In the present study, we develop a neural network with local converging input (NNLCI) for high-fidelity prediction using unstructured data.
Although Deep Learning (DL) has achieved success in complex Artificial Intelligence (AI) tasks, it suffers from various notorious problems (e. g., feature redundancy, and vanishing or exploding gradients), since updating parameters in Euclidean space cannot fully exploit the geometric structure of the solution space.
In contrast with existing research work on applying neural networks to directly solve PDEs, our method takes advantage of the local domain of dependence of the Maxwell's equation in the input solution patches, and is therefore simpler, yet still robust.
SparGE measures similarity by jointly sparse coding and graph embedding.
Inspired by the tremendous success of the self-attention mechanism in natural language processing, the Vision Transformer (ViT) creatively applies it to image patch sequences and achieves incredible performance.
Although much significant progress has been made in the research field of object detection with deep learning, there still exists a challenging task for the objects with small size, which is notably pronounced in UAV-captured images.
The new algorithm, called Identifying Differential Equations with Numerical Time evolution (IDENT), is explored for data with non-periodic boundary conditions, noisy data and PDEs with varying coefficients.