compositions to surrounding environmental conditions. Difficulties arise when designing composition gradients as incompatible materials can result in detrimental phase formation and failure of the gradient joint. As many alloys are multi-component, designing a composition gradient free of detrimental phases is difficult due to the large composition space available to explore. A framework was developed that improves the path planning algorithm and surrogate models with adaptive sampling schemes specific to their problem definition. A cost function was created to minimize a property (such as cracking susceptibility) along a path. This framework was applied to the Mo-Nb-Ta-Ti system as a case study to showcase the efficiency in building the surrogate models and in iterating different optimal compositionally graded paths.