Input Dimension Research Articles

Multifidelity Methodology for Reduced-Order Models with High-Dimensional Inputs

In the early stages of aerospace design, reduced-order models (ROMs) are crucial for minimizing computational costs associated with using physics-rich field information in many-query scenarios requiring multiple evaluations. The intricacy of aerospace design demands the use of high-dimensional design spaces to capture detailed features and design variability accurately. However, these spaces introduce significant challenges, including the curse of dimensionality, which stems from both high-dimensional inputs and outputs necessitating substantial training data and computational effort. To address these complexities, this study introduces a novel multifidelity, parametric, and nonintrusive ROM framework designed for high-dimensional contexts. It integrates machine learning techniques for manifold alignment and dimension reduction—employing proper orthogonal decomposition and model-based active subspace—with multifidelity regression for ROM construction. Our approach is validated through two test cases: the 2D RAE 2822 airfoil and the 3D NASA CRM wing, assessing various fidelity levels, training data ratios, and sample sizes. Compared to the single-fidelity principal component–active subspace (PCAS) method, our multifidelity solution offers improved cost-accuracy benefits and achieves better predictive accuracy with reduced computational demands. Moreover, our methodology outperforms the manifold-aligned ROM method by 50% in handling scenarios with large input dimensions, underscoring its efficacy in addressing the complex challenges of aerospace design.

Solving high-dimensional parametric engineering problems for inviscid flow around airfoils based on physics-informed neural networks

Engineering problems often involve solving partial differential equations (PDEs) over a range of similar problem setups, leading to high computational costs when using traditional numerical approaches to solve each setup individually. Recently developed physics-informed neural networks (PINNs) offer a novel approach to solving parametric problems, enabling the simultaneous solution of a series of similar problems. Our previous research combined PINNs with mesh transformation to learn PDE solutions in the computational space, effectively solving inviscid flow around airfoils. In this study, we expand the input dimensions of the model to include shape parameters and flow conditions, forming an input encompassing the complete state-space (i.e., all parameters determining the solution are included in the input). We spend about 18.8 h achieving the continuous solutions in a large state-space in one go, encompassing various subsonic inviscid airfoil flows encountered in engineering, thereby highlighting the model's significant advantages in addressing high-dimensional parametric problems. Once established, the model can efficiently complete airfoil flow simulation and shape inverse design tasks in about 1 s. Furthermore, we introduce a pretraining-finetuning method, enabling the fine-tuning of the model for the task of interest and quickly achieving accuracy comparable to the finite volume method.

Convergence, sampling and total order estimator effects on parameter orthogonality in global sensitivity analysis.

Dynamical system models typically involve numerous input parameters whose "effects" and orthogonality need to be quantified through sensitivity analysis, to identify inputs contributing the greatest uncertainty. Whilst prior art has compared total-order estimators' role in recovering "true" effects, assessing their ability to recover robust parameter orthogonality for use in identifiability metrics has not been investigated. In this paper, we perform: (i) an assessment using a different class of numerical models representing the cardiovascular system, (ii) a wider evaluation of sampling methodologies and their interactions with estimators, (iii) an investigation of the consequences of permuting estimators and sampling methodologies on input parameter orthogonality, (iv) a study of sample convergence through resampling, and (v) an assessment of whether positive outcomes are sustained when model input dimensionality increases. Our results indicate that Jansen or Janon estimators display efficient convergence with minimum uncertainty when coupled with Sobol and the lattice rule sampling methods, making them prime choices for calculating parameter orthogonality and influence. This study reveals that global sensitivity analysis is convergence driven. Unconverged indices are subject to error and therefore the true influence or orthogonality of the input parameters are not recovered. This investigation importantly clarifies the interactions of the estimator and the sampling methodology by reducing the associated ambiguities, defining novel practices for modelling in the life sciences.

