5 papers
Predicting Out-of-Distribution Generalization of Neural Operators via Observable Spectral Error Decomposition
Hang-Cheng Dong, Pengcheng Cheng
Neural operators have emerged as powerful surrogates for solving partial differential equations (PDEs), yet their reliability under distribution shift remains a critical barrier to…
Quotient Dynamics, Effective Curvature, and Implicit Bias in Positive Quadratic Networks
Pengcheng Cheng
Positive quadratic networks admit the low-rank representation f_U(x)=x^top UU^top x, where Uinmathbb{R}^{dtimes r} is identifiable only up to right orthogonal multiplication, repre…
Quotient Geometry, Effective Curvature, and Implicit Bias in Simple Shallow Neural Networks
Hang-Cheng Dong, Pengcheng Cheng
Overparameterized shallow neural networks admit substantial parameter redundancy: distinct parameter vectors may represent the same predictor due to hidden-unit permutations, resca…
Interpretable Operator Learning for Inverse Problems via Adaptive Spectral Filtering: Convergence and Discretization Invariance
Hang-Cheng Dong, Pengcheng Cheng, Shuhuan Li
Solving ill-posed inverse problems necessitates effective regularization strategies to stabilize the inversion process against measurement noise. While classical methods like Tikho…
Gauge-Equivariant Intrinsic Neural Operators for Geometry-Consistent Learning of Elliptic PDE Maps
Pengcheng Cheng
Learning solution operators of partial differential equations (PDEs) from data has emerged as a promising route to fast surrogate models in multi-query scientific workflows. Howeve…