Inverse Design with Dynamic Mode Decomposition

We introduce a computationally efficient method for the automation of inverse design in science and engineering. Based on simple least-square regression, the underlying dynamic mode decomposition algorithm can be used to construct a low-rank subspace spanning multiple experiments in parameter space. The proposed inverse design dynamic mode composition (ID-DMD) algorithm leverages the computed low-dimensional subspace to enable fast digital design and optimization on laptop-level computing, including the potential to prescribe the dynamics themselves. Moreover, the method is robust to noise, physically interpretable, and can provide uncertainty quantification metrics. The architecture can also efficiently scale to large-scale design problems using randomized algorithms in the ID-DMD. The simplicity of the method and its implementation are highly attractive in practice, and the ID-DMD has been demonstrated to be an order of magnitude more accurate than competing methods while simultaneously being 3-5 orders faster on challenging engineering design problems ranging from structural vibrations to fluid dynamics. Due to its speed, robustness, interpretability, and ease-of-use, ID-DMD in comparison with other leading machine learning methods represents a significant advancement in data-driven methods for inverse design and optimization, promising a paradigm shift in how to approach inverse design in practice.

SCKansformer: Fine-Grained Classification of Bone Marrow Cells via Kansformer Backbone and Hierarchical Attention Mechanisms

The incidence and mortality rates of malignant tumors, such as acute leukemia, have risen significantly. Clinically, hospitals rely on cytological examination of peripheral blood and bone marrow smears to diagnose malignant tumors, with accurate blood cell counting being crucial. Existing automated methods face challenges such as low feature expression capability, poor interpretability, and redundant feature extraction when processing high-dimensional microimage data. We propose a novel fine-grained classification model, SCKansformer, for bone marrow blood cells, which addresses these challenges and enhances classification accuracy and efficiency. The model integrates the Kansformer Encoder, SCConv Encoder, and Global-Local Attention Encoder. The Kansformer Encoder replaces the traditional MLP layer with the KAN, improving nonlinear feature representation and interpretability. The SCConv Encoder, with its Spatial and Channel Reconstruction Units, enhances feature representation and reduces redundancy. The Global-Local Attention Encoder combines Multi-head Self-Attention with a Local Part module to capture both global and local features. We validated our model using the Bone Marrow Blood Cell Fine-Grained Classification Dataset (BMCD-FGCD), comprising over 10,000 samples and nearly 40 classifications, developed with a partner hospital. Comparative experiments on our private dataset, as well as the publicly available PBC and ALL-IDB datasets, demonstrate that SCKansformer outperforms both typical and advanced microcell classification methods across all datasets. Our source code and private BMCD-FGCD dataset are available at https://github.com/JustlfC03/SCKansformer.