An abstract framework for neural flows with composition and separation structures is proven to universally approximate any operator, recovering ResNet and plain architectures via discretization.
Integral representations of S obolev spaces via ReLU k activation function and optimal error estimates for linearized networks
6 Pith papers cite this work. Polarity classification is still indexing.
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2026 6representative citing papers
The training problem for deep linear neural networks under squared loss admits an exact convex reformulation in a lifted space over a generalized completely positive cone, with dimension independent of depth.
Domain-decomposed randomized neural networks assign separate subnetworks to near and far regimes, couple them by interface conditions, and solve only output coefficients from linear least-squares for elliptic, perforated, and time-dependent PDEs on unbounded domains.
Defines Radon-domain L^p ridge integral spaces for ReLU^k networks that recover H^{k+(d+1)/2} at p=2 and sandwich Sobolev spaces otherwise via Seeger-Sogge-Stein loss, giving optimal approximation rates O(n^{-1/2 - (2k+1)/(2d)}) at p=2.
A hybrid FEM and ELM framework for parameter-dependent PDEs derives existence, uniqueness, regularity, and error estimates for inverse problems in photoacoustic tomography.
citing papers explorer
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Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations
An abstract framework for neural flows with composition and separation structures is proven to universally approximate any operator, recovering ResNet and plain architectures via discretization.
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Exact Convex Reformulations of Linear Neural Networks via Completely Positive Lifting
The training problem for deep linear neural networks under squared loss admits an exact convex reformulation in a lifted space over a generalized completely positive cone, with dimension independent of depth.
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Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains
Domain-decomposed randomized neural networks assign separate subnetworks to near and far regimes, couple them by interface conditions, and solve only output coefficients from linear least-squares for elliptic, perforated, and time-dependent PDEs on unbounded domains.
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Sharp Sobolev Sandwich and Approximation Rates of Radon-Domain $L^p$ Ridge Integral Spaces for ReLU$^k$ Networks
Defines Radon-domain L^p ridge integral spaces for ReLU^k networks that recover H^{k+(d+1)/2} at p=2 and sandwich Sobolev spaces otherwise via Seeger-Sogge-Stein loss, giving optimal approximation rates O(n^{-1/2 - (2k+1)/(2d)}) at p=2.
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Solving Inverse Parametrized Problems via Finite Elements and Extreme Learning Networks
A hybrid FEM and ELM framework for parameter-dependent PDEs derives existence, uniqueness, regularity, and error estimates for inverse problems in photoacoustic tomography.
- Adaptive Randomized Neural Networks with Locally Activation Function: Theory and Algorithm for Solving PDEs