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Solving high-dimensional partial differential equations (PDEs) efficiently requires handling multi-scale features across varying resolutions. To address this challenge, we present the Multiwavelet-based Multigrid Neural Operator (M2NO), a…

Partial differential equations (PDEs) govern a wide range of physical phenomena, but their numerical solution remains computationally demanding, especially when repeated simulations are required across many parameter settings. Recent…

Geometry is central to PDE-governed systems, motivating shape optimization and inversion. Classical pipelines conduct costly forward simulation with geometry processing, requiring substantial expert effort. Neural surrogates accelerate…

The challenge of applying learned knowledge from one domain to solve problems in another related but distinct domain, known as transfer learning, is fundamental in operator learning models that solve Partial Differential Equations (PDEs).…

For partial differential equations on domains of arbitrary shapes, existing works of neural operators attempt to learn a mapping from geometries to solutions. It often requires a large dataset of geometry-solution pairs in order to obtain a…

Modeling and simulation of High Power Microwave (HPM) breakdown, a multiscale phenomenon, is computationally expensive and requires solving Maxwell's equations (EM solver) coupled with a plasma continuity equation (plasma solver). In this…

Neural operators have emerged as powerful data-driven surrogates for learning solution operators of parametric partial differential equations (PDEs). However, widely used Fourier Neural Operators (FNOs) rely on global Fourier…

Fourier Neural Operators (FNOs) have been promoted as fast, mesh-invariant surrogates for partial-differential equation solvers, with seismic studies reporting orders-of-magnitude speedup over classical methods. We revisit those claims by…

Learning to solve the Alternating Current Optimal Power Flow (AC-OPF) problem by neural networks (NNs) is a promising approach in real-time applications. Existing methods to ensure the physical feasibility of NN outputs embed a power flow…

This research investigates the application of Multigrid Neural Operator (MgNO), a neural operator architecture inspired by multigrid methods, in the simulation for multiphase flow within porous media. The architecture is adjusted to manage…

Multifunctional metamaterials (MMM) bear promise as next-generation material platforms supporting miniaturization and customization. Despite many proof-of-concept demonstrations and the proliferation of deep learning assisted design, grand…

Fourier Neural Operators are deep learning models that learn mappings between function spaces and can be used to learn and solve partial differential equations (PDEs), in some cases significantly faster than traditional PDE solvers. Within…

In recent years, U-Net and its variants have been widely used in pathology image segmentation tasks. One of the key designs of U-Net is the use of skip connections between the encoder and decoder, which helps to recover detailed information…

We introduce DiffFNO, a novel diffusion framework for arbitrary-scale super-resolution strengthened by a Weighted Fourier Neural Operator (WFNO). Mode Rebalancing in WFNO effectively captures critical frequency components, significantly…

Learning accurate and stable time-advancement operators for nonlinear partial differential equations (PDEs) remains challenging, particularly for chaotic, stiff, and long-horizon dynamical systems. While neural operator methods such as the…

Partial differential equations (PDEs) govern a wide variety of dynamical processes in science and engineering, yet obtaining their numerical solutions often requires high-resolution discretizations and repeated evaluations of complex…

In the pursuit of accurate experimental and computational data while minimizing effort, there is a constant need for high-fidelity results. However, achieving such results often requires significant computational resources. To address this…

Physics-informed operator learning is an attractive candidate for surrogate modeling of microstructures, especially in multiscale finite-element simulations. Its practical use, however, is often limited by the high cost of loss evaluation.…

The modeling and prediction of the ultrafast nonlinear dynamics in the optical fiber are essential for the studies of laser design, experimental optimization, and other fundamental applications. The traditional propagation modeling method…

Accurate urban microclimate analysis with wind velocity and temperature is vital for energy-efficient urban planning, supporting carbon reduction, enhancing public health and comfort, and advancing the low-altitude economy. However,…