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Ziwei Li

Ziwei Li contributes to research discovery and scholarly infrastructure.

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Machine Learning Artificial Intelligence

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preprint2026arXiv

Bridging the Gap between Sparse Matrix Reordering and Factorization: A Deep Learning Framework for Fill-in Reduction

Sparse matrix reordering can significantly reduce the fill-in during matrix factorization, thereby decreasing the computational and storage requirements in sparse matrix computations. Finding a minimal fill-in ordering is known to be an NP-hard problem. Moreover, there is a paradox: matrix reordering is applied before matrix factorization, but fill-ins that matrix reordering methods aim at are generated from matrix factorization. To bridge the gap between reordering and factorization, we propose a deep learning framework to minimize a fill-in surrogate function based on spectral embedding. First, we employ a multi-grid-like GNN architecture to learn to approximate the smallest eigenvectors of its graph Laplacian matrix, i.e. spectral embedding, and capture the global structural information of the matrix. Then, another multi-grid-like GNN architecture is used to minimize the potential space where fill-in can occur based on the rank distribution. Experimental results indicate that our approach achieves competitive performance compared with traditional graph-theoretic algorithms and deep learning methods.

preprint2026arXiv

KISS - Knowledge Infrastructure for Scientific Simulation: A Scaffolding for Agentic Earth Science

Process-based simulation models encode decades of scientific understanding across the Earth sciences, yet the communities most exposed to climate risk and resource scarcity are the least able to use them. Here, we introduce knowledge infrastructure (KI), an agent-actionable scaffold that externalizes expertise into validated modelling operators, staged domain protocols, and diagnostic recovery mechanisms. Across a 3,000-trial coupled-hydrology benchmark, agents equipped with KI produced physically plausible, verifiable end-to-end simulations in up to 84% of trials, while agents without KI plateaued below 40%. KI generalizes across disciplines. We packaged its construction into a Knowledge Dissection Toolkit (KDT) that autonomously produced KI enabling end-to-end agent execution of 117 additional process-based models across 14 Earth-science domains. Across all 119 KIs, modelling decisions and failure remedies converged despite different underlying physics, showing that operational expertise is structured and extractable rather than ad hoc. Demonstrations show KI-equipped agents lowering both the access barrier between non-specialist users and process-based simulation, and the integration barrier between modelling communities. Through this scaffold, process-based science can then evolve as a living scientific commons, answerable to whoever needs to know and extendable by whoever can contribute.

preprint2026arXiv

Learning Fill-in Reduction Ordering via Graph Policy Optimization for Sparse Matrices

Matrix reordering in large sparse solvers seeks a permutation that minimizes factorization fill-in to reduce memory and computation. Because the minimum fill-in ordering problem is NP-complete and fill-in is implicit in the sparsity pattern, graph-theoretic heuristics are used. Existing reinforcement learning methods either ignore sparsity patterns--missing the global fill-in--or lack local exact fill-in feedback. We propose a graph policy optimization method, modeling fill-ins from global and local views: both the policy and value networks use a multi-hop graph neural backbone to embed global fill-in; the policy further interacts with symbolic factorization over graphs to extract local, step-level fill-ins, and the resulting feedback is aligned with the value network via an adaptive saturation function to improve convergence. On the SuiteSparse Matrix Collection, our method achieves mean reductions of 29.3 in fill-ins and 31.3 in peak memory usage over state-of-the-art baselines.

preprint2026arXiv

Self-Supervised Learning for Sparse Matrix Reordering

Rearranging the rows or columns of a sparse matrix using an appropriate ordering can significantly reduce fill-ins, i.e., new nonzeros introduced during matrix factorization, decreasing memory usage and runtime. However, finding an ordering that minimizes fill-ins is NP-complete. Existing approaches, including graph-theoretic and deep learning methods, rely on surrogate objectives without theoretical guarantees. The Fill-Path Theorem reveals a direct and intrinsic relationship between fill-in generation and the sparse structure of the matrix as path triplet inequalities. Here we first employ a multigrid graph network to capture structural information for each vertex. We then derive a triplet sampling strategy based on inequalities. Finally, we introduce an end-max chain loss function to reduce the number of triplets whose predicted scores satisfy these inequalities. Experimental evaluations on the publicly available SuiteSparse matrix collection demonstrate the superiority of the proposed method in terms of both fill-in reduction and speedup in LU factorization time.

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