Neural Modes: Self-supervised Learning of Nonlinear Modal Subspaces

TL;DR

This paper introduces a self-supervised learning method that constructs physics-based subspaces for real-time simulation by directly minimizing mechanical energy, resulting in more accurate, interpretable, and physically consistent models.

Contribution

It presents a novel self-supervised approach that improves upon geometric methods by incorporating physical energy minimization, enhancing generalization and interpretability.

Findings

Learned subspaces reflect physical equilibrium constraints

Method reduces overfitting compared to previous approaches

Produces more physically accurate and interpretable models

Abstract

We propose a self-supervised approach for learning physics-based subspaces for real-time simulation. Existing learning-based methods construct subspaces by approximating pre-defined simulation data in a purely geometric way. However, this approach tends to produce high-energy configurations, leads to entangled latent space dimensions, and generalizes poorly beyond the training set. To overcome these limitations, we propose a self-supervised approach that directly minimizes the system's mechanical energy during training. We show that our method leads to learned subspaces that reflect physical equilibrium constraints, resolve overfitting issues of previous methods, and offer interpretable latent space parameters.