Dimensionality Reduction Scheme Research Articles

Classification of the perceptual impression of source-level blending between violins in a joint performance

Quantifying auditory perception of blending between sound sources is a relevant topic in music perception, but remains poorly explored due to its complex and multidimensional nature. Previous studies were able to explain the source-level blending in musically constrained sound samples, but comprehensive modelling of blending perception that involves musically realistic samples was beyond their scope. Combining the methods of Music Information Retrieval (MIR) and Machine Learning (ML), this investigation attempts to classify sound samples from real musical scenarios having different musical excerpts according to their overall source-level blending impression. Monophonically rendered samples of 2 violins in unison, extracted from in-situ close-mic recordings of ensemble performance, were perceptually evaluated and labeled into blended and non-blended classes by a group of expert listeners. Mel Frequency Cepstral Coefficients (MFCCs) were extracted, and a classification model was developed using linear and non-linear feature transformation techniques adapted from the dimensionality reduction strategies such as Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), and t-Stochastic Neighbourhood Embedding (t-SNE), paired with Euclidean distance measure as a metric to evaluate the similarity of transformed feature clusters. Results showed that LDA transformed raw MFCCs trained and validated using a separate train-test data set and Leave-One-Out Cross-Validation (LOOCV) resulted in an accuracy of 87.5%, and 87.1% respectively in correctly classifying the samples into blended and non-blended classes. In this regard, the proposed classification model which incorporates “ecological” score-independent sound samples without requiring access to individual source recordings advances the holistic modeling of blending.

Enhancing Grid-Based 3D Object Detection in Autonomous Driving With Improved Dimensionality Reduction

Point cloud object detection is a pivotal technology in autonomous driving and robotics. Currently, the majority of cutting-edge point cloud detectors utilize Bird’s Eye View (BEV) for detection, as it allows them to take advantage of well-explored 2D detection techniques. Nevertheless, dimensionality reduction of features from 3D space to BEV space unavoidably leads to information loss, and there is a lack of research on this issue. Existing methods typically obtain BEV features by collapsing voxel or point features along the height dimension via a pooling operation or convolution, resulting in a significant decrease in geometric information. To tackle this problem, we present a new point cloud backbone network for grid-based object detection, MDRNet, which is based on adaptive dimensionality reduction and multi-level spatial residual strategies. In MDRNet, the Spatial-aware Dimensionality Reduction (SDR) is designed to dynamically concentrate on the essential components of the object during 3D-to-BEV transformation. Moreover, the Multi-level Spatial Residuals (MSR) strategy is proposed to effectively fuse multi-level spatial information in BEV feature maps. Our MDRNet can be employed on any existing grid-based object detector, resulting in a remarkable improvement in performance. Numerous experiments conducted on nuScenes, KITTI and DAIR-V have shown that MDRNet surpasses existing SOTA approaches. In particular, on the nuScenes dataset, we attained an impressive 7.2% mAP and 5.0% NDS enhancement compared with CenterPoint.

A strategy combining machine learning and physical metallurgical principles to predict mechanical properties for hot rolled Ti micro-alloyed steels

Determining the exact relationships between rolling parameters and mechanical properties is important to predict and even control the mechanical properties of hot rolled Ti micro-alloyed steel products. In this paper, two data dimension reduction strategies, respectively guided by physical metallurgical (PM) principles and data-driven (DD) strategy were proposed to preprocess the high dimensional steel composition and rolling parameters, and a comprehensive set of machine learning (ML) models was developed to predict yield strength (YS) and elongation (EL) combined with the reconstructed inputs. The artificial neural network (ANN) with the inputs including dislocation density, fractions, and sizes of ferrite and TiC precipitate transferred by PM principle outperformed that with the inputs extracted low variance feature elimination (LVFE) and autoencoder (AE) algorithms. Based on the proposed model, the effects of alloying elements, rolling temperatures, and microstructures on mechanical properties were comprehensively analyzed. Also, the variations of microstructures and mechanical properties over the strip length were discussed, which were consistent with the measured results. • PM-guided dimension reduction was proposed to transfer rolling parameters to microstructures. • The dimension reduction guided by PM performed better than that guided by DD methods with LVFE and AE. • The predicted effects of process and microstructures on YS and EL were consistent with experiments. • The predicted variations of YS and EL over strip length were consistent with measured results.

