arXiv:2410.02136cs.LG2024-10ICLR被引 3

让神经算子学会分离物理参数,提升可解释性与泛化能力。

Disentangled Representation Learning for Parametric Partial Differential Equations

  • 设计多任务神经算子+变分自编码器,从黑箱参数中解耦物理因子
  • 在监督、半监督和无监督场景下均提取出有意义的可解释特征
  • 适合需要理解物理机制的科学计算与逆问题研究者

神经算子在函数空间映射学习中表现优异,可高效近似偏微分方程(PDE)系统的前向求解。然而作为黑箱求解器,其缺乏对驱动系统物理参数的可解释表示。为此,我们提出一种新范式:从神经算子参数中学习解耦表征,以有效解决逆问题。具体地,引入DisentangO——一种新型超神经算子架构,旨在揭示并解耦嵌入于黑箱神经算子参数中的潜在物理变化因子。DisentangO的核心是多任务神经算子结构,通过任务自适应层提炼控制PDE的可变参数,并结合变分自编码器将这些变化分解为可识别的潜在因子。通过学习解耦表征,DisentangO不仅增强物理可解释性,还提升在多样化系统间的鲁棒泛化能力。在监督、半监督与无监督学习情境下的实证评估表明,DisentangO能有效提取出有意义且可解释的潜在特征,弥合了神经算子框架中预测性能与物理理解之间的差距。

原文摘要 · Abstract (English)

Neural operators (NOs) excel at learning mappings between function spaces, serving as efficient forward solution approximators for PDE-governed systems. However, as black-box solvers, they offer limited insight into the underlying physical mechanism, due to the lack of interpretable representations of the physical parameters that drive the system. To tackle this challenge, we propose a new paradigm for learning disentangled representations from NO parameters, thereby effectively solving an inverse problem. Specifically, we introduce DisentangO, a novel hyper-neural operator architecture designed to unveil and disentangle latent physical factors of variation embedded within the black-box neural operator parameters. At the core of DisentangO is a multi-task NO architecture that distills the varying parameters of the governing PDE through a task-wise adaptive layer, alongside a variational autoencoder that disentangles these variations into identifiable latent factors. By learning these disentangled representations, DisentangO not only enhances physical interpretability but also enables more robust generalization across diverse systems. Empirical evaluations across supervised, semi-supervised, and unsupervised learning contexts show that DisentangO effectively extracts meaningful and interpretable latent features, bridging the gap between predictive performance and physical understanding in neural operator frameworks.

神经算子解耦表征可解释性逆问题

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