Differential equations are involved in modeling many engineering problems. Many efforts have been devoted to solving differential equations. Due to the flexibility of neural networks, Physics Informed Neural Networks (PINNs) have recently been proposed to solve complex differential equations and have demonstrated superior performance in many applications. While the L2 loss function is usually a default choice in PINNs, it has been shown that the corresponding numerical solution is incorrect and unstable for some complex equations. In this work, we propose a new PINNs framework named Kernel Packet accelerated PINNs (KP-PINNs), which gives a new expression of the loss function using the reproducing kernel Hilbert space (RKHS) norm and uses the Kernel Packet (KP) method to accelerate the computation. Theoretical results show that KP-PINNs can be stable across various differential equations. Numerical experiments illustrate that KP-PINNs can solve differential equations effectively and efficiently. This framework provides a promising direction for improving the stability and accuracy of PINNs-based solvers in scientific computing.

This study introduces RicEns-Net, a novel Deep Ensemble model designed to predict crop yields by integrating diverse data sources through multimodal data fusion techniques. The research focuses specifically on the use of synthetic aperture radar (SAR), optical remote sensing data from Sentinel 1, 2, and 3 satellites, and meteorological measurements such as surface temperature and rainfall. The initial field data for the study were acquired through Ernst & Young's (EY) Open Science Challenge 2023. The primary objective is to enhance the precision of crop yield prediction by developing a machine-learning framework capable of handling complex environmental data. A comprehensive data engineering process was employed to select the most informative features from over 100 potential predictors, reducing the set to 15 features from 5 distinct modalities. This step mitigates the ``curse of dimensionality" and enhances model performance. The RicEns-Net architecture combines multiple machine learning algorithms in a deep ensemble framework, integrating the strengths of each technique to improve predictive accuracy. Experimental results demonstrate that RicEns-Net achieves a mean absolute error (MAE) of 341 kg/Ha (roughly corresponds to 5-6\% of the lowest average yield in the region), significantly exceeding the performance of previous state-of-the-art models, including those developed during the EY challenge.

Vietnamese, a low-resource language, is typically categorized into three primary dialect groups that belong to Northern, Central, and Southern Vietnam. However, each province within these regions exhibits its own distinct pronunciation variations. Despite the existence of various speech recognition datasets, none of them has provided a fine-grained classification of the 63 dialects specific to individual provinces of Vietnam. To address this gap, we introduce Vietnamese Multi-Dialect (ViMD) dataset, a novel comprehensive dataset capturing the rich diversity of 63 provincial dialects spoken across Vietnam. Our dataset comprises 102.56 hours of audio, consisting of approximately 19,000 utterances, and the associated transcripts contain over 1.2 million words. To provide benchmarks and simultaneously demonstrate the challenges of our dataset, we fine-tune state-of-the-art pre-trained models for two downstream tasks: (1) Dialect identification and (2) Speech recognition. The empirical results suggest two implications including the influence of geographical factors on dialects, and the constraints of current approaches in speech recognition tasks involving multi-dialect speech data. Our dataset is available for research purposes.