A dimensionality reduction and layout optimization scheme for grid-stiffened structures

ABSTRACT When directly solving the layout optimization design problem of grid-stiffened structures with large-scale discrete design variables, gradient-based methods and intelligent optimization algorithms are rendered ineffective owing to multilocal optimal traps and the discrete variable space with extremely large dimensionality. A new layout optimization design scheme for grid-stiffened structures is proposed in this study, based on the continuous representation of discrete variables and a dimensionality reduction method. In this method, first, a discrete stiffener layout is described by a bounded field with space correlation and transformed into continuous design variables using material interpolation. Then, to significantly reduce the dimensionality of the design space, a series expansion approach is adopted. Finally, a sequential optimization strategy combined with the kriging surrogate model is used to successfully solve optimization problems. Layout optimization designs, including a stiffened plate and a space-borne antenna reflector, are proposed to demonstrate the validity and applicability of the proposed method.

An efficient method for time-dependent reliability problems with high-dimensional outputs based on adaptive dimension reduction strategy and surrogate model

Time-dependent reliability analysis with high dimensional outputs is a challenge because of ‘curse of dimensionality’ and accurate reliability estimation over entire time interval is computationally expensive. In this paper, an efficient time-dependent reliability analysis method is proposed for systems with high dimensional outputs based on adaptive dimension reduction strategy and Kriging. The adaptive Kriging model is constructed in low-dimensional space after performing principal component analysis (PCA) on original time-dependent output. A new learning function and corresponding stopping criterion are developed as the guideline for selecting training samples at each iteration. The proposed learning function focuses on prediction accuracy over the entire time interval and the stopping criterion is directly linked to failure probability. Subsequently, fewer number of function evaluations is required compared with existing competitive works. Moreover, the key advantage of the proposed method is that it is a single-loop process, i.e., the selection of training samples, dimension reduction and Kriging modeling have been combined simultaneously at each iteration with adaptive manner. However, the existing competitive methods, generally, have two independent stages, i.e., stage one is collecting training samples and stage two is performing PCA and Kriging modelling for time-dependent reliability analysis. Thus, these methods cannot fully utilize the information provided by PCA to find optimal training samples. It is noteworthy that the dimension reduction is also an adaptive process in the proposed method, i.e., dimension reduction changes with the training samples at each iteration. The applicability, accuracy and efficiency of the proposed method are validated through three numerical examples and one engineering example.

An autopsy‐validated, easily deployable MRI predictor of Alzheimer’s disease tau pathology

