A Regularized Newton Method for Computing Ground States of Bose-Einstein condensates

In this paper, we propose a regularized Newton method for computing ground states of Bose-Einstein condensates (BECs), which can be formulated as an energy minimization problem with a spherical constraint. The energy functional and constraint are discretized by either the finite difference, or sine or Fourier pseudospectral discretization schemes and thus the original infinite dimensional nonconvex minimization problem is approximated by a finite dimensional constrained nonconvex minimization problem. Then an initial solution is first constructed by using a feasible gradient type method, which is an explicit scheme and maintains the spherical constraint automatically. To accelerate the convergence of the gradient type method, we approximate the energy functional by its second-order Taylor expansion with a regularized term at each Newton iteration and adopt a cascadic multigrid technique for selecting initial data. It leads to a standard trust-region subproblem and we solve it again by the feasible gradient type method. The convergence of the regularized Newton method is established by adjusting the regularization parameter as the standard trust-region strategy. Extensive numerical experiments on challenging examples, including a BEC in three dimensions with an optical lattice potential and rotating BECs in two dimensions with rapid rotation and strongly repulsive interaction, show that our method is efficient, accurate and robust.Comment: 25 pages, 6 figure

C2B Orders Decision-making in Multiple Supply Chains Under Cloud Manufacturing

Considering the background of cloud manufacturing and cluster supply chain, we build the basic model to assign the orders priority within each capacity. Then, considering the inter-chain horizontal cooperation, the extended model is proposed to parallel allocation of cross-chain orders as the orders exceeding one single- chain’s capacity. Lagrange algorithm is implemented, and the simulation analysis shown that the opportunity cost of rejected orders factor and cross-chain orders manufacturing cost factor have significant impacts on orders’ allocation decision, and there is a critical point in the combinations of those two factors. Through combinations, the cluster supply chain can make the acceptance decisions policy and production schedules of priority orders and cross- chain orders, so that customers’ satisfaction and the cluster supply chain’s total profits achieve the best situations

SeisCLIP: A seismology foundation model pre-trained by multi-modal data for multi-purpose seismic feature extraction

Training specific deep learning models for particular tasks is common across various domains within seismology. However, this approach encounters two limitations: inadequate labeled data for certain tasks and limited generalization across regions. To address these challenges, we develop SeisCLIP, a seismology foundation model trained through contrastive learning from multi-modal data. It consists of a transformer encoder for extracting crucial features from time-frequency seismic spectrum and an MLP encoder for integrating the phase and source information of the same event. These encoders are jointly pre-trained on a vast dataset and the spectrum encoder is subsequently fine-tuned on smaller datasets for various downstream tasks. Notably, SeisCLIP's performance surpasses that of baseline methods in event classification, localization, and focal mechanism analysis tasks, employing distinct datasets from different regions. In conclusion, SeisCLIP holds significant potential as a foundational model in the field of seismology, paving the way for innovative directions in foundation-model-based seismology research.Comment: 27 pages, 9 figures, 4 table

Seismic Foundation Model (SFM): a new generation deep learning model in geophysics

While computer science has seen remarkable advancements in foundation models, which remain underexplored in geoscience. Addressing this gap, we introduce a workflow to develop geophysical foundation models, including data preparation, model pre-training, and adaption to downstream tasks. From 192 globally collected 3-D seismic volumes, we create a carefully curated dataset of 2,286,422 2-D seismic images. Fully using these unlabeled images, we employ the self-supervised learning to pre-train a Transformer-based Seismic Foundation Model (SFM) for producing all-purpose seismic features that work across various tasks and surveys. Through experiments on seismic facies classification, geobody identification, interpolation, denoising, and inversion, our pre-trained model demonstrates versatility, generalization, scalability, and superior performance over baseline models. Conclusively, we provide a foundation model and vast dataset to advance AI in geophysics, addressing challenges (poor generalization, lacking labels, and repetitive training for task-specified models) of applying AI in geophysics and paving the way for future innovations in geoscience.Comment: 27 pages, 9 figures, and 4 table