Search Results - numerical approximation of high-dimensional functions

On Efficient Algorithms for Computing Near-Best Polynomial Approximations to High-Dimensional, Hilbert-Valued Functions From Limited Samples

Authors: Ben Adcock, Simone Brugiapaglia, Nick Dexter, Sebastian Moraga

Resource Type: eBook.

Subjects: Characteristic functions, Approximation theory, Polynomials

Categories: SCIENCE / Physics / Mathematical & Computational

Optimal approximation of infinite-dimensional holomorphic functions II: Recovery from i.i.d. pointwise samples: Optimal approximation of infinite-dimensional holomorphic functions. II: Recovery from i.i.d. pointwise samples

Authors: Adcock, Ben Dexter, Nick Moraga, Sebastian

Source: Journal of Complexity. 89:101933

Subject Terms: pointwise samples, Approximation by polynomials, Complexity and performance of numerical algorithms, 65D40, 41A10, 41A63, 65Y20, 41A25, Multidimensional problems, holomorphic functions, FOS: Mathematics, Numerical approximation of high-dimensional functions, sparse grids, information complexity, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), high-dimensional approximation

File Description: application/xml

Access URL: http://arxiv.org/abs/2310.16940

Near-optimal learning of Banach-valued, high-dimensional functions via deep neural networks

Authors: Ben Adcock Simone Brugiapaglia Nick Dexter et al.

Source: Neural Networks. 181:106761

Subject Terms: uncertainty quantification, 65D40 (Primary) 68T07 (Secondary) 68Q32, Computational learning theory, deep learning, Numerical approximation of high-dimensional functions, sparse grids, Numerical Analysis (math.NA), 01 natural sciences, Banach spaces, Deep Learning, deep neural networks, FOS: Mathematics, Humans, Mathematics - Numerical Analysis, Neural Networks, Computer, high-dimensional approximation, 0101 mathematics, Algorithms, Artificial neural networks and deep learning

File Description: application/xml

Access URL: https://pubmed.ncbi.nlm.nih.gov/39454372
http://arxiv.org/abs/2211.12633
https://zbmath.org/7969537
https://doi.org/10.1016/j.neunet.2024.106761

A practical existence theorem for reduced order models based on convolutional autoencoders

Authors: Franco, Nicola Rares Brugiapaglia, Simone

Source: Foundations of Data Science. 7:72-98

Subject Terms: FOS: Computer and information sciences, Computer Science - Machine Learning, Computer Science - Artificial Intelligence, Numerical approximation of high-dimensional functions, sparse grids, Numerical Analysis (math.NA), Theoretical approximation in context of PDEs, 01 natural sciences, parametrized PDEs, Machine Learning (cs.LG), convolutional autoencoders, Artificial Intelligence (cs.AI), FOS: Mathematics, Mathematics - Numerical Analysis, 0101 mathematics, approximation theory, reduced order modeling, Artificial neural networks and deep learning, neural network training

File Description: application/xml

Access URL: http://arxiv.org/abs/2402.00435

Numerical approximation based on deep convolutional neural network for high‐dimensional fully nonlinear merged PDEs and 2BSDEs

Authors: Xu Xiao Wenlin Qiu Omid Nikan

Source: Mathematical Methods in the Applied Sciences. 47:6184-6204

Subject Terms: 65M22, 60H15, 65C30, 68T07, FOS: Mathematics, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), 0101 mathematics, 01 natural sciences

Access URL: http://arxiv.org/abs/2209.04997

POLYNOMIAL APPROXIMATION VIA COMPRESSED SENSING OF HIGH-DIMENSIONAL FUNCTIONS ON LOWER SETS

Authors: CHKIFA, ABDELLAH DEXTER, NICK TRAN, HOANG et al.

Source: Mathematics of Computation, 2018 May 01. 87(311), 1415-1450.

Access URL: https://www.jstor.org/stable/90019418

Multilevel Picard approximations overcome the curse of dimensionality in the numerical approximation of general semilinear PDEs with gradient-dependent nonlinearities

Authors: Neufeld, Ariel Nguyen, Tuan Anh Wu, Sizhou

Source: Journal of Complexity. 90:101946

Subject Terms: Gradient-dependent nonlinearity, High-dimensional nonlinear PDEs, Probability (math.PR), Numerical Analysis (math.NA), Feynman-Kac representation, methods, Mathematics - Analysis of PDEs, FOS: Mathematics, Mathematics - Numerical Analysis, Multilevel Picard approximation, Monte Carlo, Complexity analysis, Mathematics - Probability, Analysis of PDEs (math.AP)

Access URL: http://arxiv.org/abs/2311.11579

An iterative method for the solution of Laplace-like equations in high and very high space dimensions

