相关论文: LNO: Laplace Neural Operator for Solving Different…
The Fourier neural operator (FNO) framework is applied to the large eddy simulation (LES) of three-dimensional compressible Rayleigh-Taylor (RT) turbulence with miscible fluids at Atwood number $A_t=0.5$, stratification parameter $Sr=1.0$,…
Constitutive modeling based on continuum mechanics theory has been a classical approach for modeling the mechanical responses of materials. However, when constitutive laws are unknown or when defects and/or high degrees of heterogeneity are…
We present a Fourier neural network (FNN) that can be mapped directly to the Fourier decomposition. The choice of activation and loss function yields results that replicate a Fourier series expansion closely while preserving a…
We introduce the Z-Domain Neural Operator (ZNO), a causal neural operator whose layers are stable low-rank multiple-input multiple-output (MIMO) rational filters parameterized directly in the $z$-plane. ZNO addresses a limitation of…
Simulating and controlling physical systems described by partial differential equations (PDEs) are crucial tasks across science and engineering. Recently, diffusion generative models have emerged as a competitive class of methods for these…
Simulation tools for photoacoustic wave propagation have played a key role in advancing photoacoustic imaging by providing quantitative and qualitative insights into parameters affecting image quality. Classical methods for numerically…
Traditionally, classical numerical schemes have been employed to solve partial differential equations (PDEs) using computational methods. Recently, neural network-based methods have emerged. Despite these advancements, neural network-based…
Diffusion models have emerged as powerful generative priors for solving PDE-constrained inverse problems. Compared to end-to-end approaches relying on massive paired datasets, explicitly decoupling the prior distribution of physical…
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…
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…
Traditionally, neural networks have been employed to learn the mapping between finite-dimensional Euclidean spaces. However, recent research has opened up new horizons, focusing on the utilization of deep neural networks to learn operators…
Deep neural network models have shown a great potential in accelerating the simulation of fluid dynamic systems. Once trained, these models can make inference within seconds, thus can be extremely efficient. However, they suffer from a…
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…
Neural operators provide fast surrogate models for time-dependent partial differential equations, but their standard autoregressive use usually assumes that the instantaneous field $u(t,\cdot)$ is a complete state. This assumption fails for…
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…
We propose Diffusion Noise Optimization (DNO), a new method that effectively leverages existing motion diffusion models as motion priors for a wide range of motion-related tasks. Instead of training a task-specific diffusion model for each…
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…
Solving complex fluid-structure interaction (FSI) problems, characterized by nonlinear partial differential equations, is crucial in various scientific and engineering applications. Traditional computational fluid dynamics (CFD) solvers are…
Recent advances in the theory of Neural Operators (NOs) have enabled fast and accurate computation of the solutions to complex systems described by partial differential equations (PDEs). Despite their great success, current NO-based…
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…