Publications (7)
Expanding the Chaos: Neural Operator for Stochastic (Partial) Differential Equations
Dai Shi, Lequan Lin, Andi Han +4
Stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs) are fundamental for modeling stochastic dynamics across the natural sciences and mode…
ATOM: A Pretrained Neural Operator for Multitask Molecular Dynamics
Luke Thompson, Davy Guan, Dai Shi +3
Molecular dynamics (MD) simulations underpin modern computational drug discovery, materials science, and biochemistry. Recent machine learning models provide high-fidelity MD predi…
Wiener Chaos Expansion based Neural Operator for Singular Stochastic Partial Differential Equations
Dai Shi, Luke Thompson, Andi Han +3
In this paper, we explore how our recently developed Wiener Chaos Expansion (WCE)-based neural operator (NO) can be applied to singular stochastic partial differential equations, e…
SGNN: Efficient Global Mixing and Local Message Passing for Long-Range Graph Learning
Dai Shi, Luke Thompson, Linhan Luo +4
Message-passing neural networks (MPNNs) often suffer from an information bottleneck when capturing long-range dependencies, leading to the oversquashing (OSQ) phenomenon. Alongside…
Learning Manifold and Itô Dynamics with Branched Neural Rough Differential Equations
Luke Thompson, Dai Shi, Lequan Lin +2
Neural rough differential equations (NRDEs) stay accurate under irregular sampling while taking far fewer integration steps than standard neural differential equations, summarising…
Explicit and Effectively Symmetric Schemes for Neural SDEs on Lie Groups
Daniil Shmelev, Luke Thompson, Cristopher Salvi
Backpropagation through (neural) SDE solvers is traditionally approached in two ways: discretise-then-optimise, which offers accurate gradients but incurs prohibitive memory costs;…
SPDEBench: An Extensive Benchmark for Learning Stochastic PDEs
Yuantu Zhu, Zheyan Li, Dai Shi +8
Stochastic Partial Differential Equations (SPDEs) driven by random noise play a central role in modeling physical processes with rough spatio-temporal dynamics, such as turbulence…