A spatial–temporal data-driven deep learning framework for enhancing ultra-short-term prediction of distributed photovoltaic power generation

Effective utilization of spatial–temporal information can improve the accuracy of ultra-short-term prediction of power generation from distributed photovoltaic (PV) stations in the region. This paper introduces an ultra-short-term spatial–temporal prediction model for distributed PV power generation, blending data-driven methodology with deep learning technique. The model integrates a self-attention mechanism (SA), a Bi-directional Convolutional Gated Recurrent Unit (BiConvGRU), and an encoder-decoder structure, called ABCGRU. The spatial–temporal attributes of PV power generation can be effectively utilized to accurately predict the output of PV power stations at different locations. Firstly, this paper proposes a 2D distributed PV measurement frame approach considering the spatial–temporal properties of PV power. The combination of Pearson correlation coefficient, the normalized Euclidean distance, the Shape-based distance (SBD) analysis based on cross-correlation and geographic distance reduces the input dimensionality. Secondly, to better capture the spatial–temporal patterns within the 2D distributed PV measurement frame, this paper proposes the ABCGRU model. Finally, the predictive performance of the model is verified through experiments. On the Birmingham dataset, the relative absolute error (RAE) for single-step (15 min) prediction is 0.13, and the average RAE for multi-step (30–60 min) prediction is about four times higher than ConvGRU. The single-step prediction RAE of Little Rock and New Orleans datasets is about 3–4 times higher than ConvGRU. In the comparison between the same series of models, the 4-layer ABCGRU has the highest accuracy. Moreover, the effectiveness of data dimensionality reduction was verified through experimental comparison. The RAE for single-step prediction on the Datong dataset is 0.0048.

Permutation-invariant linear classifiers

Invariant concept classes form the backbone of classification algorithms immune to specific data transformations, ensuring consistent predictions regardless of these alterations. However, this robustness can come at the cost of limited access to the original sample information, potentially impacting generalization performance. This study introduces an addition to these classes—the permutation-invariant linear classifiers. Distinguished by their structural characteristics, permutation-invariant linear classifiers are unaffected by permutations on feature vectors, a property not guaranteed by other non-constant linear classifiers. The study characterizes this new concept class, highlighting its constant capacity, independent of input dimensionality. In practical assessments using linear support vector machines, the permutation-invariant classifiers exhibit superior performance in permutation experiments on artificial datasets and real mutation profiles. Interestingly, they outperform general linear classifiers not only in permutation experiments but also in permutation-free settings, surpassing unconstrained counterparts. Additionally, findings from real mutation profiles support the significance of tumor mutational burden as a biomarker.

Ways and indicators of ensuring the quality of the educational process in educational institutions

Educational institutions, nowadays, are linked to the principles of quality and quality management, which in turn express the essence of education and upbringing, including all its dimensions of inputs, processes, outputs and feedback, as well as continuous interactions that lead to achieving the desired and necessary goals.

Polarization-controlled metasurface design based on deep ResNet

The accuracy of metasurface inverse design depends on the input dimension of the target light field and the output dimension of the unit structure parameters. When the two light field targets are simultaneously controlled, the designed unit structure often cannot satisfy the simultaneous directional control of the two light field target parameters due to the existence of coupling. This greatly limits the completeness of the function of metasurfaces in applications. In this paper, we apply the designed 13-layer residual network (ResNet) to the inverse design of wavefront control of dielectric metasurfaces. After the neural network training is completed, the correspondence between any amplitude, phase and the element structure parameters within a certain error range can be realized, which greatly saves the time cost in the metasurface design process. As a verification of the inverse design method, we arranged two focusing metasurfaces of different sizes. Their focusing efficiencies are more than 53%. The nanounit structure and its inverse design method proposed in this paper provide a new idea for the design of the metasurface to control the polarized light field. At the same time, it will have important applications in the intelligent design of metasurfaces.

Synthetic Benchmark for Data-Driven Pre-Si Analogue Circuit Verification

As the demand for more complex circuits increases, so does the duration of creating and testing them. The most time-consuming task in circuit development is notoriously the verification process, primarily due to the large number of simulations (hundreds or even thousands) required to ensure that the circuits adhere to the specifications regardless of the operating conditions. In order to decrease the number of required simulations, various verification algorithms have been proposed over the years, but this comes with an additional issue: the thorough validation of the algorithms. As simulations on real circuits are significantly time-consuming, synthetic circuits can offer precious insights into the capabilities of the verification algorithm. In this paper, we propose a benchmark of synthetic circuits that can be used to exhaustively validate pre-silicon (Pre-Si) verification algorithms. The newly created benchmark consists of 900 synthetic circuits (mathematical functions) with input dimensions (variables) ranging from 2 to 10. We design the benchmark to include functions of varying complexities, reflecting real-world circuit expectations. Eventually, we use this benchmark to evaluate a previously proposed state-of-the-art Pre-Si circuit verification algorithm. We show that this algorithm generally obtains relative verification errors below 2% with fewer than 150 simulations if the circuits have less than six to seven operating conditions. In addition, we demonstrate that some of the most complex circuits in the benchmark pose serious problems to the verification algorithm: the worst case is not found even when 200 simulations are used.

