GAIA introduces a geometry-adaptive integral autoencoder that unifies forward, boundary-value, and inverse PDE operator learning on arbitrary domains via geometry tokens and cross-attention.
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9 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
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Diff-ANO uses conditional consistency models and adjoint neural operator surrogates to enable fast, high-quality USCT reconstructions under sparse and partial views by replacing slow PDE solvers and enabling few-step sampling.
A PINN framework with separate networks for conductivity and potentials, multiscale wavelet excitations, and FFE recovers dominant conductivity structures from finite DtN data with 3-12% relative error on synthetic tests, with FFE aiding sharp features.
A perturbation-based conformal prediction wrapper on Fourier Neural Operators yields narrower uncertainty bands than prior methods for 2D incompressible Navier-Stokes while preserving coverage in data-scarce regimes.
Neptune infers spatiotemporal parameter fields in PDEs from as few as 45 sparse measurements using independent coordinate neural networks, outperforming PINNs and neural operators with lower errors and better extrapolation.
DeepONet learns the operator-to-function map from N-t-D data to conductivities in EIT, supported by a universal approximation theorem and numerical outperformance of IRGN.
MscaleFNO learns mappings from oscillatory media to wavefields for Helmholtz inverse problems and pairs it with diffusion regularization for partial-aperture 2D reconstructions.
A differentiable neural operator learns the mapping from granular microstructure configurations to failure envelopes, with physics-informed convexity enforcement and active learning for efficient training.
A solver-in-the-loop method combines a differentiable neural shape prior with a hard-constrained boundary integral equation solver to reconstruct 3D interfaces in EIT while enforcing the governing elliptic PDE at every step.
citing papers explorer
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GAIA: Geometry-Adaptive Operator Learning for Forward and Inverse Problems
GAIA introduces a geometry-adaptive integral autoencoder that unifies forward, boundary-value, and inverse PDE operator learning on arbitrary domains via geometry tokens and cross-attention.
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Diff-ANO: Towards Fast High-Resolution Ultrasound Computed Tomography via Conditional Consistency Models and Adjoint Neural Operators
Diff-ANO uses conditional consistency models and adjoint neural operator surrogates to enable fast, high-quality USCT reconstructions under sparse and partial views by replacing slow PDE solvers and enabling few-step sampling.
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Recovering Sharp Conductivity Features in the Finite-Data Calder\'on Problem with Physics-Informed Neural Networks
A PINN framework with separate networks for conductivity and potentials, multiscale wavelet excitations, and FFE recovers dominant conductivity structures from finite DtN data with 3-12% relative error on synthetic tests, with FFE aiding sharp features.
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Operator learning for the 2D incompressible Navier-Stokes equations: a conformal prediction approach in the data-scarce regime
A perturbation-based conformal prediction wrapper on Fourier Neural Operators yields narrower uncertainty bands than prior methods for 2D incompressible Navier-Stokes while preserving coverage in data-scarce regimes.
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Estimating Parameter Fields in Multi-Physics PDEs from Scarce Measurements
Neptune infers spatiotemporal parameter fields in PDEs from as few as 45 sparse measurements using independent coordinate neural networks, outperforming PINNs and neural operators with lower errors and better extrapolation.
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A DeepONet for inverting the Neumann-to-Dirichlet Operator in Electrical Impedance Tomography: An approximation theoretic perspective and numerical results
DeepONet learns the operator-to-function map from N-t-D data to conductivities in EIT, supported by a universal approximation theorem and numerical outperformance of IRGN.
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Multiscale Fourier Neural Operator for Inverse Wave Scattering in Highly Oscillatory Media
MscaleFNO learns mappings from oscillatory media to wavefields for Helmholtz inverse problems and pairs it with diffusion regularization for partial-aperture 2D reconstructions.
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Neural Operator Representation of Granular Micromechanics-based Failure Envelope
A differentiable neural operator learns the mapping from granular microstructure configurations to failure envelopes, with physics-informed convexity enforcement and active learning for efficient training.
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Generative Prior-Guided Neural Interface Reconstruction for 3D Electrical Impedance Tomography
A solver-in-the-loop method combines a differentiable neural shape prior with a hard-constrained boundary integral equation solver to reconstruct 3D interfaces in EIT while enforcing the governing elliptic PDE at every step.