Yangpeng Zhang | Searcharxiv

arXiv2026

An efficient and memory free algorithm for subdiffusion equation using incremental singular value decomposition

In this paper, we address the well-known challenge in the numerical solution of time-fractional partial differential equations (TFPDEs), namely, that the dependence on all previous time levels leads to storage requirements that grow linearly with the number of time steps. To overcome this difficulty, we develop an efficient algorithm based on incremental singular value decomposition (ISVD), which avoids the excessive memory demands associated with storing the full solution history. A rigorous error analysis is established, and numerical experiments are presented to validate the theoretical results. Comparisons with the direct method and a representative fast evaluation method show that the proposed ISVD approach dramatically reduces memory usage relative to the direct method and remains competitive with the fast method over the tested parameter regimes.

math.NA↗

arXiv2025

Gradient Propagation in Retrosynthetic Space: An Efficient Framework for Synthesis Plan Generation

Retrosynthesis, which aims to identify viable synthetic pathways for target molecules by decomposing them into simpler precursors, is often treated as a search problem. However, its complexity arises from multi-branched tree-structured pathways rather than linear paths. Some algorithms have been successfully applied in this task, but they either overlook the uncertainties inherent in chemical space or face limitations in practical application scenarios. To address these challenges, this paper introduces a novel gradient-propagation-based algorithmic framework for retrosynthetic route exploration. The proposed framework obtains the contributions of different nodes to the target molecule's success probability through gradient propagation and then guides the algorithm to greedily select the node with the highest contribution for expansion, thereby conducting efficient search in the chemical space. Experimental validations demonstrate that our algorithm achieves broad applicability across diverse molecular targets and exhibits superior computational efficiency compared to existing methods.

cs.AI↗