Haoxuan Chen

Luan Vejsiu, Qianyu Zheng, Haoxuan Chen et al.

Despite ASR technology being full-scale adopted by industry and for large portions of the population, ASR systems often have errors that require editors to post-edit text quality. While LLMs are powerful post-editing tools, baseline full rewrite models have inference inefficiencies because they often generate the same redundant text over and over again. Compact edit representations have existed but often lack the efficacy and context required for optimal accuracy. This paper introduces CEGER (Context-Enhanced Granular Edit Representation), a compact edit representation that was generated for highly accurate, efficient ASR post-editing. CEGER allows LLMs to generate a sequence of structured, fine-grained, contextually rich commands to modify the original ASR output. A separate expansion module deterministically reconstructs the corrected text based on the commands. Extensive experiments on the LibriSpeech dataset that were conducted, CEGER achieves state-of-the-art accuracy, achieving the lowest word error rate (WER) versus full rewrite and prior compact representations.

Zongyi Li, Hongkai Zheng, Nikola Kovachki et al.

In this paper, we propose physics-informed neural operators (PINO) that combine training data and physics constraints to learn the solution operator of a given family of parametric Partial Differential Equations (PDE). PINO is the first hybrid approach incorporating data and PDE constraints at different resolutions to learn the operator. Specifically, in PINO, we combine coarse-resolution training data with PDE constraints imposed at a higher resolution. The resulting PINO model can accurately approximate the ground-truth solution operator for many popular PDE families and shows no degradation in accuracy even under zero-shot super-resolution, i.e., being able to predict beyond the resolution of training data. PINO uses the Fourier neural operator (FNO) framework that is guaranteed to be a universal approximator for any continuous operator and discretization-convergent in the limit of mesh refinement. By adding PDE constraints to FNO at a higher resolution, we obtain a high-fidelity reconstruction of the ground-truth operator. Moreover, PINO succeeds in settings where no training data is available and only PDE constraints are imposed, while previous approaches, such as the Physics-Informed Neural Network (PINN), fail due to optimization challenges, e.g., in multi-scale dynamic systems such as Kolmogorov flows.

Yiping Lu, Haoxuan Chen, Jianfeng Lu et al.

In this paper, we study the statistical limits of deep learning techniques for solving elliptic partial differential equations (PDEs) from random samples using the Deep Ritz Method (DRM) and Physics-Informed Neural Networks (PINNs). To simplify the problem, we focus on a prototype elliptic PDE: the Schrödinger equation on a hypercube with zero Dirichlet boundary condition, which has wide application in the quantum-mechanical systems. We establish upper and lower bounds for both methods, which improves upon concurrently developed upper bounds for this problem via a fast rate generalization bound. We discover that the current Deep Ritz Methods is sub-optimal and propose a modified version of it. We also prove that PINN and the modified version of DRM can achieve minimax optimal bounds over Sobolev spaces. Empirically, following recent work which has shown that the deep model accuracy will improve with growing training sets according to a power law, we supply computational experiments to show a similar behavior of dimension dependent power law for deep PDE solvers.