13 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…
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…
Constitutive parameterized deep energy method for solid mechanics problems with random material parameters
Zhangyong Liang, Huanhuan Gao
In practical structural design and solid mechanics simulations, material properties inherently exhibit random variations within bounded intervals. However, evaluating mechanical re…