5 papers
An adaptive adjoint-oriented neural network for solving parametric optimal control problems with singularities
Zikang Yuan, Guanjie Wang, Qifeng Liao
In this work, we present an adaptive adjoint-oriented neural network (adaptive AONN) for solving parametric optimal control problems governed by partial differential equations. The…
An alternating low-rank projection approach for partial differential equations with random inputs
Guanjie Wang, Qifeng Liao
It is known that standard stochastic Galerkin methods face challenges when solving partial differential equations (PDEs) with random inputs. These challenges are typically attribut…
An adaptive ANOVA stochastic Galerkin method for partial differential equations with high-dimensional random inputs
Guanjie Wang, Smita Sahu, Qifeng Liao
It is known that standard stochastic Galerkin methods encounter challenges when solving partial differential equations with high-dimensional random inputs, which are typically caus…
Estimating Failure Probability with Neural Operator Hybrid Approach
Mujing Li, Yani Feng, Guanjie Wang
Evaluating failure probability for complex engineering systems is a computationally intensive task. While the Monte Carlo method is easy to implement, it converges slowly and, henc…
Reduced basis stochastic Galerkin methods for partial differential equations with random inputs
Guanjie Wang, Qifeng Liao
We present a reduced basis stochastic Galerkin method for partial differential equations with random inputs. In this method, the reduced basis methodology is integrated into the st…