[2603.13280] A Stability-Aware Frozen Euler Autoencoder for Physics-Informed Tracking in Continuum Mechanics (SAFE-PIT-CM)

Computer Science > Machine Learning arXiv:2603.13280 (cs) [Submitted on 27 Feb 2026 (v1), last revised 24 Mar 2026 (this version, v3)] Title:A Stability-Aware Frozen Euler Autoencoder for Physics-Informed Tracking in Continuum Mechanics (SAFE-PIT-CM) Authors:Emil Hovad View a PDF of the paper titled A Stability-Aware Frozen Euler Autoencoder for Physics-Informed Tracking in Continuum Mechanics (SAFE-PIT-CM), by Emil Hovad View PDF HTML (experimental) 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-p...