Authors: Yserentant, Harry

Source: Numerische Mathematik. 156:777-811

Subject Terms: convergence, boundary value problems, 500 Naturwissenschaften und Mathematik::510 Mathematik::510 Mathematik, Numerical Analysis (math.NA), stability, numerical approximation of high-dimensional functions, multidimensional problems, 01 natural sciences, 41A46, 41A63, 65D40, 65N12, numerical methods, FOS: Mathematics, approximation by arbitrary nonlinear expressions, Mathematics - Numerical Analysis, 0101 mathematics, PDEs

Access URL: http://arxiv.org/abs/2403.00682

Physics-based linear regression for high-dimensional forward uncertainty quantification

Authors: Ziqi Wang

Source: Journal of Computational Physics. 523:113668

Subject Terms: physics-based surrogate modeling, uncertainty quantification, Physics - Data Analysis, Statistics and Probability, FOS: Physical sciences, Numerical approximation of high-dimensional functions, sparse grids, high-dimensional regression, Data Analysis, Statistics and Probability (physics.data-an), Probabilistic models, generic numerical methods in probability and statistics

File Description: application/xml; application/pdf

Access URL: http://arxiv.org/abs/2405.08006
https://zbmath.org/7986890
https://doi.org/10.1016/j.jcp.2024.113668
https://escholarship.org/uc/item/3kz3g18j

Optimal evaluation of symmetry-adapted n-correlations via recursive contraction of sparse symmetric tensors: Optimal evaluation of symmetry-adapted \(n\)-correlations via recursive contraction of sparse symmetric tensors

Authors: Kaliuzhnyi, Illia Ortner, Christoph

Source: Journal of Numerical Mathematics. 33:87-104

Subject Terms: many-body interaction, Measures of association (correlation, canonical correlation, etc.), Multilinear algebra, tensor calculus, 0103 physical sciences, symmetric tensors, FOS: Mathematics, Numerical approximation of high-dimensional functions, sparse grids, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), 01 natural sciences, cluster expansion

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Access URL: http://arxiv.org/abs/2202.04140

Interval type-2 fuzzy systems on the basis of vague partitions and their approximation properties

Authors: Peng, Xiaoyu Pan, Xiaodong

Source: Computational and Applied Mathematics. 43

Subject Terms: overlap function, Fuzzy control/observation systems, universal approximation, Numerical approximation of high-dimensional functions, sparse grids, vague partition, approximation accuracy, interval type-2 fuzzy system

File Description: application/xml

Access URL: https://zbmath.org/7846885
https://doi.org/10.1007/s40314-024-02629-2

An iterative method for the solution of Laplace-like equations in high and very high space dimensions

Authors: Yserentant, Harry

Subject Terms: 500 Naturwissenschaften und Mathematik::510 Mathematik::510 Mathematik, approximation by arbitrary nonlinear expressions, multidimensional problems, numerical approximation of high-dimensional functions, stability, numerical methods, PDEs, boundary value problems, convergence

File Description: application/pdf

Availability: https://depositonce.tu-berlin.de/handle/11303/23801
https://doi.org/10.14279/depositonce-22614

Numerical approximation based on deep convolutional neural network for high-dimensional fully nonlinear merged PDEs and 2BSDEs

Authors: Xiao, Xu Qiu, Wenlin Nikan, Omid

Index Terms: Mathematics - Numerical Analysis, 65M22, 60H15, 65C30, 68T07, text

URL: http://arxiv.org/abs/2209.04997

Robust Feedback Control of Nonlinear PDEs by Numerical Approximation of High-Dimensional Hamilton--Jacobi--Isaacs Equations

Authors: Kalise, Dante Kundu, Sudeep Kunisch, Karl

Source: SIAM Journal on Applied Dynamical Systems

Subject Terms: 0209 industrial biotechnology, Optimization and Control (math.OC), FOS: Mathematics, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), 02 engineering and technology, 49J20, 49L20, 49N35, 93B52, 93B36, 0101 mathematics, Mathematics - Optimization and Control, 01 natural sciences

Access URL: https://nottingham-repository.worktribe.com/preview/4425261/final_siads_03_20.pdf
http://arxiv.org/abs/1905.06276
https://arxiv.org/pdf/1905.06276
https://dblp.uni-trier.de/db/journals/siamads/siamads19.html#KaliseKK20
https://epubs.siam.org/doi/abs/10.1137/19M1262139
https://ui.adsabs.harvard.edu/abs/2019arXiv190506276K/abstract
https://www.arxiv-vanity.com/papers/1905.06276/

IB-UQ: Information bottleneck based uncertainty quantification for neural function regression and neural operator learning: IB-UQ: information bottleneck based uncertainty quantification for neural function regression and neural operator learning

Authors: Ling Guo Hao Wu Yan Wang et al.