AbstractBackgroundTau pathology is a hallmark of Alzheimer’s disease, but measuring this pathology in vivo with PET is expensive. MRI represents a low‐cost alternative for measuring in vivo disease progression, but is non‐specific. We present an MR‐based marker of tau‐specific pathology using machine learning (ML).Method1851 pairs of RO948 tau‐PET and T1‐weighted MRI scans were aggregated from 1262 BioFINDER II study participants. The Braak I‐IV ROI from Cho et al., 2016 was used to represent tau‐pathology. A tau‐positive threshold (SUVR=1.41) was defined using Gaussian mixture modeling, and Braak I‐IV SUVR was z‐scored using the mean and SD of the tau‐negative group. A grid search of 80 ML pipelines with 100 rounds of nested 5‐fold cross‐validation was performed while varying estimator, dimension reduction strategy, preregression of intracranial volume (ICV), and one vs multiple scans‐per‐subject. For all models, 294 features from Freesurfer were used. The best‐performing model was then applied to 1225 participants from the ROSMAP cohort, yielding MR‐predicted tau. A subset (n=159) of these participants had postmortem AT8‐immunostained tau pathology, Braak staging, TDP‐43 and lewy body pathology.ResultThe best pipeline involved random forest regression with FDR‐based feature selection (RMSE[95%CI]=3.67[3.6‐3.8]; R2[95%CI]=0.42[0.40‐0.45]; Figure1; Figure2A). (Lack of) ICV pre‐regression had the biggest positive impact across pipelines. This model significantly predicted zTau in both tau‐postive and tau‐negative individuals (Figure2B), and showed fair weighted precision (0.84) and recall (0.80) in tau‐positivity classification (Figure2C). Temporoparietal and medial temporal regions contributed most to predictions (Figure2D). When applied to ROSMAP, antemoretem MR‐predicted tau predicted postmortem tau pathology (p=0.001) and Braak stage (p=0.005; Figure3A) but not other pathologies (Figure3B), predicted clinical diagnosis and progression (Figure3C), and outperformed a common neurodegeneration marker (Figure3D‐F).ConclusionWe create an easily deployable tau‐specific MRI biomarker, which was validated using postmortem tau pathology in a separate dataset. MR‐predicted tau provides a more specific non‐invasive biomarker for researchers without access to PET.

An autopsy‐validated, easily deployable MRI predictor of Alzheimer’s disease tau pathology

AbstractBackgroundTau pathology is a hallmark of Alzheimer’s disease, but measuring this pathology in vivo with PET is expensive. MRI represents a low‐cost alternative for measuring in vivo disease progression, but is non‐specific. We present an MR‐based marker of tau‐specific pathology using machine learning (ML).Method1851 pairs of RO948 tau‐PET and T1‐weighted MRI scans were aggregated from 1262 BioFINDER II study participants. The Braak I‐IV ROI from Cho et al., 2016 was used to represent tau‐pathology. A tau‐positive threshold (SUVR=1.41) was defined using Gaussian mixture modeling, and Braak I‐IV SUVR was z‐scored using the mean and SD of the tau‐negative group. A grid search of 80 ML pipelines with 100 rounds of nested 5‐fold cross‐validation was performed while varying estimator, dimension reduction strategy, preregression of intracranial volume (ICV), and one vs multiple scans‐per‐subject. For all models, 294 features from Freesurfer were used. The best‐performing model was then applied to 1225 participants from the ROSMAP cohort, yielding MR‐predicted tau. A subset (n=159) of these participants had postmortem AT8‐immunostained tau pathology, Braak staging, TDP‐43 and lewy body pathology.ResultThe best pipeline involved random forest regression with FDR‐based feature selection (RMSE[95%CI]=3.67[3.6‐3.8]; R2[95%CI]=0.42[0.40‐0.45]; Figure1; Figure2A). (Lack of) ICV pre‐regression had the biggest positive impact across pipelines. This model significantly predicted zTau in both tau‐postive and tau‐negative individuals (Figure2B), and showed fair weighted precision (0.84) and recall (0.80) in tau‐positivity classification (Figure2C). Temporoparietal and medial temporal regions contributed most to predictions (Figure2D). When applied to ROSMAP, antemoretem MR‐predicted tau predicted postmortem tau pathology (p=0.001) and Braak stage (p=0.005; Figure3A) but not other pathologies (Figure3B), predicted clinical diagnosis and progression (Figure3C), and outperformed a common neurodegeneration marker (Figure3D‐F).ConclusionWe create an easily deployable tau‐specific MRI biomarker, which was validated using postmortem tau pathology in a separate dataset. MR‐predicted tau provides a more specific non‐invasive biomarker for researchers without access to PET.

Envirome-wide associations enhance multi-year genome-based prediction of historical wheat breeding data.

