error analysis 1high-dimensional pdes 1inf-sup optimization 1neural networks 1saddle-point methods 1
From the 1 of 3 linked papers with an AI index.
3 papers
math.NA2026
Inf-Sup Neural Networks for High Dimensional PDEs
Ziren Chen, Hailiang Liu
The paper introduces a neural‑network framework that rewrites high‑dimensional partial differential equations as inf‑sup (saddle‑point) optimization problems using a Lagrange multi…
cs.LG2026
Neural solver for Wasserstein Geodesics and optimal transport dynamics
Hailiang Liu, Yan-Han Chen
In recent years, the machine learning community has increasingly embraced the optimal transport (OT) framework for modeling distributional relationships. In this work, we introduce…
cs.LG2025
Global Convergence in Neural ODEs: Impact of Activation Functions
Tianxiang Gao, Siyuan Sun, Hailiang Liu +1
Neural Ordinary Differential Equations (ODEs) have been successful in various applications due to their continuous nature and parameter-sharing efficiency. However, these unique ch…