A Stability-Aware Frozen Euler Autoencoder for Physics-Informed Tracking in Continuum Mechanics (SAFE-PIT-CM)

TL;DR

SAFE-PIT-CM is a novel autoencoder that uses a stability-aware frozen Euler approach with sub-stepping to accurately recover material diffusion coefficients and physical fields from coarse temporal data, ensuring stability and efficiency.

Contribution

It introduces a stability-aware frozen Euler autoencoder with sub-stepping for PDE-based tracking, enabling stable and accurate parameter and field recovery from coarse temporal observations.

Findings

Restores stability with negligible cost using sub-stepping.

Achieves near-perfect accuracy in recovering diffusion coefficients and fields.

Generalizes to any PDE with convolutional finite-difference discretization.

Abstract

Material parameters such as thermal diffusivity govern how microstructural fields evolve during processing, but difficult to measure directly. The Stability-Aware Frozen Euler Physics-Informed Tracking for Continuum Mechanics (SAFE-PIT-CM), is an autoencoder that embeds a frozen convolutional layer as a differentiable PDE solver in its latent-space transition to jointly recover diffusion coefficients and the underlying physical field from temporal observations. When temporal snapshots are saved at intervals coarser than the simulation time step, a single forward Euler step violates the von Neumann stability condition, forcing the learned coefficient to collapse to an unphysical value. Sub-stepping with SAFE restores stability at negligible cost each sub-step is a single frozen convolution, far cheaper than processing more frames with recovery error converging monotonically with substep count. Validated on thermal diffusion in metals, the method recovers both the diffusion coefficient and the physical field with near-perfect accuracy, both with and yet without pre-training. Backpropagation through the frozen operator supervises an attention-based parameter estimator without labelled data. The architecture generalises to any PDE with a convolutional finite-difference discretisation.