Research on urban water demand prediction based on machine learning and feature engineering

ABSTRACT Urban water demand prediction is not only the foundation of water resource planning and management, but also an important component of water supply system optimization and scheduling. Therefore, predicting future water demand is of great significance. For univariate time series data, the issue of outliers can be solved through data preprocessing. Then, the data input dimension is increased through feature engineering, and finally, the LightGBM (Light Gradient Boosting Machine) model is used to predict future water demand. The results demonstrate that cubic polynomial interpolation outperforms the Prophet model and the linear method in the context of missing value interpolation tasks. In terms of predicting water demand, the LightGBM model demonstrates excellent forecasting performance and can effectively predict future water demand trends. The evaluation indicators MAPE (mean absolute percentage error) and NSE (Nash–Sutcliffe efficiency coefficient) on the test dataset are 4.28% and 0.94, respectively. These indicators can provide a scientific basis for short-term prediction of water supply enterprises.

Enhancing Arabic Language Learning in Class VIII MTsN 5 Jombang: An Evaluation Using the CIPP Model

This qualitative study used CIPP model to assess Arabic language learning for Class VIII at MTsN 5 Jombang. Data collection was carried out by interviews, observation and documentation. The research respondents consisted of 3 Arabic teachers and 29 students of Class VIII-F, including 15 boys and 14 girls. Analysis of the findings including contextual, input, process and product dimensions. The results show that Arabic learning is enhanced by a supportive environment, good infrastructure, and cultural elements with rich Islamic cultural heritage. The program is supported by a balanced curriculum and well-equipped facilities. However, the curriculum must be updated following the latest national curriculum, Emancipated Curriculum, and teachers must be trained to remain relevant. Constant supervision is required to improve the quality of teaching and student engagement. The results of the evaluation showed that 80% of students met the minimum competency standards. However, more interactive teaching for speaking skills need improvement.

A multi-agent reinforcement learning method for distribution system restoration considering dynamic network reconfiguration

Extreme weather, chain failures, and other events have increased the probability of wide-area blackouts, which highlights the importance of rapidly and efficiently restoring the affected loads. This paper proposes a multi-agent reinforcement learning method for distribution system restoration. Firstly, considering that the topology of the distribution system may change during network reconfiguration, a dynamic agent network (DAN) architecture is designed to address the challenge of input dimensions changing in neural network. Two encoders are created to capture observations of the environment and other agents respectively, and an attention mechanism is used to aggregate an arbitrary-sized neighboring agent feature set. Then, considering the operation constraints of the DSR, an action mask mechanism is implemented to filter out invalid actions, ensuring the security of the strategy. Finally, an IEEE 123-node test system is used for validation, and the experimental results showed that the proposed algorithm can effectively assist agents in accomplishing collaborative DSR tasks.

An Analysis of the Effect of Functional Load on ESL Learners' Perception of Vowel Contrasts

Functional load (FL), which ranks segmental contrasts based on their communicative value in pronunciation, is essential to the development of pronunciation instruction in that it indicates the priority of certain segmental contrasts that may seriously affect the intelligibility and comprehensibility of spoken language for English as a Second Language (ESL) learners. Despite the widespread use of FL in pronunciation pedagogy for ESL learners, there is little evidence on whether FL affects ESL learners perception of vowel contrasts. In this paper, 20 ESL learners from two Chinese universities are selected to participate in two tasks to observe their performance in discriminating vowel contrasts with different FLs in listening and word pronunciation. The effects of functional load on ESL learners perception of vowel contrasts are investigated in terms of both input and output dimensions. The overall findings indicate that high FL vowel contrasts are more likely to be captured in listening and more consciously distinguished in pronunciation, a piece of evidence proving the necessity of applying FL principle to English pronunciation teaching.

