arXiv Machine Learning
Jun 30
Learned iterative networks: An operator learning perspective
arXiv:2512. 08444v2 Announce Type: replace-cross Abstract: Learned image reconstruction has become a pillar in computational imaging and inverse problems.
Operator learning for models of tear film breakup
arXiv:2601. 08001v2 Announce Type: replace-cross Abstract: Tear film (TF) breakup is a key driver of understanding dry eye disease, yet estimating TF thickness and osmolarity from fluorescence (FL) imaging typically requires solving computationally expensive inverse problems.
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arXiv Machine Learning
Aug 7
A neural operator view on U-Nets for inverse imaging problems
arXiv:2608. 05839v1 Announce Type: cross Abstract: Deep neural networks have shown great empirical success in the solution of a wide variety of ill-posed inverse problems in imaging.
arXiv Machine Learning
Jun 17
From Theory to Application: A Practical Introduction to Neural Operators in Scientific Computing
arXiv:2503. 05598v2 Announce Type: replace-cross Abstract: This review examines neural operator architectures for learning solution operators of parametric partial differential equations (PDEs), with an emphasis on conceptual clarity and practical implementation.
arXiv Machine Learning
Jun 3
Let There Be Light: Reflection, Refraction and Scattering for Neural Operators
arXiv:2606. 03262v1 Announce Type: new Abstract: Neural operators learn mappings between infinite-dimensional function spaces and provide a data-driven surrogate modeling paradigm for parametric partial differential equations (PDEs).
arXiv Machine Learning
Jun 30
Machine Learning-Augmented Acceleration of Iterative Ptychographic Reconstruction
arXiv:2605. 01122v2 Announce Type: replace Abstract: Iterative ptychographic reconstruction algorithms are widely used for coherent diffractive imaging but can exhibit slow convergence under realistic experimental conditions.
arXiv AI
Jul 29
COMPOL: A Unified Neural Operator Framework for Scalable Multi-Physics Simulations
arXiv:2501. 17296v4 Announce Type: replace-cross Abstract: Multiphysics simulations play an essential role in accurately modeling complex interactions across diverse scientific and engineering domains Although neural operators especially the Fourier Neural Operator FNO have significantly improved computational efficiency they often fail to effectively capture intricate correlations inherent in coupled physical processes To address this limitation we introduce COMPOL a novel coupled multiphysics operator learning framework COMPOL extends conventional operator architectures by incorporating sophisticated recurrent and attentionbased aggregation mechanisms effectively modeling interdependencies among interacting physical processes within latent feature spaces Our approach is architectureagnostic and seamlessly integrates into various neural operator frameworks that involve latent space transformations Extensive experiments on diverse benchmarksincluding biological reactiondiffusion systems patternforming chemical reactions multiphase geological flows and thermohydromechanical processes demonstrate that COMPOL consistently achieves superior predictive accuracy compared to stateoftheart methods.
arXiv Machine Learning
Jun 2
Preconditioned One-Step Generative Modeling for Bayesian Inverse Problems in Function Spaces
arXiv:2603. 14798v2 Announce Type: replace-cross Abstract: We propose a machine-learning algorithm for Bayesian inverse problems in the function-space regime.
arXiv AI
1d ago
A Two-Stage Learning PINN Approach for Solving the Inverse Problem of the 1D Porous Medium Equation
arXiv:2608. 16475v1 Announce Type: cross Abstract: The Porous Medium Equation (PME), given by $u_t = \Delta(u^m)$ for $m > 1$, is a degenerate nonlinear parabolic partial differential equation that arises in various physical applications such as fluid flow in porous media, heat transfer in plasmas, and population dynamics.
arXiv Machine Learning
Jun 18
Starter-Iterator Neural Operator: A Unified Architecture for High-Fidelity Forward and Inverse PDE Problems
arXiv:2606. 18305v1 Announce Type: cross Abstract: Operator learning is an emerging interdisciplinary field that integrates machine learning with scientific computing.
arXiv AI
Jul 15
Deep Learning-based Surrogate Modelling of the LOD Method for Multiscale Problems
arXiv:2607. 12570v1 Announce Type: cross Abstract: Multiscale problems are notoriously difficult to tackle using traditional numerical methods, as accurately resolving fine-scale features often requires prohibitively fine discretizations.
arXiv AI
Jun 3
Physics-informed diffusion models in spectral space
arXiv:2602. 09708v2 Announce Type: replace-cross Abstract: We propose physics-informed spectral diffusion (PISD), a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of partial differential equations (PDEs) conditioned on partial observations, which includes, in particular, forward and inverse PDE problems.
arXiv Machine Learning
Jul 8
A Convex Approximation Framework for Neural Likelihood-Based Bayesian Inverse Problems
arXiv:2607. 06252v1 Announce Type: cross Abstract: Many problems in science and engineering are difficult to model accurately, either due to unknown physical mechanisms, poorly quantified measurement uncertainty, or prohibitive computational costs of high-fidelity simulations.