Hanting Guan | Searcharxiv

arXiv2025

Adaptively Point-weighting Curriculum Learning

Curriculum learning (CL) mimics human learning, in which easy samples are learned first, followed by harder samples, and has become an effective method for training deep networks. However, many existing automatic CL methods maintain a preference for easy samples during the entire training process regardless of the constantly evolving training state. This is just like a human curriculum that fails to provide individualized instruction, which can delay learning progress. To address this issue, we propose an adaptively point-weighting (APW) curriculum learning method that assigns a weight to each training sample based on its training loss. The weighting strategy of APW follows the easy-to-hard training paradigm, guided by the current training state of the network. We present a theoretical analysis of APW, including training effectiveness, training stability, and generalization performance. Experimental results validate these theoretical findings and demonstrate the superiority of the proposed APW method.

cs.LG↗

arXiv2022

Revisiting PINNs: Generative Adversarial Physics-informed Neural Networks and Point-weighting Method

Physics-informed neural networks (PINNs) provide a deep learning framework for numerically solving partial differential equations (PDEs), and have been widely used in a variety of PDE problems. However, there still remain some challenges in the application of PINNs: 1) the mechanism of PINNs is unsuitable (at least cannot be directly applied) to exploiting a small size of (usually very few) extra informative samples to refine the networks; and 2) the efficiency of training PINNs often becomes low for some complicated PDEs. In this paper, we propose the generative adversarial physics-informed neural network (GA-PINN), which integrates the generative adversarial (GA) mechanism with the structure of PINNs, to improve the performance of PINNs by exploiting only a small size of exact solutions to the PDEs. Inspired from the weighting strategy of the Adaboost method, we then introduce a point-weighting (PW) method to improve the training efficiency of PINNs, where the weight of each sample point is adaptively updated at each training iteration. The numerical experiments show that GA-PINNs outperform PINNs in many well-known PDEs and the PW method also improves the efficiency of training PINNs and GA-PINNs.

cs.LG↗