BelNet: basis enhanced learning, a mesh-free neural operator

Zhang, Zecheng; Wing Tat, Leung; Schaeffer, Hayden

doi:10.1098/rspa.2023.0043

Cited by 7 publications

(2 citation statements)

References 42 publications

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“…Autism Spectrum Disorder (hereafter ASD) is considered a type of syndrome or just autism, a set of developmental disorders and "abnormalities" that can have a substantial impact on a child's ability to interact socially, communicate effectively, and behave appropriately throughout their whole life (Fernandez & Scherer, 2017). Deficits cause prominent disabilities in autistic children, such as their educational life as learning, social life as interaction, daily life functioning such as behaviors, and their professional life as well (Zhang et al, 2023). Autism is a neurodevelopmental condition with biological roots that is defined by "abnormalities" in two key areas: social interaction and communication, as well as limited repetitive patterns of behavior, interests, and activities.…”

Section: Autism Spectrum Disordermentioning

confidence: 99%

Neural Trigger of Speaking Skills in Autistic Children: An Intervention-Based Study

Saram,

Ali,

Mahmood

et al. 2023

J. educ. soc. stud.

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Autism is a pivotal language deficit among speakers all over the globe, and it is a restricting neural process that blocks the simultaneous exponential evolution of language usage; hence, it must be focused with some therapy stimuli. This study is an attempt to channel neural mechanisms underlying autistic children with controlled systemic interventions (CSI). Many previously conducted studies reported that speaking deficit in individuals at all levels reduces neural processing that blocks smooth speaking, and it is due to anatomical and neurophysiological underpinning factors. In this context of autism, anatomical factors are genetic, but neurophysiological can be reversed via controlled systemic intervention (CSI) that is used in this study. For providing neuropsychological reverse, many interventions have been constructed, but this study is only taking Repeat After Me (RAM) as an intervention using computer-assisted. For achieving neural triggers, this study adopts an experimental methodology. Autistic children were recruited via snowball sampling technique, and they are 48 (mean age=2-6 years, boys=28, girls=20). On their willingness to participate in the study, they were divided into two groups: control and experimental. The interventions were provided within six weeks, and the children were assessed via WSSPI-III before the interventions and after the interventions. The overall results of the study predict that in post-assessments, there is a significant satisfactory result. The study implies that 'RAM' should be adopted by parents in home settings and therapists in institutional settings to expedite neural processing that will help boost children's speaking skills with smooth fluency.

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Section: Autism Spectrum Disordermentioning

confidence: 99%

Neural Trigger of Speaking Skills in Autistic Children: An Intervention-Based Study

Saram,

Ali,

Mahmood

et al. 2023

J. educ. soc. stud.

View full text Add to dashboard Cite

show abstract

“…Deep neural networks have emerged as a fast and reliable alternative for solving many scientific problems [1,2]. Recent advancements in hardware and software have made it possible to train extensive neural networks, e.g., physics-informed neural networks [2][3][4], deep operator networks [5][6][7][8][9], and neural operators [10][11][12][13], that accurately estimate and predict complex engineering and physical systems. However, constructing these models requires a large number of data samples for training.…”

Section: Introductionmentioning

confidence: 99%

A Physics-Guided Bi-Fidelity Fourier-Featured Operator Learning Framework for Predicting Time Evolution of Drag and Lift Coefficients

Mollaali,

Sahin,

Raza

et al. 2023

Fluids

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In the pursuit of accurate experimental and computational data while minimizing effort, there is a constant need for high-fidelity results. However, achieving such results often requires significant computational resources. To address this challenge, this paper proposes a deep operator learning-based framework that requires a limited high-fidelity dataset for training. We introduce a novel physics-guided, bi-fidelity, Fourier-featured deep operator network (DeepONet) framework that effectively combines low- and high-fidelity datasets, leveraging the strengths of each. In our methodology, we begin by designing a physics-guided Fourier-featured DeepONet, drawing inspiration from the intrinsic physical behavior of the target solution. Subsequently, we train this network to primarily learn the low-fidelity solution, utilizing an extensive dataset. This process ensures a comprehensive grasp of the foundational solution patterns. Following this foundational learning, the low-fidelity deep operator network’s output is enhanced using a physics-guided Fourier-featured residual deep operator network. This network refines the initial low-fidelity output, achieving the high-fidelity solution by employing a small high-fidelity dataset for training. Notably, in our framework, we employ the Fourier feature network as the trunk network for the DeepONets, given its proficiency in capturing and learning the oscillatory nature of the target solution with high precision. We validate our approach using a well-known 2D benchmark cylinder problem, which aims to predict the time trajectories of lift and drag coefficients. The results highlight that the physics-guided Fourier-featured deep operator network, serving as a foundational building block of our framework, possesses superior predictive capability for the lift and drag coefficients compared to its data-driven counterparts. The bi-fidelity learning framework, built upon the physics-guided Fourier-featured deep operator, accurately forecasts the time trajectories of lift and drag coefficients. A thorough evaluation of the proposed bi-fidelity framework confirms that our approach closely matches the high-fidelity solution, with an error rate under 2%. This confirms the effectiveness and reliability of our framework, particularly given the limited high-fidelity dataset used during training.

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Generalization error guaranteed auto-encoder-based nonlinear model reduction for operator learning

Liu,

Dahal,

Lai

et al. 2025

Applied and Computational Harmonic Analysis

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BelNet: basis enhanced learning, a mesh-free neural operator

Cited by 7 publications

References 42 publications

Neural Trigger of Speaking Skills in Autistic Children: An Intervention-Based Study

Neural Trigger of Speaking Skills in Autistic Children: An Intervention-Based Study

A Physics-Guided Bi-Fidelity Fourier-Featured Operator Learning Framework for Predicting Time Evolution of Drag and Lift Coefficients

Generalization error guaranteed auto-encoder-based nonlinear model reduction for operator learning

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