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Predicting the microstructural and morphological evolution of materials through phase-field modelling is computationally intensive, particularly for high-throughput parametric studies. While neural operators such as the Fourier neural…

Partial differential equations (PDEs) are central to describing complex physical system simulations. Their expensive solution techniques have led to an increased interest in deep neural network based surrogates. However, the practical…

Dirichlet-Neumann Operators (DNOs) are important to the formulation, analysis, and simulation of many crucial models found in engineering and the sciences. For instance, these operators permit moving-boundary problems, such as the classical…

Neural operators serve as fast, data-driven surrogates for scientific modeling but typically rely on a monolithic, single-pass inference procedure that struggles to resolve high-frequency details, a limitation known as spectral bias. We…

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…

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…

Partial differential equations (PDEs) underpin quantitative descriptions across the physical sciences and engineering, yet high-fidelity simulation remains a major computational bottleneck for many-query, real-time, and design tasks.…

We present an end-to-end framework to learn partial differential equations that brings together initial data production, selection of boundary conditions, and the use of physics-informed neural operators to solve partial differential…

Physics-Informed Neural Operators provide efficient, high-fidelity simulations for systems governed by partial differential equations (PDEs). However, most existing studies focus only on multi-scale, multi-physics systems within a single…

Neural operators have emerged as powerful tools for learning mappings between function spaces, enabling efficient solutions to partial differential equations across varying inputs and domains. Despite the success, existing methods often…

The weighted essentially non-oscillatory (WENO) schemes are a popular class of high order accurate numerical methods for solving hyperbolic partial differential equations (PDEs). However when the spatial dimensions are high, the number of…

Partial differential equations (PDEs) are fundamental to modeling complex and nonlinear physical phenomena, but their numerical solution often requires significant computational resources, particularly when a large number of forward full…

Neural operators have achieved strong performance in learning solution operators of partial differential equations (PDEs), but their inherently continuous representations struggle to capture discontinuities and sharp transitions. Existing…

Engineering problems frequently require solution of governing equations with spatially-varying discontinuous coefficients. Even for linear elliptic problems, mapping large ensembles of coefficient fields to solutions can become a major…

This paper proposes a physics-informed neural operator (PINO) framework for solving inverse scattering problems, enabling rapid and accurate reconstructions under diverse measurement conditions. In the proposed approach, the dielectric…

Discovering hidden physical laws and identifying governing system parameters from sparse observations are central challenges in computational science and engineering. Existing data-driven methods, such as physics-informed neural networks…

Fourier Neural Operators (FNOs) excel on tasks using functional data, such as those originating from partial differential equations. Such characteristics render them an effective approach for simulating the time evolution of quantum…

Laplace Neural Operators (LNOs) have recently emerged as a promising approach in scientific machine learning due to the ability to learn nonlinear maps between functional spaces. However, this framework often requires substantial amounts of…

In recent years, deep learning for modeling physical phenomena which can be described by partial differential equations (PDEs) have received significant attention. For example, for learning Hamiltonian mechanics, methods based on deep…

Accurate modeling of spatiotemporal dynamics is crucial to understanding complex phenomena across science and engineering. However, this task faces a fundamental challenge when the governing equations are unknown and observational data are…