4 papers
Loss Landscape Diagnosis for Gradient-Based Gray-Scott System Inversion: Disentangling the Roles of PINN Components
Yan Yang
Gradient-based inversion of reaction-diffusion systems is typically approached via surrogate models or physics-informed neural networks (PINNs), while the most direct route, backpr…
Optimization over the intersection of manifolds
Yan Yang, Bin Gao, Ya-xiang Yuan
Optimization over the intersection of two manifolds arises in a broad range of applications, but is hindered by the coupled geometry of the feasible region. In this paper, we prove…
Variational analysis of determinantal varieties
Yan Yang, Bin Gao, Ya-xiang Yuan
Determinantal varieties -- the sets of bounded-rank matrices or tensors -- have attracted growing interest in low-rank optimization. The tangent cone to low-rank sets is widely stu…
A space-decoupling framework for optimization on bounded-rank matrices with orthogonally invariant constraints
Yan Yang, Bin Gao, Ya-xiang Yuan
Imposing additional constraints on low-rank optimization has garnered growing interest. However, the geometry of coupled constraints hampers the well-developed low-rank structure a…