15 papers
Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers
Zhangyong Liang, Huanhuan Gao
Energy natural gradient descent (ENGD) aligns parameter updates with the curvature of an underlying function-space energy, but existing formulations assume an unconstrained Euclide…
Interface-Aware Neural Newton Preconditioning for Robust Cohesive Zone Model Simulations
Zhangyong Liang, Huanhuan Gao
Cohesive Zone Models (CZMs) are widely used to simulate interface fracture, delamination, adhesive failure, and fiber--matrix debonding in aerospace composite structures. In implic…
Hybrid Iterative Neural Low-Regularity Integrator for Nonlinear Dispersive Equations
Zhangyong Liang, Huanhuan Gao
We propose HIN-LRI, a hybrid framework that augments a classical numerical solver with a neural operator trained to correct the solver's structured truncation error. A base low-reg…
Parameterized Representations via Implicit Stochastic Modulation for High-Dimensional and High-Order Neural PDE Solvers
Zhangyong Liang, Huanhuan Gao
Solving high-dimensional and high-order PDEs is challenged by the coupled growth of spatial dimensionality and derivative order. Recent stochastic derivative estimators reduce this…
Conflict-Aware Harmonized Rotational Gradient for Multiscale Kinetic Regimes
Zhangyong Liang
In this paper, we propose a harmonized rotational gradient method, termed HRGrad, for simultaneously tackling multiscale time-dependent kinetic problems with varying small paramete…
Categorical Optimization with Bayesian Anchored Latent Trust Regions for Structural Design under High-Dimensional Uncertainty
Zhangyong Liang, Jie Hou, Huanhuan Gao +1
Categorical structural optimization under aleatoric uncertainty is challenging because each design variable must be selected from a finite catalog of admissible instances, while ea…