相关论文: Time Marching Neural Operator FE Coupling: AI Acce…

Finite element (FE) modeling is essential for structural analysis but remains computationally intensive, especially under dynamic loading. While operator learning models have shown promise in replicating static structural responses at FEM…

Traditional numerical schemes for simulating fluid flow and transport in porous media can be computationally expensive. Advances in machine learning for scientific computing have the potential to help speed up the simulation time in many…

We consider solving complex spatiotemporal dynamical systems governed by partial differential equations (PDEs) using frequency domain-based discrete learning approaches, such as Fourier neural operators. Despite their widespread use for…

Neural operators aim to learn mappings between infinite-dimensional function spaces, but their performance often degrades on complex or irregular geometries due to the lack of geometry-aware representations. We propose the Finite Element…

Simulators based on neural networks offer a path to orders-of-magnitude faster electromagnetic wave simulations. Existing models, however, only address narrowly tailored classes of problems and only scale to systems of a few dozen degrees…

Herein, we present a new data-driven multiscale framework called FE${}^\text{ANN}$ which is based on two main keystones: the usage of physics-constrained artificial neural networks (ANNs) as macroscopic surrogate models and an autonomous…

Accurately learning solution operators for time-dependent partial differential equations (PDEs) from sparse and irregular data remains a challenging task. Recurrent DeepONet extensions inherit the discrete-time limitations of…

Simulating physical systems is essential in engineering, but analytical solutions are limited to straightforward problems. Consequently, numerical methods like the Finite Element Method (FEM) are widely used. However, the FEM becomes…

In the near future, massively parallel computing systems will be necessary to solve computation intensive applications. The key bottleneck in massively parallel implementation of numerical algorithms is the synchronization of data across…

We propose an approach to solving partial differential equations (PDEs) using a set of neural networks which we call Neural Basis Functions (NBF). This NBF framework is a novel variation of the POD DeepONet operator learning approach where…

We propose a novel hybrid domain decomposition method that couples sub-domain-local high-fidelity finite element (FE) models with reduced order models (ROMs) using the Schwarz alternating method. By integrating the noninstrusive Operator…

Machine-learning force fields can deliver accurate molecular dynamics (MD) at high computational cost. For SO(3)-equivariant models such as MACE, there is little systematic evidence on whether reduced-precision arithmetic and GPU-optimized…

The use of neural networks to approximate partial differential equations (PDEs) has gained significant attention in recent years. However, the approximation of PDEs with localised phenomena, e.g., sharp gradients and singularities, remains…

Continuous-time neural processes are performant sequential decision-makers that are built by differential equations (DE). However, their expressive power when they are deployed on computers is bottlenecked by numerical DE solvers. This…

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).…

Developing fast surrogates for Partial Differential Equations (PDEs) will accelerate design and optimization in almost all scientific and engineering applications. Neural networks have been receiving ever-increasing attention and…

The development of novel materials in recent years has been accelerated greatly by the use of computational modelling techniques aimed at elucidating the complex physics controlling microstructure formation in materials, the properties of…

Operator learning enables fast surrogate modeling of high-dimensional dynamical systems, but existing approaches face two fundamental limitations: quadratic inference complexity and unreliable uncertainty quantification in safety-critical…

With the increased prevalence of neural operators being used to provide rapid solutions to partial differential equations (PDEs), understanding the accuracy of model predictions and the associated error levels is necessary for deploying…

Solving partial differential equations is difficult. Recently proposed neural resolution-invariant models, despite their effectiveness and efficiency, usually require equispaced spatial points of data. However, sampling in spatial domain is…