相关论文: PGOT: A Physics-Geometry Operator Transformer for …

Topology optimization is used for the design of high-performance structures but remains fundamentally limited by its iterative nature, requiring repeated finite element analyses that prevent real-time deployment and large-scale design…

Feature transformation plays a critical role in enhancing machine learning model performance by optimizing data representations. Recent state-of-the-art approaches address this task as a continuous embedding optimization problem, converting…

While data-driven methods such as neural operator have achieved great success in solving differential equations (DEs), they suffer from domain shift problems caused by different learning environments (with data bias or equation changes),…

Domain generalization (DG) aims to avoid the performance degradation of the model when the distribution shift between the limited training data and unseen test data occurs. Recently, foundation models with enormous parameters have been…

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…

This research introduces the Theory of Partial Symmetry Enforced Attention Decomposition (PSEAD), a new and rigorous group-theoretic framework designed to seamlessly integrate local symmetry awareness into the core architecture of…

Parameter-efficient tunings (PETs) have demonstrated impressive performance and promising perspectives in training large models, while they are still confronted with a common problem: the trade-off between learning new content and…

Inverse problems governed by partial differential equations (PDEs) are crucial in science and engineering. They are particularly challenging due to ill-posedness, data sparsity, and the added complexity of irregular geometries. Classical…

We tackle the task of synthesizing novel views of an object given a few input images and associated camera viewpoints. Our work is inspired by recent 'geometry-free' approaches where multi-view images are encoded as a (global) set-latent…

Learning complex dynamics driven by partial differential equations directly from data holds great promise for fast and accurate simulations of complex physical systems. In most cases, this problem can be formulated as an operator learning…

Transformers have attained outstanding performance across various modalities, owing to their simple but powerful scaled-dot-product (SDP) attention mechanisms. Researchers have attempted to migrate Transformers to graph learning, but most…

We propose a novel framework, Continuous_Time Attention, which infuses partial differential equations (PDEs) into the Transformer's attention mechanism to address the challenges of extremely long input sequences. Instead of relying solely…

The recent rise of generative artificial intelligence (AI), powered by Transformer networks, has achieved remarkable success in natural language processing, computer vision, and graphics. However, the application of Transformers in…

Physics-informed neural networks (PINNs) effectively embed physical principles into machine learning, but often struggle with complex or alternating geometries. We propose a novel method for integrating geometric transformations within…

Recent advances in Transformer-based Neural Operators have enabled significant progress in data-driven solvers for Partial Differential Equations (PDEs). Most current research has focused on reducing the quadratic complexity of attention to…

Physics-informed deep operator networks (DeepONets) have emerged as a promising approach toward numerically approximating the solution of partial differential equations (PDEs). In this work, we aim to develop further understanding of what…

Time series forecasting remains a critical challenge across various domains, often complicated by high-dimensional data and long-term dependencies. This paper presents a novel transformer architecture for time series forecasting,…

This paper introduces Dynamic Embeddings with Task-Oriented prompting (DETOT), a novel approach aimed at improving the adaptability and efficiency of machine learning models by implementing a flexible embedding layer. Unlike traditional…

We introduce the Graded Transformer framework, a new class of sequence models that embeds algebraic inductive biases through grading transformations on vector spaces. Extending Graded Neural Networks (GNNs), we propose two architectures:…

We introduce methods for obtaining pretrained Geometric Neural Operators (GNPs) that can serve as basal foundation models for use in obtaining geometric features. These can be used within data processing pipelines for machine learning tasks…