An Analysis of the Effect of Functional Load on ESL Learners' Perception of Vowel Contrasts

Functional load (FL), which ranks segmental contrasts based on their communicative value in pronunciation, is essential to the development of pronunciation instruction in that it indicates the priority of certain segmental contrasts that may seriously affect the intelligibility and comprehensibility of spoken language for English as a Second Language (ESL) learners. Despite the widespread use of FL in pronunciation pedagogy for ESL learners, there is little evidence on whether FL affects ESL learners perception of vowel contrasts. In this paper, 20 ESL learners from two Chinese universities are selected to participate in two tasks to observe their performance in discriminating vowel contrasts with different FLs in listening and word pronunciation. The effects of functional load on ESL learners perception of vowel contrasts are investigated in terms of both input and output dimensions. The overall findings indicate that high FL vowel contrasts are more likely to be captured in listening and more consciously distinguished in pronunciation, a piece of evidence proving the necessity of applying FL principle to English pronunciation teaching.

Evaluating the Integration of Islamic Values in Primary Education: A Logic Model Approach

This study examined the acquisition of Islamic values in an Islamic primary school using a logic model-based evaluative approach to assess input, output, and outcome dimensions. The research aimed to evaluate the effectiveness of educational practices in promoting Islamic values among students. Data were gathered through interviews, observation, and documentation, and were analyzed through iterative stages of collection, reduction, display, and conclusion. Findings indicate that the structural input for Islamic values learning involves coordinated efforts among various school departments. The school's cultural climate excels in academic, communal, security, and institutional areas. The output is reflected in diverse activities such as morning murâja’ah sessions, Quran reading and writing guidance using the Ummi method, congregational prayers, and rituals like Clean Friday and Blessed Friday. These activities lead to outcomes that foster individual piety, integrity, discipline, honesty, responsibility, creativity, and social consciousness among students. The study underscores the importance of instilling Islamic values from an early age, highlighting its potential to foster lifelong adherence to these principles. In conclusion, the research affirms the efficacy of these educational practices in transmitting Islamic values, emphasizing the pivotal role of primary education in cultivating a deep-rooted commitment to these values for the future.

PATH-13. LEARNED RESIZING WITH EFFICIENT TRAINING (LRET) FACILITATES IMPROVED PERFORMANCE OF LARGE-SCALE BRAIN TUMOR HISTOLOGY IMAGE CLASSIFICATION MODELS

Abstract BACKGROUND Histologic examination is vital in oncology research and diagnostics. The adoption of digital scanning of whole slide images (WSI) has created an opportunity to leverage deep learning-based image classification methods to enhance diagnosis and risk stratification. However, technical limitations prevent training and deployment of accurate comprehensive multiclass deep convolutional neural networks (DCNN) models for histopathology image classification. The input dimensions of DCNN architectures are small compared to the typical pathologist field of view, degrading performance by excluding important architectural features. Furthermore, data requirements for comprehensive models are sufficiently large to overwhelm the system memory during training. METHODS A method termed Learned Resizing with Efficient Training (LRET) was developed to address the main limitations of traditional histopathology classification model training. The LRET method couples efficient training techniques with image resizing to facilitate seamless integration of larger histology image patches into state-of-the-art classification models while preserving important structural information. The LRET method was coupled with two distinct resizing techniques to train three diverse histology image datasets using five different DCNN architectures. Performance metrics were compared on cross validation and hold out test sets. RESULTS LRET-trained models were flexible to multiple input patch dimensions and DCNN models. We demonstrated performance improvement across all datasets while significantly reducing the training time and resources over traditional methods. Using a large-scale, multiclass brain tumor classification dataset consisting of 74 distinct histopathologic classes, LRET-trained models outperformed existing methods by 15-28% in accuracy, yielding 94% accuracy for the best model. CONCLUSION The LRET method for DCNN training significantly enhances the performance of large-scale multiclass histopathology image classification. The implications of this work extend to broader applications within medical imaging and beyond, where efficient integration of high-resolution images into deep learning pipelines is paramount for driving advancements research and clinical practice.

