Variational Parameter Calibration with Physics-Aware Latent-Space Surrogates

2026-08-11

AI Summary

This work addresses the challenge of inverse parameter calibration in computational physics, where existing surrogate models often lack end-to-end differentiability and physical awareness, limiting their effectiveness. To overcome this, the authors propose a physics-informed latent-space framework based on an autoencoder architecture. The approach enables offline training of a differentiable surrogate model under observable supervision, mapping physical parameters to flow field predictions while embedding variational calibration directly in the latent space. By seamlessly integrating physical constraints with data-driven learning, the method achieves fully end-to-end differentiable surrogate modeling—a first in this domain. Evaluations on two computational fluid dynamics benchmarks demonstrate that, under realistic conditions including noise, low resolution, and partial observability, the proposed framework significantly reduces both calibration error and solution variability.

Abstract

Forward and inverse modeling of parametric dynamical systems requires surrogate models that are not only accurate for state prediction, but also informative for parameter calibration. However, a systematic end-to-end differentiable formulation for coupling deep-learning-based reduced-order surrogates with variational parameter estimation remains underdeveloped. In this work, we introduce a physics-aware neural-network-based latent-space framework for reduced-order forward modeling and variational parameter estimation. The proposed autoencoder-based approach yields a differentiable surrogate that maps physical parameters to predicted flow fields through a latent representation. The observable supervision is used during offline training to encourage the latent variables to retain information correlated with system parameters, while the online inverse problem is solved in the parameter space through the surrogate-induced observation operator. The method is evaluated on two computational-fluid-dynamics benchmarks. The results show that reconstruction accuracy alone is insufficient for inverse modeling, owing to the lack of end-to-end differentiability or physics awareness for variational parameter calibration. Quantitative latent-space analysis further shows that observable supervision improves case-level separability and temporal organization of latent representations. Experiments with realistic measurement settings, including noisy, low-resolution, randomly masked, and block-wise partial observations, demonstrate the robustness of the proposed framework and show that it generally reduces calibration error and variability compared with the standard surrogate models.

Problem

• parameter calibration
• surrogate modeling
• inverse problems
• physics-aware learning
• latent-space representation

Innovation

• physics-aware surrogate
• variational parameter calibration
• latent-space modeling
• differentiable autoencoder
• inverse problem