新的变分方法提高了长时程偏微分方程预测的稳定性

作者 PulseAugur 编辑部 · [1 个来源] · 2026-09-16 04:00

研究人员开发了一种新的变分方法，以提高神经偏微分方程（PDE）求解器的长时程预测能力。该方法引入了潜在马尔可夫动力学，其中物理状态由分布表示并通过概率转换进行演化。该框架被实例化为变分自编码马尔可夫算子（VAMO），结合了潜在场、结构化高斯扰动和神经算子转换，以正则化学习到的动力学并减少误差累积。在流体动力学基准测试上的实证结果表明，与现有基线相比，VAMO在扩展时程上显著提高了滚动稳定性和预测精度。 AI

影响增强了复杂物理系统中长期预测的神经网络模型的稳定性和准确性。

排序理由详细介绍求解偏微分方程新方法的学术论文。[lever_c_demoted from research: ic=1 ai=1.0]

在 arXiv stat.ML 阅读 →

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报道来源 [1]

arXiv stat.ML TIER_1 English(EN) · Junyi Liao, Johann Guilleminot, Vahid Tarokh · 2026-09-16 04:00

Stable by Construction: Variational Latent Markov Operators for Long-Horizon PDE Prediction

arXiv:2609.16621v1 Announce Type: cross Abstract: Neural PDE solvers provide efficient surrogates for time-dependent physical systems, but autoregressive prediction over long horizons remains challenging because local errors can induce distribution shift and accumulate under recu…

本文如何被排名

报道来源 [1]

Stable by Construction: Variational Latent Markov Operators for Long-Horizon PDE Prediction

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