Linking high-throughput environmental data (enviromics) to genomic prediction (GP) is a cost-effective strategy for increasing selection intensity under genotype-by-environment interactions (G × E). This study developed a data-driven approach based on Environment-Phenotype Association (EPA) aimed at recycling important G × E information from historical breeding data. EPA was developed in two applications: (1) scanning a secondary source of genetic variation, weighted from the shared reaction-norms of past-evaluated genotypes and (2) pinpointing weights of the similarity among trial-sites (locations), given the historical impact of each envirotyping data variable for a given site. These results were then used as a dimensionality reduction strategy, integrating historical data to feed multi-environment GP models, which led to the development of four new G × E kernels considering genomics, enviromics, and EPA outcomes. The wheat trial data used included 36 locations, 8 years, and three target populations of environments (TPEs) in India. Four prediction scenarios and six kernel models within/across TPEs were tested. Our results suggest that the conventional GBLUP, without enviromic data or when omitting EPA, is inefficient in predicting the performance of wheat lines in future years. Nevertheless, when EPA was introduced as an intermediary learning step to reduce the dimensionality of the G × E kernels while connecting phenotypic and environmental-wide variation, a significant enhancement of G × E prediction accuracy was evident. EPA revealed that the effect of seasonality makes strategies such as "covariable selection" unfeasible because G × E is year-germplasm specific. We propose that the EPA effectively serves as a "reinforcement learner" algorithm capable of uncovering the effect of seasonality over the reaction-norms, with the benefits of better forecasting the similarities between past and future trialing sites. EPA combines the benefits of dimensionality reduction while reducing the uncertainty of genotype-by-year predictions and increasing the resolution of GP for the genotype-specific level.

Delay-Dependent Distributed Kalman Fusion Estimation With Dimensionality Reduction in Cyber-Physical Systems.

This article studies the distributed dimensionality reduction fusion estimation problem with communication delays for a class of cyber-physical systems (CPSs). The raw measurements are preprocessed in each sink node to obtain the local optimal estimate (LOE) of a CPS, and the compressed LOE under dimensionality reduction encounters with communication delays during the transmission. Under this case, a mathematical model with compensation strategy is proposed to characterize the dimensionality reduction and communication delays. This model also has the property of reducing the information loss caused by the dimensionality reduction and delays. Based on this model, a recursive distributed Kalman fusion estimator (DKFE) is derived by optimal weighted fusion criterion in the linear minimum variance sense. A stability condition for the DKFE, which can be easily verified by the exiting software, is derived. In addition, this condition can guarantee that the estimation error covariance matrix of the DKFE converges to the unique steady-state matrix for any initial values and, thus, the steady-state DKFE (SDKFE) is given. Note that the computational complexity of the SDKFE is much lower than that of the DKFE. Moreover, a probability selection criterion for determining the dimensionality reduction strategy is also presented to guarantee the stability of the DKFE. Two illustrative examples are given to show the advantage and effectiveness of the proposed methods.

Dimensionality reduction strategies for land use land cover classification based on airborne hyperspectral imagery: a survey.

Hyperspectral image (HSI) contains hundreds of adjacent spectral bands, which can effectively differentiate the region of interest. Nevertheless, many irrelevant and highly correlated spectral bands lead to the Hughes phenomenon. Consequently, hyperspectral image dimensionality reduction is necessary to select the most informative and significant spectral band and eliminate the redundant spectral band. To this end, this paper represents an extensive and systematic survey of hyperspectral dimensionality reduction approaches for land use land cover (LULC) classification. Moreover, this paper reviewed the following important points: (1) hyperspectral imaging data acquisition methods, (2) the difference between hyperspectral and multispectral images, (3) hyperspectral image dimensionality reduction based on machine learning (ML) and deep learning (DL) techniques, (4) the popular benchmark hyperspectral datasets with the performance metrics for LULC classification, and (5) the significant challenges with the future trends for hyperspectral dimensionality reduction.

