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arxiv: 2507.10647 · v2 · submitted 2025-07-14 · ⚛️ physics.comp-ph

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

Seung Whan Chung , Christopher Miller , Youngsoo Choi , Paul Tranquilli , H. Keo Springer , Kyle Sullivan This is my paper

Pith reviewed 2026-05-19 04:42 UTC · model grok-4.3

classification ⚛️ physics.comp-ph
keywords latent space dynamicsinterface trackingreduced-order modelingshock-induced pore collapseauto-encoderGaussian processdata-driven modelinghigh explosives
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The pith

A revised auto-encoder in latent dynamics identification tracks moving material interfaces in shock-induced pore collapse with errors below 9 percent.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces LaSDI-IT to handle systems with sharp evolving interfaces by learning dynamics in a low-dimensional latent space. It relies on a revised auto-encoder that reconstructs both the physical field and an indicator function marking material regions, which lets the model follow complex boundary changes without explicit physical rules or remeshing. The approach is shown on shock-induced pore collapse in high explosives, where it recovers pore area and hot spot formation while using only half the usual training data. Predictions run 106 times faster than full simulations, which matters for repeated runs across different conditions. This points to a data-efficient way to model discontinuity-heavy physics problems.

Core claim

LaSDI-IT combines a revised auto-encoder that jointly reconstructs the physical field and a material indicator function with linear regression for latent dynamics and Gaussian process interpolation for parameter generalization. Applied to shock-induced pore collapse, this framework achieves relative prediction errors below 9 percent, accurately captures pore area and hot spot formation, matches dense training performance with half the data, and provides predictions 106 times faster than high-fidelity simulations.

What carries the argument

The revised auto-encoder architecture that jointly reconstructs the physical field and an indicator function for material regions or phases.

If this is right

  • Relative prediction errors remain below 9 percent across the parameter space.
  • Key quantities of interest such as pore area and hot spot formation are recovered accurately.
  • The method matches the performance of dense training while using only half the data.
  • Latent dynamics predictions run 106 times faster than conventional high-fidelity simulations.
  • The framework extends to other systems with sharp interfaces such as multiphase flows and fracture mechanics.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the joint field-plus-indicator reconstruction succeeds here, the same encoding step could support interface tracking in phase-change problems without changing the mesh.
  • Gaussian process interpolation over the latent space may reduce the number of full simulations needed when exploring wider ranges of material properties.
  • Data efficiency at half the samples suggests the approach could lower the upfront cost of building training sets for similar discontinuity-rich models in other fields.

Load-bearing premise

That jointly reconstructing the physical field and an indicator function for material regions will enable accurate tracking of complex interface evolution without detailed physical models or mesh adaptation.

What would settle it

A new simulation run on a different pore geometry or shock strength where the predicted interfaces and hot spots deviate from high-fidelity results by more than 9 percent relative error.

Figures

Figures reproduced from arXiv: 2507.10647 by Christopher Miller, H. Keo Springer, Kyle Sullivan, Paul Tranquilli, Seung Whan Chung, Youngsoo Choi.

Figure 1
Figure 1. Figure 1: Schematic diagram of latent space dynamics identification framework. [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 1
Figure 1. Figure 1: If initial training data is scarce in parameter space and not sufficient for effective parametric model training, data at additional parameter points must be collected on the fly in the training process. Gaussian process also provides the uncertainties in the dynamics coefficients, which are useful er￾ror metrics in the absence of ground truth. In GPLaSDI framework, The uncertainties of Ξ(p ∗ ) (22a) are f… view at source ↗
Figure 2
Figure 2. Figure 2: (a) Temperature field T of high explosive (HE) material with 0K indicating non-HE region, and (b) T with mask T > 0. features a temperature field defined only outside an interface that evolves over time. As discussed in Section 2, standard autoencoders suffer from spectral bias, favoring smooth, low-frequency features while underrepresent￾ing high-frequency or discontinuous structures. This makes them ill-… view at source ↗
Figure 3
Figure 3. Figure 3: Schematic of autoencoder architecture. While the encoder could also be modified to take ϕ as an input as well, we take the rationale that the autoencoder must be capable of extracting 13 [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Geometric parameterization p = (p1, p2) of the elliptical pore. simulations involve a 3 µm thick aluminum flyer impacting a slab of HE con￾taining a single pore, generating a shock pressure of approximately 11.5 GPa. 17 [PITH_FULL_IMAGE:figures/full_fig_p018_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (a) Reconstruction of the state field with the standard AE, and (b) its point-wise [PITH_FULL_IMAGE:figures/full_fig_p020_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Loss history of the standard AE and revised AE. [PITH_FULL_IMAGE:figures/full_fig_p022_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: (a) Reconstruction of the temperature field with the AE in LaSDI-IT, and (b) [PITH_FULL_IMAGE:figures/full_fig_p022_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Temporal (a) average and (b) standard deviation of HE temperature ( [PITH_FULL_IMAGE:figures/full_fig_p023_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Gaussian-process based coefficient interpolation at the 14th iteration: (a) Mean [PITH_FULL_IMAGE:figures/full_fig_p025_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Gaussian-process based greedy sampling: (a) solution uncertainty (23) and [PITH_FULL_IMAGE:figures/full_fig_p026_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: The worst case prediction (12◦ , 1.2µm) from greedy-sampling training: (a) hot spot area (T > 800K); (b) pore area; and (c) maximum temperature. and the instantaneous maximum temperature Tk,max(p) = max x Tk(x; p). (39) [PITH_FULL_IMAGE:figures/full_fig_p028_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Ground truth (left), prediction (middle), and the error (right) of the worst case [PITH_FULL_IMAGE:figures/full_fig_p029_12.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces LaSDI-IT, a data-driven framework for modeling physical systems with moving material interfaces. It features a revised auto-encoder that jointly reconstructs the physical field and an indicator function for material regions, learns linear latent dynamics via regression, and generalizes across parameters using Gaussian process interpolation with greedy sampling. The framework is applied to shock-induced pore collapse in high explosives, claiming relative prediction errors below 9%, accurate recovery of pore area and hot spot formation, matching dense training performance with half the data, and a 106x speedup compared to high-fidelity simulations.

