Latent Space Dynamics Identification for Interface Tracking with Application to Shock-Induced Pore Collapse

TL;DR

LaSDI-IT is a data-driven framework that accurately models moving interfaces in physical systems using latent space dynamics and interface-aware auto-encoders, demonstrated on shock-induced pore collapse.

Contribution

It introduces a novel auto-encoder architecture combining physical field reconstruction with interface encoding, enabling efficient interface tracking without detailed physical models.

Findings

Achieves <9% prediction error across parameter space.

Recovers key quantities like pore area and hot spot formation.

106x faster than high-fidelity simulations.

Abstract

Capturing sharp, evolving interfaces remains a central challenge in reduced-order modeling, especially when data is limited and the system exhibits localized nonlinearities or discontinuities. We propose LaSDI-IT (Latent Space Dynamics Identification for Interface Tracking), a data-driven framework that combines low-dimensional latent dynamics learning with explicit interface-aware encoding to enable accurate and efficient modeling of physical systems involving moving material boundaries. At the core of LaSDI-IT is a revised auto-encoder architecture that jointly reconstructs the physical field and an indicator function representing material regions or phases, allowing the model to track complex interface evolution without requiring detailed physical models or mesh adaptation. The latent dynamics are learned through linear regression in the encoded space and generalized across parameter regimes using Gaussian process interpolation with greedy sampling. We demonstrate LaSDI-IT on the problem of shock-induced pore collapse in high explosives, a process characterized by sharp temperature gradients and dynamically deforming pore geometries. The method achieves relative prediction errors below 9% across the parameter space, accurately recovers key quantities of interest such as pore area and hot spot formation, and matches the performance of dense training with only half the data. This latent dynamics prediction was 106 times faster than the conventional high-fidelity simulation, proving its utility for multi-query applications. These results highlight LaSDI-IT as a general, data-efficient framework for modeling discontinuity-rich systems in computational physics, with potential applications in multiphase flows, fracture mechanics, and phase change problems.