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New neural operator models non-Markovian PDEs with history-space approach

By PulseAugur Editorial · [2 sources] ·

Researchers have developed the History-Space Fourier Neural Operator (HS-FNO), a novel neural operator designed to model non-Markovian partial differential equations (PDEs). Unlike standard autoregressive models that assume instantaneous states are complete, HS-FNO accounts for historical dependencies crucial in systems with memory or delays. The model decomposes updates into learned predictions for new data slices and exact transport for known history, demonstrating significant error reduction in autoregressive predictions compared to existing methods. AI

IMPACT Introduces a novel neural operator architecture that improves modeling accuracy for complex, history-dependent scientific simulations.

RANK_REASON The cluster contains an arXiv preprint detailing a new model architecture for a specific class of scientific modeling problems.

Read on arXiv stat.ML →

AI-generated summary · Google Gemini · from 2 sources. How we write summaries →

New neural operator models non-Markovian PDEs with history-space approach

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The cluster contains an arXiv preprint detailing a new model architecture for a specific class of scientific modeling problems.
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COVERAGE [2]

  1. arXiv stat.ML TIER_1 English(EN) · Lennon J. Shikhman ·

    HS-FNO: History-Space Fourier Neural Operator for Non-Markovian Partial Differential Equations

    arXiv:2605.09523v2 Announce Type: replace-cross Abstract: Neural operators provide fast surrogate models for time-dependent partial differential equations, but their standard autoregressive use usually assumes that the instantaneous field $u(t,\cdot)$ is a complete state. This as…

  2. arXiv stat.ML TIER_1 English(EN) · Lennon J. Shikhman ·

    HS-FNO: History-Space Fourier Neural Operator for Non-Markovian Partial Differential Equations

    Neural operators provide fast surrogate models for time-dependent partial differential equations, but their standard autoregressive use usually assumes that the instantaneous field $u(t,\cdot)$ is a complete state. This assumption fails for delay equations, distributed-memory sys…

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