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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12 Pith papers cite this work. Polarity classification is still indexing.
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2026 12representative citing papers
Function graph transformers use graph measures to provide a measure-theoretic framework where standard transformer components universally approximate operators between function spaces while preserving single-valued function outputs.
Small FNOs are piecewise-linear and can be encoded exactly into Z3 for sound proofs and counterexamples on positivity and mass properties, exposing a clear soundness-scalability tradeoff.
FLUIDSPLAT models flow fields with K anisotropic Gaussian primitives, proves an O(K^{-s/d}) approximation rate under Sobolev smoothness s, derives optimal K scaling with N sensors, and reports 11-28% error reduction on four flow benchmarks.
A hypernetwork conditions a conservative-form CNN to predict WENO5 weights from mesh and initial-condition metadata, preserving conservation and generalizing across resolutions for 1D hyperbolic conservation laws.
ACT blocks enable neural operators to learn adaptive coordinate systems via differentiable sampling, yielding consistent accuracy gains on PDE benchmarks by reducing spatial misalignment and operator complexity.
Neural operators reframed via an auxiliary base-space act as efficient interpolators for finite-dimensional functions, matching or exceeding MLPs and KANs in accuracy with fewer parameters on analytic benchmarks and achieving 198 keV RMSE on nuclear mass corrections.
Adversarial optimal transport objectives jointly learn summary statistics and a chaotic-system emulator from a single noisy trajectory, improving long-term statistical fidelity over handcrafted-feature baselines.
LASER couples a latent world model with a GRPO-trained RL policy to adaptively reposition sensors for sparse continuum field reconstruction, outperforming fixed and offline-optimized placement strategies across PDE and real-world benchmarks.
Derives discretization error bounds and input-to-state stability guarantees for SS-NOs and FNOs, with empirical validation on 1D and 2D PDE benchmarks.
A constrained hypothesis-class framework for identifying mesoscopic dynamics from data, backed by uniform well-posedness and stability guarantees derived from a generalized Onsager principle.
A differentiable chemistry solver is added to PINNs along with parameterized network architecture and stiffness-tailored residual weighting to solve initial/boundary value problems, inverse parameter identification, and parameterized PDEs for hydrogen combustion.
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.
-
Function graph transformers universally approximate operators between function spaces
Function graph transformers use graph measures to provide a measure-theoretic framework where standard transformer components universally approximate operators between function spaces while preserving single-valued function outputs.
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Can We Formally Verify Neural PDE Surrogates? SMT Compilation of Small Fourier Neural Operators
Small FNOs are piecewise-linear and can be encoded exactly into Z3 for sound proofs and counterexamples on positivity and mass properties, exposing a clear soundness-scalability tradeoff.
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FLUIDSPLAT: Reconstructing Physical Fields from Sparse Sensors via Gaussian Primitives
FLUIDSPLAT models flow fields with K anisotropic Gaussian primitives, proves an O(K^{-s/d}) approximation rate under Sobolev smoothness s, derives optimal K scaling with N sensors, and reports 11-28% error reduction on four flow benchmarks.
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Hypernetwork-Conditioned WENO5 Conservative-Form CNNs for One-Dimensional Conservation Laws
A hypernetwork conditions a conservative-form CNN to predict WENO5 weights from mesh and initial-condition metadata, preserving conservation and generalizing across resolutions for 1D hyperbolic conservation laws.
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Adaptive Coordinate Transforms for Neural Operators
ACT blocks enable neural operators to learn adaptive coordinate systems via differentiable sampling, yielding consistent accuracy gains on PDE benchmarks by reducing spatial misalignment and operator complexity.
-
Neural Operators as Efficient Function Interpolators
Neural operators reframed via an auxiliary base-space act as efficient interpolators for finite-dimensional functions, matching or exceeding MLPs and KANs in accuracy with fewer parameters on analytic benchmarks and achieving 198 keV RMSE on nuclear mass corrections.
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Learning to Emulate Chaos: Adversarial Optimal Transport Regularization
Adversarial optimal transport objectives jointly learn summary statistics and a chaotic-system emulator from a single noisy trajectory, improving long-term statistical fidelity over handcrafted-feature baselines.
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LASER: Learning Active Sensing for Continuum Field Reconstruction
LASER couples a latent world model with a GRPO-trained RL policy to adaptively reposition sensors for sparse continuum field reconstruction, outperforming fixed and offline-optimized placement strategies across PDE and real-world benchmarks.
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Stability and Discretization Error of State Space Model Neural Operators
Derives discretization error bounds and input-to-state stability guarantees for SS-NOs and FNOs, with empirical validation on 1D and 2D PDE benchmarks.
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Hypothesis-driven construction of mesoscopic dynamics
A constrained hypothesis-class framework for identifying mesoscopic dynamics from data, backed by uniform well-posedness and stability guarantees derived from a generalized Onsager principle.
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Differentiable Chemistry in PINNs for Solving Parameterized and Stiff Reaction Systems
A differentiable chemistry solver is added to PINNs along with parameterized network architecture and stiffness-tailored residual weighting to solve initial/boundary value problems, inverse parameter identification, and parameterized PDEs for hydrogen combustion.