Distributed Dimensionality Reduction Fusion Estimation for Stochastic Uncertain Systems With Fading Measurements Subject to Mixed Attacks

In this article, the distributed fusion estimation issue with the dimensionality reduction strategy under DoS attacks and deception attacks is investigated for a class of stochastic uncertain systems with fading measurements. The stochastic uncertainties existed in the system and measurement equations are represented by state-dependent noises. The fading measurements are depicted by stochastic variables with known statistics. Then, a novel attack and compensation model is proposed to display the randomly occurring behaviors of the DoS attacks and the deception attacks within a unified framework. Furthermore, a distributed multisensor fusion estimation (DMSFE) algorithm is presented. An explicit form of dimensionality reduction is designed against attacks. Stability conditions are derived such that the mean square errors (MSEs) of the proposed DMSFE are bounded. A sequential covariance intersection fusion estimator (SCIFE) is designed to prevent the cross fusion covariance matrices calculating, which owns lower accuracy by smaller computation cost than DMSFE. An illustrative example is provided to show the effectiveness and merits of the proposed algorithm.

Artificial Neural Network for Dimensionality Reduction and Its Application to Microwave Filters Inverse Modeling

The purpose of filters’ inverse modeling is to acquire the values of physical or geometrical parameters for the specified electrical response. In this article, a dimensionality reduction (DR) strategy is proposed through the artificial neural network (ANN) approach, for the first time, to simplify the filters’ inverse modeling. First, all physical/geometrical variables are divided into two parts, partial variables and other ones, through a selection mechanism, and only partial variables are to be determined in the inverse modeling solution. Then, an ANN for DR (DR-ANN) is constructed to form the relationship between partial variables and other ones for given electrical response. Third, the predicted partial variables are set as known input and then run the DR-ANN to acquire the value of remaining variables. The proposed DR-ANN framework can be easily introduced to many existing inverse modeling problems. Specifically, a multivalued neural network approach and a well-known differential evolutional (DE) optimization method are combined with DR-ANN. The improvement of the modified methods is demonstrated with some examples, including coupling matrix extraction and waveguide filter optimization. The experiment results show that the proposed solution is more robust with faster convergence in comparison with existing methods.

Time-efficient surrogate models of thermal modeling in laser powder bed fusion

Two time-efficient surrogate models are proposed to emulate the nonlinear heat equation in the context of laser powder bed fusion, the performance of which is compared in accuracy and online execution time. Fast-computed numerical solvers are critical in implementing the digital twin framework in the additive manufacturing process addressing one of its main open problems: lack of quality assurance. The first surrogate model is the reduced Gaussian process emulator. It is a data-driven model equipped with a nonlinear dimension reduction scheme and manages to predict temperature profiles almost instantly (around 0.036s on average) with an accuracy of 95% for 99.38% of tests. Another surrogate model is the sketched emulator with local projection. It projects the accurate but high-dimensional finite element method solution on a low-dimensional basis and then bypasses the majority of costly computations for the temperature-dependent matrices in the projected model by randomized sketching. It has higher accuracy (97.78% of tests with relative errors below 1%) while spending comparably more time online (around 42.23s on average). Although compared with the finite element model both surrogates promote time efficiency with some minor controlled compromise in accuracy, the reduced Gaussian process emulator enables real-time implementation while the sketched emulator with local projection offers comparably higher levels of accuracy. A series of numerical experiments are carried out, which assumes a three-layer printing process with a fixed laser beam trajectory using a small number of printing control parameters as inputs, namely the laser power, scan speed, and time coordinates. Both surrogates are also principally feasible in other thermal-driven additive manufacturing to obtain better quality assurance with techniques like uncertainty management and closed-loop control.

