Auto-regressive partial differential equation (PDE) foundation models have shown great potential in handling time-dependent data. However, these models suffer from error accumulation caused by the shortcut problem deeply rooted in auto-regressive prediction. The challenge becomes particularly evident for out-of-distribution data, as the pretraining performance may approach random model initialization for downstream tasks with long-term dynamics. To deal with this problem, we propose physics-informed temporal alignment (PITA), a self-supervised learning framework inspired by inverse problem solving. Specifically, PITA aligns the physical dynamics discovered at different time steps on each given PDE trajectory by integrating physics-informed constraints into the self-supervision signal. The alignment is derived from observation data without relying on known physics priors, indicating strong generalization ability to out-of-distribution data. Extensive experiments show that PITA significantly enhances the accuracy and robustness of existing foundation models on diverse time-dependent PDE data. The code is available at https://github.com/SCAILab-USTC/PITA.

Adaptive training methods for Physics-informed neural network (PINN) require dedicated constructions of the distribution of weights assigned at each training sample. To efficiently seek such an optimal weight distribution is not a simple task and most existing methods choose the adaptive weights based on approximating the full distribution or the maximum of residuals. In this paper, we show that the bottleneck in the adaptive choice of samples for training efficiency is the behavior of the tail distribution of the numerical residual. Thus, we propose the Residual-Quantile Adjustment (RQA) method for a better weight choice for each training sample. After initially setting the weights proportional to the p-th power of the residual, our RQA method reassign all weights above q-quantile (90% for example) to the median value, so that the weight follows a quantile-adjusted distribution derived from the residuals. This iterative reweighting technique, on the other hand, is also very easy to implement. Experiment results show that the proposed method can outperform several adaptive methods on various partial differential equation (PDE) problems.

Three-dimensional (3D) convolutional neural network (CNN) is widely used for action recognition. However, it performs same on time and space, which dose not match asymmetry of time. To overcome this problem, we propose the time-asymmetric 3D CNN based on the hypothesis that the early frames persist. Our time-asymmetric 3D CNN performs better on Kinetics-400 than normal 3D CNN with less parameters. And it can get comparable results on UCF101 among leading methods, which indicates that our time-asymmetric 3D CNN is a good choice for action recognition.

Color constancy considers the problem of restoring the original color of an illuminated scene. Benefiting from the development of Convolutional Neural Network (CNN), substantial progress on color constancy has been made. High-level features of CNN structure contain semantic information while low-level features show local details. If both are taken into account, they would help achieve a more accurate illuminant estimation. However, previous works paid little attention to the latter for there lacks frameworks which can combine those two kinds of features together. Inspired by the pyramid model, a top-down network that successively propagates high-level information to low-level layers is proposed. This network, named Top-down Semantic Aggregation for Color Constancy (TDCC), takes full advantage of the multi-scale representations with strong semantics. As a result, objects with intrinsic colors are captured and a better estimation is obtained. Experiments on three benchmark datasets demonstrate that TDCC significantly outperforms state-of-the-art color constancy methods.

Images obtained from an illuminated scene often have their original colour contaminated. Colour constancy is a study considering how to restore them. Substantial progress on colour constancy has been made in recent years due to the development of a convolutional neural network (CNN). In a CNN structure, high‐level features contain semantic information while low‐level features show local details. If both are taken into account, they would help achieve a more accurate illuminant estimation. However, previous works paid little attention to the latter for lack of frameworks, which can combine those two kinds of features together. Inspired by the pyramid model, a top‐down network that successively propagates high‐level information to low‐level layers is proposed. This network, named top‐down semantic aggregation for colour constancy (TDCC), takes full advantage of the multi‐scale representations with strong semantics. As a result, objects with intrinsic colours are captured and a better estimation is obtained. Experiments on three benchmark datasets demonstrate that TDCC significantly outperforms state‐of‐the‐art colour constancy methods.