5 papers · 1 filter
Di-BiLPS: Denoising induced Bidirectional Latent-PDE-Solver under Sparse Observations
Zhonghao Li, Chaoyu Liu, Qian Zhang
Partial differential equations (PDEs) are fundamental for modeling complex natural and physical phenomena. In many real-world applications, however, observational data are extremel…
Adaptive Correction for Ensuring Conservation Laws in Neural Operators
Chaoyu Liu, Yangming Li, Zhongying Deng +2
Physical laws, such as the conversation of mass and momentum, are fundamental principles in many physical systems. Neural operators have achieved promising performance in learning…
Enhancing Fourier Neural Operators with Local Spatial Features
Chaoyu Liu, Davide Murari, Lihao Liu +3
Partial Differential Equation (PDE) problems often exhibit strong local spatial structures, and effectively capturing these structures is critical for approximating their solutions…
Inverse Evolution Data Augmentation for Neural PDE Solvers
Chaoyu Liu, Chris Budd, Carola-Bibiane Schönlieb
Neural networks have emerged as promising tools for solving partial differential equations (PDEs), particularly through the application of neural operators. Training neural operato…
Generative Unordered Flow for Set-Structured Data Generation
Yangming Li, Chaoyu Liu, Carola-Bibiane Schönlieb
Flow-based generative models have demonstrated promising performance across a broad spectrum of data modalities (e.g., image and text). However, there are few works exploring their…