Geographical traceability of germplasm resources of Paris polyphylla var. yunnanensis based on multi-block information integration platform

Paris polyphylla var. yunnanensis (Franchet) Handel-Mazzetti as a perennial herb has a medicinal history of about 1800 years in China. Therein, the seeds are the core to ensuring the quality of Chinese herbal medicines. Due to the effect of environmental, climatic, and human factors, the quality of germplasm resources and medicinal materials in different geographical is mixed. Therefore, building a convenient platform for quickly detecting geographic information of P. polyphylla var. yunnanensis germplasm resources is crucial. In this study, multi-block information integration technology (MIR and NIR) combined with pattern recognition methods (PLS-DA and SVM) was adopted to investigate and analyzed the 423 seed samples from six geographical locations in Yunnan Province. The results demonstrated that there were variances in spectral information among germplasm resources from diverse geographical origins; The PLS-DA model based on the LVs dimension reduction strategy and the SVM model based on the VIP dimension reduction strategy could successfully distinguish geographic information of P. polyphylla var. yunnanensis germplasm resources. Among them, the best test set accuracy of PLS-DA model is 96.03%, and the F1 score reaches 96.01%. This study provides a novel and rapid method for selecting excellent germplasm resources of P. polyphylla var. yunnanensis, and ensures that the quality of medicinal materials is controlled by the source.

A Malware Detection Scheme via Smart Memory Forensics for Windows Devices

With the introduction of 4G/5G Internet and the increase in the number of users, the malicious cyberattacks on computing devices have been increased making them vulnerable to external threats. High availability windows servers are designed to ensure delivery of consistent services such as business activities and e-services to their customers without any interruption. At the same time, a cyberattack on any of the clustered computer can put servers and customer devices in danger. A memory dump mechanism can capture the contents of memory in the event of a system or device crash such as corrupted files, damaged hardware, or irregular CPU power consumption. In this paper, we present a smart memory forensics scheme to recognize malicious attacks over high availability servers by capturing the memory dump of suspicious processes in the form of RGB visual images. Second, the local and global properties of malware images are captured using local binary patterns (LBP) and gray-level co-occurrence matrices (GLCM). A state-of-the-art t-distributed stochastic neighbor embedding scheme (t-SNE) is applied to reduce data dimensionality and improve the detection time of unknown malwares and their variants. An optimized CNN model is designed to predict malicious files harming servers or user devices. Throughout this study, we employed public data set of 4294 malicious samples covering malware variants and benign executables. A baseline is prepared to compare the performance of proposed model with state-of-the-art malware detection methods. The combined LBP + GLCM feature extraction along with t-SNE dimensionality reduction scheme further improved the detection accuracy by 98%, whereas the detection time is also increased by 73x. The overall performance shows that memory forensics is more effective for malware detection in terms accuracy and response time.

Interval-valued data correlation modeling approach for uncertain nonlinear and non-Gaussian process monitoring

Process monitoring is a crucial part of ensuring the safety and quality of industrial production, and fault detection is a particularly critical step. As a departure from the dimensionality reduction strategy commonly used in fault detection methods, this paper aims to create a statistical model by directly extracting complex correlations among variables with nonlinearity and non-Gaussian properties. Uncertainties in measurement data in an actual process can significantly impact the control decision based on a monitoring model, so interval-valued description strategy is introduced to effectively take the uncertainties into account. Moreover, we improved upon the traditional interval-valued data generation method using moving window technology combine the receiver-operator characteristic curve to construct intervals based on sample mean and standard deviation (SD), which makes full use of the data information. This paper proposes a mean-SD interval vine copula (MSIVC) model for complex industrial process fault detection. The high density region and density quantile theory are introduced to determine the control boundary. The process monitoring performance of the MSIVC method is evaluated by a numerical example and the Tennessee-Eastman process. The results show that the proposed model is stable, sensitive to process faults, and yields effective monitoring results.

