← Back to all news
arXiv Machine Learning By Chenhao Si, Zishan Qian, Shing-Tung Yau, Rongling Wu, Ming Yan

Latent dynamics for reconstructing fine-scale PDE trajectories from coarse observations

Read the original on arXiv Machine Learning →

The paper introduces Structured Latent Dynamics (SLD), a method that reconstructs high‑resolution partial differential equation (PDE) trajectories from coarse, downsampled observations. SLD interpolates input in time, applies a learned temporal correction, and updates a hidden state using learned gated responses combined with spatial differences and a Laplacian term. Two Haar wavelet synthesis branches then map the hidden state and refined coarse input to produce fine‑scale fields, achieving lower error than baseline models on several benchmark PDE systems.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

Related stories

Hugging Face Trending Papers
Aug 12

RECAST: A Machine-Learning Framework for Correction and Super-Resolution of Coarse-Grid PDE Solvers

Coarse-grid numerical solvers can substantially reduce the computational cost of time-dependent PDE simulation, but under-resolution often degrades both the trajectory and the spatial fidelity of the solution. We introduce RECAST (Recurrent Error Correction And Super-resolution of coarse-grid Trajectories), a machine-learning framework designed to restore this lost accuracy while retaining coarse-grid evolution.

diffusion
More like this →
arXiv Machine Learning
Aug 20

Flux-form spatiotemporal neural operators for coarse-grained dynamics of multiscale PDEs

The paper introduces flux‑form spatiotemporal neural operators for predicting coarse‑grained dynamics of multiscale PDEs without relying on closure models. It learns a surrogate evolution operator from filtered high‑fidelity data, using Fourier convolution for spatial mixing and a causal kernel with time‑lag attention for temporal mixing. The method incorporates a flux‑form inductive bias to maintain conservation and provides a data‑driven rule for selecting memory length, achieving stable, accurate long‑horizon rollouts on benchmark equations and turbulent flow simulations.

By Junfeng Chen
safety
More like this →