Search Results - "Numerical approximation of high-dimensional functions"

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

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

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

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

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

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

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

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

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

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

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

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

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

Reduced-order modeling on a near-term quantum computer

Authors: Katherine Asztalos René Steijl Romit Maulik

Source: Journal of Computational Physics. 510:113070

Subject Terms: Fluid Dynamics (physics.flu-dyn), FOS: Physical sciences, Numerical approximation of high-dimensional functions, sparse grids, fluid dynamics, Physics - Fluid Dynamics, Dynamical Systems (math.DS), Computational Physics (physics.comp-ph), Numerical methods for initial value problems involving ordinary differential equations, 01 natural sciences, quantum computing, reduced-order modeling, Quantum computation, 0103 physical sciences, FOS: Mathematics, dynamic mode decomposition, Mathematics - Dynamical Systems, Physics - Computational Physics, vortex-dominated flows

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Access URL: http://arxiv.org/abs/2306.08087

Geometrically parametrised reduced order models for studying the hysteresis of the Coanda effect in finite element-based incompressible fluid dynamics

Authors: Bravo Martínez, José Raúl Stabile, Giovanni Hess, Martin et al.

Contributors: Bravo Martínez, José Raúl Stabile, Giovanni Hess, Martin et al.

Source: UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)
Journal of Computational Physics

Subject Terms: Hysteresis, ECM hyper-reduction, Proper Orthogonal Decomposition, Fluid Dynamics (physics.flu-dyn), FOS: Physical sciences, Numerical approximation of high-dimensional functions, sparse grids, Geometric Parametrisation, ECM Hyper-reduction, Physics - Fluid Dynamics, Àrees temàtiques de la UPC::Física::Física de fluids, proper orthogonal decomposition, Coanda effect, hysteresis, Coanda Effect, geometric parametrisation, Mecànica de fluids, Fluid mechanics, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Finite element methods applied to problems in fluid mechanics, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

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Access URL: http://arxiv.org/abs/2307.05227
https://hdl.handle.net/2117/407508
https://doi.org/10.1016/j.jcp.2024.113058
https://hdl.handle.net/11382/565853
https://doi.org/10.1016/j.jcp.2024.113058

A Physics and Data Co-Driven Surrogate Modeling Method for High-Dimensional Rare Event Simulation: A physics and data co-driven surrogate modeling method for high-dimensional rare event simulation

Authors: Jianhua Xian Ziqi Wang

Source: Journal of Computational Physics. 510:113069

Subject Terms: FOS: Computer and information sciences, Numerical optimization and variational techniques, uncertainty quantification, Numerical approximation of high-dimensional functions, sparse grids, Statistics - Computation, Statistics - Applications, surrogate modeling, Probabilistic models, generic numerical methods in probability and statistics, rare event simulation, importance sampling, high-dimensional, active learning, Applications (stat.AP), Computation (stat.CO)

File Description: application/xml

Access URL: http://arxiv.org/abs/2310.00261
https://zbmath.org/8021035
https://doi.org/10.1016/j.jcp.2024.113069