Octopus bimaculoides’ arm recruitment and use during visually evoked prey capture

Octopus' limb hyper-redundancy complicates traditional motor control system theory due to its extensive sensory inputs, subsequent decision-making, and arm coordination. Octopuses are thought to reduce flexibility control complexity by relying on highly stereotypical motor primitives (e.g., reaching1,2,3,4 and crawling5) and multi-level processes to coordinate movement,6,7 utilizing extensive peripheral nervous system (PNS) processing.2,8,9 Division of labor along the anterior-posterior axis10 and limb specialization of the four anterior arms in T-maze food retrieval11 further simplify control. However, specific arm recruitment and coordination during visually guided reaching behavior remains poorly understood. Here, we investigated visually evoked Octopus bimaculoides' prey capture capabilities12,13 by eliciting and examining prey-specific arm recruitment. When striking crabs, octopuses preferred synchronous arm recruitment, while sequential arm recruitment with a characteristic swaying movement is employed for shrimp. Such behavioral selection aligns with specific prey escape strategies and the octopus' flexible arm biomechanical constraints. Although side bias existed, we found significant bilateral symmetry, with one side being functionally a mirror of the other rather than anterior arm use being functionally equal and differing to posterior arm use. Among arms, the second limb is unequivocally dominant for goal-directed monocularly driven prey capture. Although the eight arms share gross anatomy and are considered equipotential,10,14 such arm use for specific actions could reflect subtle evolutionary adaptations. Finally, we quantitatively show, corroborating earlier observations,10,15 that octopuses employ a dimension reduction strategy by actively deciding to recruit adjacent arms over other available arms during either sequential or synchronous visually evoked prey attack.

Gaussian process emulation of spatio-temporal outputs of a 2D inland flood model

The computational limitations of complex numerical models have led to adoption of statistical emulators across a variety of problems in science and engineering disciplines to circumvent the high computational costs associated with numerical simulations. In flood modelling, many hydraulic and hydrodynamic numerical models, especially when operating at high spatiotemporal resolutions, have prohibitively high computational costs for tasks requiring the instantaneous generation of very large numbers of simulation results. This study examines the appropriateness and robustness of Gaussian Process (GP) models to emulate the results from a hydraulic inundation model. The developed GPs produce real-time predictions based on the simulation output from LISFLOOD-FP numerical model. An efficient dimensionality reduction scheme is developed to tackle the high dimensionality of the output space and is combined with the GPs to investigate the predictive performance of the proposed emulator for estimation of the inundation depth. The developed GP-based framework is capable of robust and straightforward quantification of the uncertainty associated with the predictions, without requiring additional model evaluations and simulations. Further, this study explores the computational advantages of using a GP-based emulator over alternative methodologies such as neural networks, by undertaking a comparative analysis. For the case study data presented in this paper, the GP model was found to accurately reproduce water depths and inundation extent by classification and produce computational speedups of approximately 10,000 times compared with the original simulator, and 80 times for a neural network-based emulator.

Dimension reduction based adaptive dynamic programming for optimal control of discrete-time nonlinear control-affine systems

Dynamic programming based methods have been widely used in solving discrete-time nonlinear constrained optimal control problems. However, applying these methods in real-time is challenging because a large amount of memory is needed and the associated computational cost is high. Here, a search space dimension reduction strategy is proposed for a class of nonlinear discrete-time systems that are control-affine and invertible. Specifically, a bio-inspired motion rule is combined with inverse dynamics to reduce the value iteration search space to one dimension. The corresponding suboptimal control algorithm is developed and its optimality is analysed. An adaptation rule is developed to estimate uncertainties and improve the base policy. The closed-loop system is proven to be asymptotically stable. The advantages of the algorithm including much smaller computational cost and significantly reduced memory usage are demonstrated with two simulation examples.

An efficient finite element method based on dimension reduction scheme for a fourth-order Steklov eigenvalue problem

AbstractIn this article, an effective finite element method based on dimension reduction scheme is proposed for a fourth-order Steklov eigenvalue problem in a circular domain. By using the Fourier basis function expansion and variable separation technique, the original problem is transformed into a series of radial one-dimensional eigenvalue problems with boundary eigenvalue. Then we introduce essential polar conditions and establish the discrete variational form for each radial one-dimensional eigenvalue problem. Based on the minimax principle and the approximation property of the interpolation operator, we prove the error estimates of approximation eigenvalues. Finally, some numerical experiments are provided, and the numerical results show the efficiency of the proposed algorithm.