Disentangled Representation Learning for Parametric Partial Differential Equations

TL;DR

This paper introduces DisentangO, a neural operator architecture that learns interpretable latent physical factors from neural operator parameters, improving physical understanding and generalization in PDE systems.

Contribution

It proposes a novel hyper-neural operator with disentangled representations, combining multi-task learning and variational autoencoders for interpretability in neural operators.

Findings

Effectively extracts meaningful latent features.

Enhances physical interpretability of neural operators.

Improves generalization across diverse PDE systems.

Abstract

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.