Management efficiency of Chinese toll road operating companies and influencing factors

This study measured the management efficiency of Chinese toll road operating companies and examined the influencing factors from the internal input and external policy dimensions. The results revealed that the management efficiency of operating companies was low and that listed toll road companies (LTRCs) were generally more efficient than wholly state-owned toll road companies (STRCs). Levels of utilization in different production inputs varied among the operating companies, with LTRCs being better at exploiting the advantages of all production inputs. Macro-industrial policies affected management efficiency by changing the use of production input factors.

SpaDE: Semantic Locality Preserving Biclustering for Neuroimaging Data.

The most discriminative and revealing patterns in the neuroimaging population are often confined to smaller subdivisions of the samples and features. Especially in neuropsychiatric conditions, symptoms are expressed within micro subgroups of individuals and may only underly a subset of neurological mechanisms. As such, running a whole-population analysis yields suboptimal outcomes leading to reduced specificity and interpretability. Biclustering is a potential solution since subject heterogeneity makes one-dimensional clustering less effective in this realm. Yet, high dimensional sparse input space and semantically incoherent grouping of attributes make post hoc analysis challenging. Therefore, we propose a deep neural network called semantic locality preserving auto decoder (SpaDE), for unsupervised feature learning and biclustering. SpaDE produces coherent subgroups of subjects and neural features preserving semantic locality and enhancing neurobiological interpretability. Also, it regularizes for sparsity to improve representation learning. We employ SpaDE on human brain connectome collected from schizophrenia (SZ) and healthy control (HC) subjects. The model outperforms several state-of-the-art biclustering methods. Our method extracts modular neural communities showing significant (HC/SZ) group differences in distinct brain networks including visual, sensorimotor, and subcortical. Moreover, these bi-clustered connectivity substructures exhibit substantial relations with various cognitive measures such as attention, working memory, and visual learning.

Asymptotic generalization errors in the online learning of random feature models

Deep neural networks are widely used prediction algorithms whose performance often improves as the number of weights increases, leading to over-parametrization. We consider a two-layered neural network whose first layer is frozen while the last layer is trainable, known as the random feature model. We study over-parametrization in the context of a student-teacher framework by deriving a set of differential equations for the learning dynamics. For any finite ratio of hidden layer size and input dimension, the student cannot generalize perfectly, and we compute the non-zero asymptotic generalization error. Only when the student's hidden layer size is exponentially larger than the input dimension, an approach to perfect generalization is possible. Published by the American Physical Society 2024

Data-driven learning of structure augments quantitative prediction of biological responses.

Multi-factor screenings are commonly used in diverse applications in medicine and bioengineering, including optimizing combination drug treatments and microbiome engineering. Despite the advances in high-throughput technologies, large-scale experiments typically remain prohibitively expensive. Here we introduce a machine learning platform, structure-augmented regression (SAR), that exploits the intrinsic structure of each biological system to learn a high-accuracy model with minimal data requirement. Under different environmental perturbations, each biological system exhibits a unique, structured phenotypic response. This structure can be learned based on limited data and once learned, can constrain subsequent quantitative predictions. We demonstrate that SAR requires significantly fewer data comparing to other existing machine-learning methods to achieve a high prediction accuracy, first on simulated data, then on experimental data of various systems and input dimensions. We then show how a learned structure can guide effective design of new experiments. Our approach has implications for predictive control of biological systems and an integration of machine learning prediction and experimental design.

Nonparametric Machine Learning for Stochastic Frontier Analysis: A Bayesian Additive Regression Tree Approach

The stochastic frontier model is widely used in economics, finance, and management to estimate the production function and efficiency of a firm or industry. In the current literature of stochastic frontier analysis, parametric forms of production functions, such as Cobb-Douglas and Translog, are often assumed a priori without validation, which may suffer from model misspecification and lead to biased estimates of efficiency. To address this issue, a new set of stochastic frontier models is proposed, namely, 1) monBART-SFM that constructs a monotone-constrained nonparametric production function via an extension of the monotone Bayesian Additive Regression Tree (monBART) framework; 2) softBART-SFM that is built upon softBART, a smooth version of BART, where both models offer greater flexibility in modeling complex and nonlinear production functions that may have high dimensional inputs. The performance of the proposed method is illustrated through simulation studies and a real data application.