2 citations · 3 across the 5 of their papers we have counts for
5 papers
Flux-form spatiotemporal neural operators for coarse-grained dynamics of multiscale PDEs
Junfeng Chen
We study data-driven prediction of coarse-grained dynamics in multiscale PDE systems. Adopting a closure-free operator-learning viewpoint, we apply a linear coarse-graining map and…
Diagnosing the conditional-mean barrier in scientific machine-learning surrogates
Junfeng Chen
Many prediction tasks in computational science and engineering become one-to-many after coarse graining and partial observation. In such settings, deterministic surrogates trained…
DUE: A Deep Learning Framework and Library for Modeling Unknown Equations
Junfeng Chen, Kailiang Wu, Dongbin Xiu
Equations, particularly differential equations, are fundamental for understanding natural phenomena and predicting complex dynamics across various scientific and engineering discip…
Positional Knowledge is All You Need: Position-induced Transformer (PiT) for Operator Learning
Junfeng Chen, Kailiang Wu
Operator learning for Partial Differential Equations (PDEs) is rapidly emerging as a promising approach for surrogate modeling of intricate systems. Transformers with the self-atte…
Deep-OSG: Deep Learning of Operators in Semigroup
Junfeng Chen, Kailiang Wu
This paper proposes a novel deep learning approach for learning operators in semigroup, with applications to modeling unknown autonomous dynamical systems using time series data co…