With the developments in advanced sensor technology and the associated data collection and storage power of computers, the presence of huge datasets is a common theme in chemical and biological manufacturing [1]. In many cases the data come in the format of tensors which are generalizations of matrices to higher order arrays. For example, the liquid chromatography-mass spectroscopy (LC-MS) used during mRNA manufacturing produces the third-order tensorial data with samples, mass spectral, and elution time dimensions. The quantity and complexity of the data increase steeply with the tensor order and the number of allowed values in each order in the tensorial data. Tensor decomposition is an effective approach for multiway data analytics that has been demonstrated to improve the accuracy of data-driven models constructed for the monitoring of biopharmaceutical manufacturing processes [2,3,4]. However, efficiently and accurately computing the tensor decomposition is nontrivial, preventing taking full advantage of tensor decomposition methods in many contexts [5], especially for real-time adaptive monitoring applications in which the tensorial decomposition would be computed online to update the process models based on the most recent measurements (e.g., see [6,7] and citations therein). In this work, we propose and test a new quantum-inspired method for complex chemical tensor decomposition. The new method is inspired from direct inversion of the iterative subspace (DIIS) [8] extrapolation procedures used in the context of accelerating and stabilizing the convergence of the Hartree–Fock self-consistent field method. The performance of the proposed method is validated on both a variety of simulated datasets and real datasets including different types of spectroscopy data. The proposed method is observed to significantly accelerate the computation of the standard tensor decomposition while maintaining favorable accuracy. The method reduces the number of iterations needed for convergence while being numerically robust. Specifically, the proposed method computes results of similar numerical accuracy while reducing computational cost by 400% compared to the widely used line search-based extrapolation tensor decomposition algorithm. The proposed methodology has the potential of boosting the application of tensor modeling in biopharmaceutical manufacturing and more broadly in biochemical engineering, and we deem it to be a powerful solution for handling the analytical and computational challenges of massive multi-way chemical data.
Reference:
[1] W. Sun and R. D. Braatz. Opportunities in tensorial data analytics for chemical and biological manufacturing processes. Computers & Chemical Engineering, 143, 107099, 2020.
[2] Kunlun Hu and JingqiYuan. Batch process monitoring with tensor factorization. Journal of Process Control, 2009, 19(2), 288–296, 2009.
[3] L. Luo, S. Bao, Z. Gao, and J. Yuan. Batch process monitoring with GTucker2 model. Industrial & Engineering Chemistry Research, 53(39), 15101–15110, 2014.
[4] Fabian Mohr, Moo Sun Hong, Chris D. Castro, Benjamin T. Smith, Jacqueline M. Wolfrum, Stacy L. Springs, Anthony J. Sinskey, Roger A. Hart, Tom Mistretta, and Richard D. Braatz. Computers & Chemical Engineering, 182, 108557, 2024.
[5] K. Abed-Meraim, N. L. Trung, and A. Hafiane. A contemporary and comprehensive survey on streaming tensor decomposition. IEEE Transactions on Knowledge and Data Engineering, 35(11), 10897–10921, 2022.
[6] Chunhui Zhao, Fuli Wang, Furong Gao, Ningyun Lu, and Mingxing Jia. Adaptive monitoring method for batch processes based on phase dissimilarity updating with limited modeling data. Industrial & Engineering Chemistry Research, 46(14), 4943–4953, 2007.
[7] Weihua Li, H. Henry Yue, Sergio Valle-Cervantes, and S. Joe Qin. Recursive PCA for adaptive process monitoring. Journal of Process Control, 10(5), 471–486, 2000.
[8] C. Seidl and G. M. Barca. Q-Next: A fast, parallel, and diagonalization-free alternative to direct inversion of the iterative subspace. Journal of Chemical Theory and Computation, 18(7), 4164–4176, 2022.
