4 papers
Accelerated Learning of High Dimensional Functions with a Tensor-Featured Training Network
Karl Pierce, Yuehaw Khoo, Haizhao Yang
In this work we present a method to accelerate the optimization of learning high dimensional functions using deep neural network (DNN). This optimization procedure introduces conte…
Global Convergence and Error Propagation in Neural Gradient Flows: A Riemannian Optimization Framework
Shixin Zheng, Yiwei Wang, Haizhao Yang
We develop a geometric convergence theory for neural-network optimization within the minimizing movement scheme (MMS) framework. Reformulating each neural MMS step as a minimizatio…
Multi-Scale Finite Expression Method for PDEs with Oscillatory Solutions on Complex Domains
Gareth Hardwick, Haizhao Yang
Solving partial differential equations (PDEs) with highly oscillatory solutions on complex domains remains a challenging and important problem. High-frequency oscillations and intr…
Solving High-Dimensional Partial Integral Differential Equations: The Finite Expression Method
Gareth Hardwick, Senwei Liang, Haizhao Yang
In this paper, we introduce a new finite expression method (FEX) to solve high-dimensional partial integro-differential equations (PIDEs). This approach builds upon the original FE…