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AI for partial differential equations (PDEs) has garnered significant attention, particularly with the emergence of Physics-informed neural networks (PINNs). The recent advent of Kolmogorov-Arnold Network (KAN) indicates that there is potential to revisit and enhance the previously MLP-based PINNs. Compared to MLPs, KANs offer interpretability and require fewer parameters. PDEs can be described in various forms, such as strong form, energy form, and inverse form. While mathematically equivalent, these forms are not computationally equivalent, making the exploration of different PDE formulations significant in computational physics. Thus, we propose different PDE forms based on KAN instead of MLP, termed Kolmogorov-Arnold-Informed Neural Network (KINN). We systematically compare MLP and KAN in various numerical examples of PDEs, including multi-scale, singularity, stress concentration, nonlinear hyperelasticity, heterogeneous, and complex geometry problems. Our results demonstrate that KINN significantly outperforms MLP in terms of accuracy and convergence speed for numerous PDEs in computational solid mechanics, except for the complex geometry problem. This highlights KINN's potential for more efficient and accurate PDE solutions in AI for PDEs.

Linguistic steganography provides convenient implementation to hide messages, particularly with the emergence of AI generation technology. The potential abuse of this technology raises security concerns within societies, calling for powerful linguistic steganalysis to detect carrier containing steganographic messages. Existing methods are limited to finding distribution differences between steganographic texts and normal texts from the aspect of symbolic statistics. However, the distribution differences of both kinds of texts are hard to build precisely, which heavily hurts the detection ability of the existing methods in realistic scenarios. To seek a feasible way to construct practical steganalysis in real world, this paper propose to employ human-like text processing abilities of large language models (LLMs) to realize the difference from the aspect of human perception, addition to traditional statistic aspect. Specifically, we systematically investigate the performance of LLMs in this task by modeling it as a generative paradigm, instead of traditional classification paradigm. Extensive experiment results reveal that generative LLMs exhibit significant advantages in linguistic steganalysis and demonstrate performance trends distinct from traditional approaches. Results also reveal that LLMs outperform existing baselines by a wide margin, and the domain-agnostic ability of LLMs makes it possible to train a generic steganalysis model (Both codes and trained models are openly available in https://github.com/ba0z1/Linguistic-Steganalysis-with-LLMs).

Homogenization is an essential tool for studying multiscale physical phenomena. However, traditional numerical homogenization, heavily reliant on finite element analysis, requires extensive computation costs, particularly in handling complex geometries, materials, and high-resolution problems. To address these limitations, we propose a numerical homogenization model based on operator learning: HomoGenius. The proposed model can quickly provide homogenization results for arbitrary geometries, materials, and resolutions, increasing the efficiency by a factor of 80 compared to traditional numerical homogenization methods. We validate effectiveness of our model in predicting the effective elastic modulus on periodic materials (TPMS: Triply Periodic Minimal Surface), including complex geometries, various Poisson's ratios and elastic modulus, and different resolutions for training and testing. The results show that our model possesses high precision, super efficiency, and learning capability.