Related papers: MMET: A Multi-Input and Multi-Scale Transformer fo…
Solving partial differential equations (PDEs) by numerical methods meet computational cost challenge for getting the accurate solution since fine grids and small time steps are required. Machine learning can accelerate this process, but…
Solving Partial Differential Equations (PDEs) is the core of many fields of science and engineering. While classical approaches are often prohibitively slow, machine learning models often fail to incorporate complete system information.…
We present a novel graph transformer framework, HAMLET, designed to address the challenges in solving partial differential equations (PDEs) using neural networks. The framework uses graph transformers with modular input encoders to directly…
Many important problems in science and engineering require solving the so-called parametric partial differential equations (PDEs), i.e., PDEs with different physical parameters, boundary conditions, shapes of computation domains, etc.…
The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to…
While Transformers have demonstrated remarkable potential in modeling Partial Differential Equations (PDEs), modeling large-scale unstructured meshes with complex geometries remains a significant challenge. Existing efficient architectures…
Partial differential equations (PDEs) have become an essential tool for modeling complex physical systems. Such equations are typically solved numerically via mesh-based methods, such as finite element methods, with solutions over the…
Many important problems in science and engineering require solving the so-called parametric partial differential equations (PDEs), i.e., PDEs with different physical parameters, boundary conditions, shapes of computational domains, etc.…
Partial differential equations (PDEs) are often computationally challenging to solve, and in many settings many related PDEs must be be solved either at every timestep or for a variety of candidate boundary conditions, parameters, or…
A key scalability challenge in neural solvers for industrial-scale physics simulations is efficiently capturing both fine-grained local interactions and long-range global dependencies across millions of spatial elements. We introduce the…
Transformers have empowered many milestones across various fields and have recently been applied to solve partial differential equations (PDEs). However, since PDEs are typically discretized into large-scale meshes with complex geometries,…
This paper studies numerical solutions for parameterized partial differential equations (P-PDEs) with deep learning (DL). P-PDEs arise in many important application areas and the computational cost using traditional numerical schemes can be…
Solving partial differential equations (PDEs) by learning the solution operators has emerged as an attractive alternative to traditional numerical methods. However, implementing such architectures presents two main challenges: flexibility…
Dimensionality reduction (DR) plays a crucial role in various fields, including data engineering and visualization, by simplifying complex datasets while retaining essential information. However, achieving both high DR accuracy and strong…
Parameter-efficient transfer learning (PETL) has shown great potential in adapting a vision transformer (ViT) pre-trained on large-scale datasets to various downstream tasks. Existing studies primarily focus on minimizing the number of…
Although Vision Transformers (ViTs) have recently advanced computer vision tasks significantly, an important real-world problem was overlooked: adapting to variable input resolutions. Typically, images are resized to a fixed resolution,…
Many geometry processing techniques require the solution of partial differential equations (PDEs) on manifolds embedded in $\mathbb{R}^2$ or $\mathbb{R}^3$, such as curves or surfaces. Such manifold PDEs often involve boundary conditions…
Multi-task learning (MTL) is an inductive transfer mechanism designed to leverage useful information from multiple tasks to improve generalization performance compared to single-task learning. It has been extensively explored in traditional…
Density matrix embedding theory (DMET) is a powerful quantum embedding method for solving strongly correlated quantum systems. Theoretically, the performance of a quantum embedding method should be limited by the computational cost of the…
Quantum embedding methods enable the study of large, strongly correlated quantum systems by (usually self-consistent) decomposition into computationally manageable subproblems, in the spirit of divide-and-conquer methods. Among these,…