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We introduce SONO, a novel method leveraging Second-Order Neural Ordinary Differential Equations (Second-Order NODEs) to enhance cross-modal few-shot learning. By employing a simple yet effective architecture consisting of a Second-Order…

Driven by rapid advances in artificial intelligence and modern GPU computing capabilities, deep learning methods based on the optimization paradigm have provided new pathways to solve spatiotemporal physical problems, whose mathematical…

Memory complexity and data scarcity have so far prohibited learning solution operators of partial differential equations (PDEs) at high resolutions. We address these limitations by introducing a new data efficient and highly parallelizable…

Neural Operators offer a powerful, data-driven tool for solving parametric PDEs as they can represent maps between infinite-dimensional function spaces. In this work, we employ physics-informed Neural Operators in the context of…

The numerical solution of partial differential equations (PDEs) is fundamental to scientific and engineering computing. In the presence of strong anisotropy, material heterogeneity, and complex geometries, however, classical iterative…

Machine-learning-based surrogate models offer significant computational efficiency and faster simulations compared to traditional numerical methods, especially for problems requiring repeated evaluations of partial differential equations.…

Neural operators for time-dependent PDEs face a structural tension: spectral architectures (FNO and descendants) inherit exponential rollout-error growth from their one-step Lipschitz constant, while hierarchical U-Net operators trade…

Classical sequential models employed in time-series prediction rely on learning the mappings from the past to the future instances by way of a hidden state. The Hidden states characterise the historical information and encode the required…

Neural operators have emerged as powerful tools for learning solution operators of partial differential equations. However, in time-dependent problems, standard training strategies such as teacher forcing introduce a mismatch between…

Learning maps between function spaces with a strong inductive bias is a central challenge in soft computing, especially when training data are scarce and standard deep architectures overfit. We introduce a \emph{neural integral operator}…

Thrombosis involves processes spanning large-scale fluid flow to sub-cellular events such as platelet activation. Traditional CFD approaches often treat blood as a continuum, which can limit their ability to capture these microscale…

Learning PDE dynamics from limited data with unknown physics is challenging. Existing neural PDE solvers either require large datasets or rely on known physics (e.g., PDE residuals or handcrafted stencils), leading to limited applicability.…

Learning partial differential equations' (PDEs) solution operators is an essential problem in machine learning. However, there are several challenges for learning operators in practical applications like the irregular mesh, multiple input…

Pretraining methods gain increasing attraction recently for solving PDEs with neural operators. It alleviates the data scarcity problem encountered by neural operator learning when solving single PDE via training on large-scale datasets…

The UNet-enhanced Fourier Neural Operator (UFNO) extends the Fourier Neural Operator (FNO) by incorporating a parallel UNet pathway, enabling the retention of both high- and low-frequency components. While UFNO improves predictive accuracy…

Surrogate modeling of wave propagation and scattering (i.e. the wave speed and source to wave field map) in heterogeneous media has significant potential in applications such as seismic imaging and inversion. High-contrast settings, such as…

The purpose of the current work is the development of a so-called physics-encoded Fourier neural operator (PeFNO) for surrogate modeling of the quasi-static equilibrium stress field in solids. Rather than accounting for constraints from…

Shape optimization under uncertainty (OUU) is computationally intensive for classical PDE-based methods due to the high cost of repeated sampling-based risk evaluation across many uncertainty realizations and varying geometries, while…

The recent development of Neural Operator (NeurOp) learning for solutions to the elastic wave equation shows promising results and provides the basis for fast large-scale simulations for different seismological applications. In this paper,…

We propose Super-resolution Neural Operator (SRNO), a deep operator learning framework that can resolve high-resolution (HR) images at arbitrary scales from the low-resolution (LR) counterparts. Treating the LR-HR image pairs as continuous…