Qingsong Zou

Wentao Zhang, Yujun Huang, Tong Zhang et al.

Currently intelligent diagnosis systems lack the ability of continually learning to diagnose new diseases once deployed, under the condition of preserving old disease knowledge. In particular, updating an intelligent diagnosis system with training data of new diseases would cause catastrophic forgetting of old disease knowledge. To address the catastrophic forgetting issue, an Adapter-based Continual Learning framework called ACL is proposed to help effectively learn a set of new diseases at each round (or task) of continual learning, without changing the shared feature extractor. The learnable lightweight task-specific adapter(s) can be flexibly designed (e.g., two convolutional layers) and then added to the pretrained and fixed feature extractor. Together with a specially designed task-specific head which absorbs all previously learned old diseases as a single "out-of-distribution" category, task-specific adapter(s) can help the pretrained feature extractor more effectively extract discriminative features between diseases. In addition, a simple yet effective fine-tuning is applied to collaboratively fine-tune multiple task-specific heads such that outputs from different heads are comparable and consequently the appropriate classifier head can be more accurately selected during model inference. Extensive empirical evaluations on three image datasets demonstrate the superior performance of ACL in continual learning of new diseases. The source code is available at https://github.com/GiantJun/CL_Pytorch.

Yujie Liu, Junping Wang, Qingsong Zou

This article presents a new finite element method for convection-diffusion equations by enhancing the continuous finite element space with a flux space for flux approximations that preserve the important mass conservation locally on each element. The numerical scheme is based on a constrained flux optimization approach where the constraint was given by local mass conservation equations and the flux error is minimized in a prescribed topology/metric. This new scheme provides numerical approximations for both the primal and the flux variables. It is shown that the numerical approximations for the primal and the flux variables are convergent with optimal order in some discrete Sobolev norms. Numerical experiments are conducted to confirm the convergence theory. Furthermore, the new scheme was employed in the computational simulation of a simplified two-phase flow problem in highly heterogeneous porous media. The numerical results illustrate an excellent performance of the method in scientific computing.

Hailong Guo, Zhimin Zhang, Qingsong Zou

In this paper, we develop a straightforward $C^0$ linear finite element method for sixth-order elliptic equations. The basic idea is to use gradient recovery techniques to generate higher-order numerical derivatives from a $C^0$ linear finite element function. Both theoretical analysis and numerical experiments show that the proposed method has the optimal convergence rate under the energy norm. The method avoids complicated construction of conforming $C^2$ finite element basis or nonconforming penalty terms and has a low computational cost.

Waixiang Cao, Zhimin Zhang, Qingsong Zou

We present and analyze a finite volume scheme of arbitrary order for elliptic equations in the one-dimensional setting. In this scheme, the control volumes are constructed by using the Gauss points in subintervals of the underlying mesh. We provide a unified proof for the inf-sup condition, and show that our finite volume scheme has optimal convergence rate under the energy and $L^2$ norms of the approximate error. Furthermore, we prove that the derivative error is superconvergent at all Gauss points and in some special case, the convergence rate can reach $h^{2r}$, where $r$ is the polynomial degree of the trial space. All theoretical results are justified by numerical tests.

Shangyou Zhang, Zhimin Zhang, Qingsong Zou

We analyze the flux conservation property of the finite element method. It is shown that the finite element solution does approximate the flux locally in the optimal order, i.e., the same order as that of the nodal interpolation operator. We propose two methods, post-processing the finite element solutions locally. The new solutions, remaining as optimal-order solutions, are flux-conserving elementwise. In one of our methods, the processed solution also satisfies the original finite element equations. While the high-order finite volume schemes are still under construction, our methods produce finite-volume-like finite element solution of any order. In particular, our methods avoid solving non-symmetric finite volume equations. Numerical tests in 2D and 3D verify our findings.

Zhimin Zhang, Qingsong Zou

In this paper, we analyze vertex-centered finite volume method (FVM) of any order for elliptic equations on rectangular meshes. The novelty is a unified proof of the inf-sup condition, based on which, we show that the FVM approximation converges to the exact solution with the optimal rate in the energy norm. Furthermore, we discuss superconvergence property of the FVM solution. With the help of this superconvergence result, we find that the FVM solution also converges to the exact solution with the optimal rate in the $L^2$-norm. Finally, we validate our theory with several numerical experiments.

Liqin Tan, Pin Chen, Menghan Liu et al.

We present MatUQ, a benchmark framework for evaluating graph neural networks (GNNs) on out-of-distribution (OOD) materials property prediction with uncertainty quantification (UQ). MatUQ comprises 1,375 OOD prediction tasks constructed from six materials datasets using five OFM-based and a newly proposed structure-aware splitting strategy, SOAP-LOCO, which captures local atomic environments more effectively. We evaluate 12 representative GNN models under a unified uncertainty-aware training protocol that combines Monte Carlo Dropout and Deep Evidential Regression (DER), and introduce a novel uncertainty metric, D-EviU, which shows the strongest correlation with prediction errors in most tasks. Our experiments yield two key findings. First, the uncertainty-aware training approach significantly improves model prediction accuracy, reducing errors by an average of 70.6\% across challenging OOD scenarios. Second, the benchmark reveals that no single model dominates universally: earlier models such as SchNet and ALIGNN remain competitive, while newer models like CrystalFramer and SODNet demonstrate superior performance on specific material properties. These results provide practical insights for selecting reliable models under distribution shifts in materials discovery.