标题： EB-gMCR：基于能量的信号解混与多变量曲线分辨生成建模 显示英文标题

标题： EB-gMCR: Energy-Based Generative Modeling for Signal Unmixing and Multivariate Curve Resolution

摘要： 信号解混分析将数据分解为基本模式，并广泛应用于化学和生物研究中。多变量曲线解析（MCR）是信号解混的一个分支，它将混合的化学信号分离为基础模式（成分）及其浓度，在理解组成方面起着关键作用。经典的MCR通常被表述为矩阵分解（MF），并需要用户指定成分数量，而在实际数据中这个数量通常是未知的。随着数据集大小或成分数量的增加，基于MF的MCR的可扩展性和可靠性面临重大挑战。本研究将MCR重新表述为生成过程（gMCR），并引入了一种基于能量的深度学习求解器EB-gMCR，该求解器能够自动发现最小的成分集合，以准确重建数据。EB-gMCR从一个大的候选池（例如，1024个光谱）开始，并使用可微分的门控网络仅保留活跃的成分同时估计它们的浓度。在包含最多256个潜在源的噪声合成数据集上，EB-gMCR保持R^2 >= 0.98，并在5%以内恢复了成分数量；在较低噪声下，它实现了R^2 >= 0.99，并且几乎精确地估计了成分数量。额外的化学先验条件，如非负性或非线性混合，作为简单的插件函数引入，使得模型能够适应其他仪器或领域而无需改变核心学习过程。通过结合高容量的生成建模和硬性成分选择，EB-gMCR为大规模信号解混分析提供了一条实用的路径，包括化学库驱动的场景。源代码可在https://github.com/b05611038/ebgmcr_solver获取。 显示英文摘要

摘要： Signal unmixing analysis decomposes data into basic patterns and is widely applied in chemical and biological research. Multivariate curve resolution (MCR), a branch of signal unmixing, separates mixed chemical signals into base patterns (components) and their concentrations, playing a key role in understanding composition. Classical MCR is typically framed as matrix factorization (MF) and requires a user-specified component count, usually unknown in real data. As dataset size or component count increases, the scalability and reliability of MF-based MCR face significant challenges. This study reformulates MCR as a generative process (gMCR), and introduces an energy-based deep learning solver, EB-gMCR, that automatically discovers the smallest component set able to reconstruct the data faithfully. EB-gMCR starts from a large candidate pool (e.g., 1024 spectra) and employs a differentiable gating network to retain only active components while estimating their concentrations. On noisy synthetic datasets containing up to 256 latent sources, EB-gMCR maintained R^2 >= 0.98 and recovered the component count within 5% of the ground truth; at lower noise it achieved R^2 >= 0.99 with near exact component estimation. Additional chemical priors, such as non-negativity or nonlinear mixing, enter as simple plug-in functions, enabling adaptation to other instruments or domains without altering the core learning process. By uniting high-capacity generative modeling and hard component selection, EB-gMCR offers a practical route to large-scale signal unmixing analysis, including chemical library-driven scenarios. The source code is available at https://github.com/b05611038/ebgmcr_solver.