16 papers
PMosFM: Preconditioned Manifold Matching for One-Step Physics-Constrained Generation
Zhangyong Liang, Haibin Ling
Physics-constrained generative models aim to generate physical fields that match a target distribution and satisfy prescribed constraints. However, enforcing these constraints ofte…
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…
Stochastic-Dimension Frozen Sampled Neural Network for High-Dimensional Gross-Pitaevskii Equations on Unbounded Domains
Zhangyong Liang
This paper introduces the Stochastic-Dimension Frozen Sampled Neural Network (SD-FSNN), a novel computational framework for solving high-dimensional Gross-Pitaevskii equation (GPE)…
Constitutive parameterized deep energy method for solid mechanics problems with random material parameters
Zhangyong Liang, Jihong Zhu, Huanhuan Gao
In practical structural design and solid mechanics simulations, material properties inherently exhibit random variations within bounded intervals. However, evaluating mechanical re…
Stochastic Dimension Implicit Functional Projections for Global Integral Conservation in High-Dimensional PINNs
Zhangyong Liang, Huanhuan Gao, Manyu Xiao
Enforcing prescribed global integral constraints in mesh-free neural PDE solvers is challenging in high-dimensional domains. Existing projection methods for spatial integrals are o…
Stochastic Dimension Zeroth-Order Estimator: Stable and Memory-Efficient Training of PINNs
Zhangyong Liang, Huanhuan Gao
Physics-Informed Neural Networks (PINNs) for high-dimensional and high-order partial differential equations (PDEs) are primarily constrained by the spatial deriv…
Manifold-Orthogonal Dual-spectrum Extrapolation for Parameterized Physics-Informed Neural Networks
Zhangyong Liang, Huanhuan Gao
Physics-informed neural networks (PINNs) have achieved notable success in modeling dynamical systems governed by partial differential equations (PDEs). To avoid computationally exp…
Parameterized Temporal Extrapolation of PDEs via Disentangled Latent Dynamics Manifold Fusion
Zhangyong Liang, Jihong Zhu, Huanhuan Gao
Generalizing neural surrogate models across different PDE parameters remains difficult because changes in PDE coefficients often make learning harder and optimization less stable.…
Error Estimate and Convergence Analysis for Data Valuation
Zhangyong Liang, Huanhuan Gao, Ji Zhang
Data valuation quantifies data importance, but existing methods cannot ensure validity in a single training process. The neural dynamic data valuation (NDDV) method [3] addresses t…
Neural Multiscale Decomposition for Solving The Nonlinear Klein-Gordon Equation with Time Oscillation
Zhangyong Liang, Huanhuan Gao*
In this paper, we propose a neural multiscale decomposition method (NeuralMD) for solving the nonlinear Klein-Gordon equation (NKGE) with a dimensionless parameter $\varepsilon\in(…
Neural Dynamic Data Valuation via Stochastic State-Adjoint Trajectories
Zhangyong Liang, Ji Zhang, Huanhuan Gao
Classical data valuation defines a data point's value through the finite marginal contribution , but estimating this quantity over coalitions requires repeated…