Adversarial Disentanglement by Backpropagation with Physics-Informed Variational Autoencoder

TL;DR

This work tackles the challenge of inference under partial physics knowledge in structural health monitoring by introducing a Disentangled Physics-Informed VAE (DPIVAE). The model partitions latent space into physics-grounded and data-driven components and employs adversarial training to prevent the data-driven path from overriding the known physics, enabling interpretable, domain- and class-aware representations. Through three synthetic SHM case studies (beam, oscillator, bridge), DPIVAE demonstrates the ability to disentangle physics from confounders, perform conditional generation, and provide calibrated uncertainty bounds, while achieving competitive predictive performance. The approach advances physics-informed machine learning by combining interpretability with data-driven flexibility, offering practical benefits for damage identification and uncertainty quantification in engineering systems.

Abstract

Inference and prediction under partial knowledge of a physical system is challenging, particularly when multiple confounding sources influence the measured response. Explicitly accounting for these influences in physics-based models is often infeasible due to epistemic uncertainty, cost, or time constraints, resulting in models that fail to accurately describe the behavior of the system. On the other hand, data-driven machine learning models such as variational autoencoders are not guaranteed to identify a parsimonious representation. As a result, they can suffer from poor generalization performance and reconstruction accuracy in the regime of limited and noisy data. We propose a physics-informed variational autoencoder architecture that combines the interpretability of physics-based models with the flexibility of data-driven models. To promote disentanglement of the known physics and confounding influences, the latent space is partitioned into physically meaningful variables that parametrize a physics-based model, and data-driven variables that capture variability in the domain and class of the physical system. The encoder is coupled with a decoder that integrates physics-based and data-driven components, and constrained by an adversarial training objective that prevents the data-driven components from overriding the known physics, ensuring that the physics-grounded latent variables remain interpretable. We demonstrate that the model is able to disentangle features of the input signal and separate the known physics from confounding influences using supervision in the form of class and domain observables. The model is evaluated on a series of synthetic case studies relevant to engineering structures, demonstrating the feasibility of the proposed approach.

Figures (12)

• Figure 1: Illustrative examples of the problem setting: a) Beam, b) Oscillator, and c) One member of a population of bridges. The objective is to learn components of the measured response (bottom row) that are not explicitly included in the nominal physics-based model (top row) using observations of related quantities.
• Figure 2: Demonstration of the data-driven component of the decoder $g_{\bm{\theta}}(\bm{z}_\mathrm{c}, \bm{z}_\mathrm{y})$ overriding the physics-based model $f(\bm{z}_\mathrm{x})$. The effect of varying the position of the load $x_\mathrm{F}$ should be described by the known physics, but is instead captured by the data-driven components.
• Figure 3: a) Schematic diagram illustrating the components of the model and the encoder-decoder architecture, and b) Detailed structure of the dependencies in the generative and inference models.
• Figure 4: Illustration of the procedure used to obtain the full and nominal physics-based models (left), and to generate the datasets used in the case studies (right).
• Figure 5: Mean prediction and $\pm 2\sigma$ uncertainty bounds for the physics-based $\hat{\bm{x}}_\mathrm{p}$ and data-driven $\hat{\bm{x}}_\mathrm{d}$ components, and combined prediction $\hat{\bm{x}}$ while traversing the generative factors. The input response measurements are denoted as dots in the bottom row.