Source: Journal of Computational Physics. 510:113089

Subject Terms: FOS: Computer and information sciences, Numerical optimization and variational techniques, Computer Science - Machine Learning, uncertainty quantification, information bottleneck, Numerical approximation of high-dimensional functions, sparse grids, Monte Carlo methods, 02 engineering and technology, Numerical Analysis (math.NA), Machine Learning (cs.LG), operator learning, deep neural networks, 13. Climate action, 0202 electrical engineering, electronic engineering, information engineering, FOS: Mathematics, Mathematics - Numerical Analysis, Artificial neural networks and deep learning

File Description: application/xml

Access URL: http://arxiv.org/abs/2302.03271
https://zbmath.org/8021047
https://doi.org/10.1016/j.jcp.2024.113089

Dynamic, Bifurcation, and Lyapunov Analysis of Fractional Rössler Chaos Using Two Numerical Methods.

Authors: Allogmany, Reem Alzahrani, S. S.

Source: Mathematics (2227-7390); Nov2025, Vol. 13 Issue 22, p3642, 19p

Subject Terms: BIFURCATION theory, LYAPUNOV functions, SENSITIVITY analysis, SYSTEM dynamics, NUMERICAL analysis, ITERATIVE methods (Mathematics)

SPARSE SPECTRAL APPROXIMATIONS OF HIGH-DIMENSIONAL PROBLEMS BASED ON HYPERBOLIC CROSS

Authors: SHEN, JIE WANG, LI-LIAN

Source: SIAM Journal on Numerical Analysis, 2010 Jan 01. 48(3), 1087-1109.

Access URL: https://www.jstor.org/stable/41062634

Operator learning with Gaussian processes

Authors: Carlos Mora Amin Yousefpour Shirin Hosseinmardi et al.

Source: Computer Methods in Applied Mechanics and Engineering. 434:117581

Subject Terms: FOS: Computer and information sciences, Computer Science - Machine Learning, Applications of functional analysis in optimization, convex analysis, mathematical programming, economics, Gaussian processes, Numerical approximation of high-dimensional functions, sparse grids, neural operators, Machine Learning (stat.ML), Machine Learning (cs.LG), operator learning, KdV equations (Korteweg-de Vries equations), Statistics - Machine Learning, Initial-boundary value problems for second-order parabolic equations, optimal recovery, Nonparametric regression and quantile regression, zero-shot learning, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs, Artificial neural networks and deep learning

File Description: application/xml

Access URL: http://arxiv.org/abs/2409.04538
https://zbmath.org/7972888
https://doi.org/10.1016/j.cma.2024.117581

Polytopic autoencoders with smooth clustering for reduced-order modeling of flows

Authors: Jan Heiland Yongho Kim

Source: submitted to Journal of Computational Physics

Subject Terms: polytopic LPV system, FOS: Computer and information sciences, Computer Science - Machine Learning, Computer Vision and Pattern Recognition (cs.CV), Computer Science - Computer Vision and Pattern Recognition, Numerical approximation of high-dimensional functions, sparse grids, Dynamical Systems (math.DS), Numerical methods for initial value problems involving ordinary differential equations, Machine Learning (cs.LG), convolutional autoencoders, model order reduction, Numerical methods for matrix equations, convex polytope, FOS: Mathematics, linear parameter-varying (LPV) systems, Mathematics - Dynamical Systems, Artificial neural networks and deep learning, clustering

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Access URL: http://arxiv.org/abs/2401.10620
https://zbmath.org/7974271
https://doi.org/10.1016/j.jcp.2024.113526
http://hdl.handle.net/21.11116/0000-000E-464D-E
http://hdl.handle.net/21.11116/0000-000E-464B-0

On Some Numerical Integration Formulas on the d-Dimensional Simplex

Authors: Filomena Di Tommaso Benaissa Zerroudi

Source: Mediterranean Journal of Mathematics. 17

Subject Terms: Financial economics, Economics, General Mathematics, Quadrature Formulas, Evolutionary biology, Quadrature (astronomy), Mathematical analysis, 01 natural sciences, Orthogonal Polynomials, Convergence Analysis of Iterative Methods for Nonlinear Equations, Numerical integration, Cubature, Simplex, High-dimensional Integration and Quasi-Monte Carlo Methods, FOS: Mathematics, 0101 mathematics, Approximation, Biology, Numerical Analysis, Numerical approximation, Applied Mathematics, Simplex, Physics, 4. Education, Optics, 16. Peace & justice, High-dimensional Integration, Quadrature Methods, Function (biology), Boundary (topology), Combinatorics, Derivative (finance), Physical Sciences, Numerical integration, Numerical Integration, Mathematics, Numerical analysis

Access URL: https://link.springer.com/content/pdf/10.1007/s00009-020-01579-3.pdf
https://iris.unical.it/handle/20.500.11770/306892
https://link.springer.com/content/pdf/10.1007/s00009-020-01579-3.pdf
https://link.springer.com/article/10.1007/s00009-020-01579-3
https://www.openaccessrepository.it/record/79593