相关论文: Neural Operators for Accelerating Scientific Simul…

Neural operators (NOs) are designed to learn maps between infinite-dimensional function spaces. We propose a novel reframing of their use. By introducing an auxiliary base-space, any finite-dimensional function can be viewed as an operator…

Designing mechanically efficient geometry for architectural structures like shells, towers, and bridges, is an expensive iterative process. Existing techniques for solving such inverse problems rely on traditional optimization methods,…

Time domain simulation, i.e., modeling the system's evolution over time, is a crucial tool for studying and enhancing power system stability and dynamic performance. However, these simulations become computationally intractable for…

High-fidelity direct numerical simulation of turbulent flows for most real-world applications remains an outstanding computational challenge. Several machine learning approaches have recently been proposed to alleviate the computational…

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…

Reliability analysis is a formidable task, particularly in systems with a large number of stochastic parameters. Conventional methods for quantifying reliability often rely on extensive simulations or experimental data, which can be costly…

We consider solving a probably infinite dimensional operator equation, where the operator is not modeled by physical laws but is specified indirectly via training pairs of the input-output relation of the operator. Neural operators have…

PDEs arise ubiquitously in science and engineering, where solutions depend on parameters (physical properties, boundary conditions, geometry). Traditional numerical methods require re-solving the PDE for each parameter, making parameter…

The finite element method (FEM) is a well-established numerical method for solving partial differential equations (PDEs). However, its mesh-based nature gives rise to substantial computational costs, especially for complex multiscale…

We integrate neural operators with diffusion models to address the spectral limitations of neural operators in surrogate modeling of turbulent flows. While neural operators offer computational efficiency, they exhibit deficiencies in…

Seismic wave propagation forms the basis for most aspects of seismological research, yet solving the wave equation is a major computational burden that inhibits the progress of research. This is exacerbated by the fact that new simulations…

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.…

Numerical simulation of ordinary differential equations (ODEs) can be challenging when the system exhibits high accelerations and rapidly changing dynamics. Under these conditions the ODE solver often needs to take very small time steps in…

Deep neural networks are an attractive alternative for simulating complex dynamical systems, as in comparison to traditional scientific computing methods, they offer reduced computational costs during inference and can be trained directly…

Long-term, high-fidelity simulation of slow-changing physical systems, such as the ocean and climate, presents a fundamental challenge in scientific computing. Traditional autoregressive machine learning models often fail in these tasks as…

Surrogate models are critical for accelerating computationally expensive simulations in science and engineering, particularly for solving parametric partial differential equations (PDEs). Developing practical surrogate models poses…

The scientific computation methods development in conjunction with artificial intelligence technologies remains a hot research topic. Finding a balance between lightweight and accurate computations is a solid foundation for this direction.…

Modelling complex multiphysics systems governed by nonlinear and strongly coupled partial differential equations (PDEs) is a cornerstone in computational science and engineering. However, it remains a formidable challenge for traditional…

Recently, neural operators have emerged as powerful tools for learning mappings between function spaces, enabling data-driven simulations of complex dynamics. Despite their successes, a deeper understanding of their learning mechanisms…

Numerical solvers for PDEs often struggle to balance computational cost with accuracy, especially in multiscale and time-dependent systems. Neural operators offer a promising way to accelerate simulations, but their practical deployment is…