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New learned preconditioner McMg accelerates Helmholtz equation solutions · 4 sources tracked

By PulseAugur Editorial · [5 sources] ·

Researchers have developed a new learned preconditioner called McMg for solving heterogeneous Helmholtz equations, which significantly reduces the number of iterations and computational time compared to classical methods. This approach retains unresolved local wave information by carrying learned coefficients for amplitude, phase, direction, and scattering at each coarse node, rather than a single scalar unknown. The models demonstrate generalization capabilities across different scales and problems, outperforming existing neural preconditioners. AI

IMPACT This research could lead to more efficient computational methods for solving complex physics problems, potentially impacting fields that rely on simulations.

RANK_REASON The cluster contains multiple arXiv papers detailing new research in computational methods and machine learning.

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 5 sources. How we write summaries →

New learned preconditioner McMg accelerates Helmholtz equation solutions · 4 sources tracked

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COVERAGE [5]

  1. arXiv cs.LG TIER_1 English(EN) · Gal Lifshitz, Shahar Zuler, Ori Fouks, Dan Raviv ·

    L-SR1: Learned Symmetric-Rank-One Preconditioning

    arXiv:2508.12270v3 Announce Type: replace Abstract: End-to-end deep learning has achieved impressive results but often relies on large labeled datasets, exhibits limited generalization to unseen scenarios, and incurs substantial computational cost. Classical optimization methods,…

  2. arXiv cs.AI TIER_1 English(EN) · Jiwei Jia, Xinliang Liu, Juntao Wang, Jinchao Xu ·

    McMg: A Learned Phase-Space Multi-channel Multigrid Preconditioner for Helmholtz Equation

    arXiv:2606.30495v1 Announce Type: cross Abstract: Solving heterogeneous Helmholtz equations at high wavenumbers remains challenging because the discretized operator is indefinite, pollution degrades phase accuracy, and scalar coarse-grid correction can discard the local phase and…

  3. arXiv cs.AI TIER_1 English(EN) · Jinchao Xu ·

    McMg: A Learned Phase-Space Multi-channel Multigrid Preconditioner for Helmholtz Equation

    Solving heterogeneous Helmholtz equations at high wavenumbers remains challenging because the discretized operator is indefinite, pollution degrades phase accuracy, and scalar coarse-grid correction can discard the local phase and propagation-direction information carried by osci…

  4. arXiv cs.LG TIER_1 English(EN) · Annie Marsden, Elad Hazan ·

    The Power of Second Order Methods for Sequence Preconditioning

    arXiv:2605.08390v2 Announce Type: replace Abstract: Sequence prediction methods for linear dynamical systems with long memory, i.e. marginally stable systems, typically achieve regret that grows linearly with the hidden dimension of the underlying generative model. While many met…

  5. arXiv stat.ML TIER_1 English(EN) · Max Hird, Florian Maire, Jeffrey Negrea ·

    A Non-asymptotic Analysis for Learning and Applying a Preconditioner in MCMC

    arXiv:2602.10714v2 Announce Type: replace-cross Abstract: Preconditioning is a common method applied to modify Markov chain Monte Carlo algorithms with the goal of making them more efficient. In practice it is often extremely effective, even when the preconditioner is learned fro…

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