Significance. If substantiated, the results demonstrate a general and data-efficient approach for reduced-order modeling of discontinuity-rich systems. The explicit handling of interfaces via the indicator function reconstruction addresses a significant challenge in latent space methods for problems involving sharp gradients and deforming geometries. The reported speedup and data efficiency would be particularly valuable for multi-query scenarios in computational physics, such as parameter studies in explosive modeling. The work builds on latent dynamics identification with an interface-aware extension.

major comments (2)
  1. [Abstract] Abstract: The central performance claims (relative errors below 9%, accurate recovery of pore area and hot spot formation, 106x speedup, and matching dense training with half the data) rest on an unexamined experimental setup. No details are provided on training data volume, validation splits, error bar computation, or separate quantification of indicator function reconstruction error versus field error.
  2. [Section 3] Section 3 (Methodology, auto-encoder description): The revised auto-encoder jointly reconstructs the physical field and indicator function to enable interface tracking without physical models or mesh adaptation. For shock-induced pore collapse with sharp temperature gradients and deforming geometries, it is unclear if the architecture or loss explicitly enforces discontinuity preservation (e.g., via level-set penalties or gradient-based terms). Standard auto-encoder smoothing could propagate into the linear latent regression and GP interpolation, directly threatening the reported accuracy and data-efficiency results.
minor comments (2)
  1. [Figures] Figure captions should specify the exact parameter values and time instances for the visualized snapshots to improve reproducibility and allow direct comparison with the reported errors.
  2. [Section 3] The notation distinguishing the latent variables for the physical field versus the indicator function component should be clarified in the equations to avoid ambiguity in the joint reconstruction loss.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and insightful comments. We address each major comment point by point below, providing clarifications based on the manuscript content and making revisions where they strengthen the presentation without misrepresenting the work.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central performance claims (relative errors below 9%, accurate recovery of pore area and hot spot formation, 106x speedup, and matching dense training with half the data) rest on an unexamined experimental setup. No details are provided on training data volume, validation splits, error bar computation, or separate quantification of indicator function reconstruction error versus field error.

    Authors: We agree that the abstract would be strengthened by briefly summarizing the experimental setup to better support the performance claims. The manuscript provides these details in Sections 4 (Data Generation and Training) and 5 (Numerical Results), including the number of high-fidelity simulations used, the train/validation approach, and error metrics. To address the comment directly, we have revised the abstract to include a concise statement on the training configuration and added a dedicated paragraph in Section 5 that separately quantifies the indicator function reconstruction error relative to the physical field error. This change improves transparency while preserving the original results and claims. revision: yes

  2. Referee: [Section 3] Section 3 (Methodology, auto-encoder description): The revised auto-encoder jointly reconstructs the physical field and indicator function to enable interface tracking without physical models or mesh adaptation. For shock-induced pore collapse with sharp temperature gradients and deforming geometries, it is unclear if the architecture or loss explicitly enforces discontinuity preservation (e.g., via level-set penalties or gradient-based terms). Standard auto-encoder smoothing could propagate into the linear latent regression and GP interpolation, directly threatening the reported accuracy and data-efficiency results.

    Authors: The referee correctly notes that the original description leaves open the question of explicit discontinuity preservation. The joint reconstruction objective in the revised auto-encoder is designed to mitigate smoothing by requiring accurate recovery of the indicator function at material boundaries, which in turn guides the latent representation. No explicit level-set penalties or additional gradient terms were present in the loss. We have therefore revised Section 3 to include a clearer explanation of this design choice and its rationale for the present application, along with supporting analysis showing that interface sharpness is maintained sufficiently to achieve the reported accuracy. This addition addresses the concern without requiring architectural changes. revision: partial

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The LaSDI-IT framework trains a revised auto-encoder on simulation snapshots to jointly reconstruct fields and material indicator functions, then fits linear latent dynamics via regression and generalizes via Gaussian process interpolation with greedy sampling. Reported relative errors below 9% and recovery of pore area/hot spots are measured on held-out parameter instances and compared against dense training baselines, not on the same fitted quantities. No equation or claim reduces a prediction to an input by construction, no uniqueness theorem is imported from self-citation to force the architecture, and the speed-up claim is a direct timing comparison against high-fidelity simulation. The derivation chain is therefore self-contained empirical validation of a data-driven pipeline.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The central claim rests on the premise that joint reconstruction of field and indicator function suffices to capture interface motion without explicit physics or mesh adaptation; no free parameters, axioms, or invented entities are enumerated in the abstract.

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