Physics-Informed Framework for Impact Identification in Aerospace Composites

This application paper presents DebrisTracer, a framework for the reliable tracking of debris in hypervelocity impact fast imaging. These noisy and highly specific datasets capture the ejection of a large number of debris fragments after the impact of a projectile launched at hypervelocity into a target material. The reliable estimation of debris mass and speed distributions is of major importance in aerospace applications. We document how to extend an off-the-shelf topology tracking framework based on critical point extraction and matching, in order to incorporate domain knowledge and physical assumptions. Our approach automatically produces an accurate and reliable debris tracking, enabling an interpretable visual analysis of this complex space-time phenomenon. Extensive experiments demonstrate the accuracy improvements provided by our approach over established tools used by domain experts in terms of physical validation, specifically via the prediction of the experimental ejected mass and crater depth profiles. We illustrate the utility of our approach across several use cases (with varying impact angles and physics). We show that our statistical summaries enable the visual identification of distinct regimes within the debris population, corroborating and refining prior expectations of domain experts. Our database and our C++ implementation are available at this address: https://github.com/tloloum/DebrisTracer.

We present a physics-informed framework for system identification based on randomized stable atomic features. Impulse responses are represented as random superpositions of stable atoms, namely damped complex exponentials associated with poles sampled inside a prescribed disk. Identification is then cast as a convex regularized least-squares problem with optional linear, second-order-cone, and KYP constraints. The approach generalizes random Fourier and random Laplace features to the damped, nonstationary regime relevant to engineering systems while retaining modal interpretability and scalable finite-dimensional computation. The main analytic point is an operator-theoretic Disk-Bochner viewpoint: positive measures over stable poles generate positive-definite kernels with a radius-dependent shift defect, while a converse scalar disk moment representation for an arbitrary kernel is characterized by subnormality of the canonical shift. We prove this statement, establish an RKHS-to-l1 embedding, show that sampled poles induce a valid finite atomic gauge, discuss random-feature convergence, and state sparse-recovery guarantees conditionally on the restricted-eigenvalue properties of the realized disk-Vandermonde or input-output design matrix. We also connect the normalized transfer function problem to Nevanlinna-Pick interpolation and LFT set-membership. The framework directly encodes stability margins, modal localization, DC-gain bounds, monotonicity, passivity, relative degree, settling-time targets, and time/frequency-domain error bounds. Numerical comparisons illustrate how physically meaningful priors can compensate for poor excitation and improve constrained impulse-response recovery in an under-informative data setting.

Physics-informed machine learning is often assessed by curve error, although engineering use depends on downstream decisions: ranking candidates, avoiding infeasible designs and limiting regret. We introduce pinn-gym, an open benchmark for material-conditioned lattice design that couples a transparent reduced-order crush-and-impact oracle with five printable polymer cards, dimensionless force-response targets and a protocol spanning curve fidelity, physical admissibility, top-k retrieval and mass regret. Across per-material, pooled and cross-material settings, low nRMSE is frequently insufficient to identify useful design selections. Physics-informed losses alter trade-offs rather than monotonically improving all metrics, and dimensionless conditioning improves comparability without making transfer symmetric. The benchmark is not a certified material model; within the released oracle, candidate generator and material cards, pinn-gym provides a reproducible testbed for evaluating PIML surrogates as decision systems rather than curve predictors alone.