arXiv subjects

Peiyi Chen

Publications and source records attributed to Peiyi Chen.

6 recordsLinked to original sources

arXiv2026

Stability of the reconstruction of the heat reflection coefficient in the phonon transport equation

The reflection coefficient is an important thermal property of materials, especially at the nanoscale, and determining this property requires solving an inverse problem based on macroscopic temperature measurements. In this manuscript, we investigate the stability of this inverse problem to infer the reflection coefficient in the phonon transport equation. We show that the problem becomes ill-posed as the system transitions from the ballistic to the diffusive regime, characterized by the Knudsen number converging to zero. Such a stability estimate clarifies the discrepancy observed in previous studies on the well-posedness of this inverse problem. Furthermore, we quantify the rate at which the stability deteriorates with respect to the Knudsen number and confirm the theoretical result with numerical evidence.

math.AP↗

arXiv2026

Inference of interacting kernel in the mean-field regime

We study the problem of reconstructing interaction kernels in systems of interacting agents from macroscopic measurements when posed as an optimization problem. The reconstruction procedure depends on the formulation of the forward model, which may be given either by a finite-dimensional coupled ODE system tracking individual agent trajectories or by a mean-field PDE describing the evolution of the agent density. We investigate the similarities and differences between these two formulations in the mean-field regime. While the first variation derived from the particle system does not provide an unbiased estimator of the first variation associated with the limiting PDE, we prove that, under mild assumptions, the two are close in a weak sense with a convergence rate $\mathcal{O}(N^{-1/2})$. This rate is further confirmed by numerical evidences.

math.NA↗

arXiv2026

Control of a Uniformly Magnetized Plasma with External Electric Fields

Stabilizing plasma dynamics through externally applied electric and magnetic fields is a fundamental control problem. We study this question for a plasma evolving under a uniform external magnetic field. Although the governing dynamics are nonlinear, a linear analysis based on the Laplace-Fourier transform yields actionable insight. In particular, by controlling the location of the roots of the dispersion relation, we propose a general control strategy that restores stability, with the free-streaming solution recovered as a special case. Numerical experiments for Gaussian equilibria and for the Dory-Guest-Harris instability show that the proposed control suppresses the unstable modes and stabilizes the dynamics, in agreement with our theoretical predictions.

physics.plasm-ph↗

arXiv2026

SEW: Strengthening Robustness of Black-box DNN Watermarking via Specificity Enhancement

To ensure the responsible distribution and use of open-source deep neural networks (DNNs), DNN watermarking has become a crucial technique to trace and verify unauthorized model replication or misuse. In practice, black-box watermarks manifest as specific predictive behaviors for specially crafted samples. However, due to the generalization nature of DNNs, the keys to extracting the watermark message are not unique, which would provide attackers with more opportunities. Advanced attack techniques can reverse-engineer approximate replacements for the original watermark keys, enabling subsequent watermark removal. In this paper, we explore black-box DNN watermarking specificity, which refers to the accuracy of a watermark's response to a key. Using this concept, we introduce Specificity-Enhanced Watermarking (SEW), a new method that improves specificity by reducing the association between the watermark and approximate keys. Through extensive evaluation using three popular watermarking benchmarks, we validate that enhancing specificity significantly contributes to strengthening robustness against removal attacks. SEW effectively defends against six state-of-the-art removal attacks, while maintaining model usability and watermark verification performance.

cs.CR↗

arXiv2025

Evaporative Refrigeration Effect in Evaporation and Condensation between Two Parallel Plates

It is well-known that evaporation can lead to cooling. However, little is known that evaporation can actually create a refrigeration effect, i.e., the vapor phase temperature can drop below the temperature of the cooling wall. This possibility was recently pointed out via modeling based on an approximate quasi-continuum approach. This work examines this effect rigorously by studying evaporation and condensation between two parallel plates by coupling the solution of the Boltzmann transport equation in the vapor phase with the continuum treatments in both liquid films. Numerical results show that the vapor phase temperature at the evaporating side can be much lower than the coldest wall temperature at the condensing surface, reaffirming the evaporative refrigeration effect. The present work further reveals that this effect is caused by two mechanisms. While the dominant mechanism is the asymmetry in the molecular distribution between the outgoing and the incoming molecules at the interface, additional cooling occurs within the Knudsen layer due to the sudden expansion, similar to the Joule-Thomson effect, although with subtle differences in that the interfacial expansion is not an isenthalpic process. The impacts of key parameters, including liquid thickness, Knudsen number, and accommodation coefficient, are investigated. The numerical simulation shows that with a thicker vapor, a thinner liquid film, and a larger accommodation coefficient, leads to stronger evaporative refrigeration effect. This work will motivate future experiments to further confirm this prediction and explore its potential applications in air-conditioning, refrigeration, and membrane distillation.

cond-mat.stat-mech↗

arXiv2025

Reconstruction of heat relaxation index in phonon transport equation

For nano-materials, heat conductivity is an ill-defined concept. This classical concept assumes the validity of Fourier's law, which states the heat flux is proportional to temperature gradient, with heat conductivity used to denote this ratio. However, this macroscopic constitutive relation breaks down at nano-scales. Instead, heat is propagated using phonon transport equation, an ab initio model derived from the first principle. In this equation, a material's thermal property is coded in a coefficient termed the relaxation time ($τ$). We study an inverse problem in this paper, by using material's temperature response upon heat injection to infer the relaxation time. This inverse problem is formulated in a PDE-constrained optimization, and numerically solved by Stochastic Gradient Descent (SGD) method and its variants. In the execution of SGD, Fréchet derivative is computed and Lipschitz continuity is proved. This approach, in comparison to the earlier studies, honors the nano-structure of of heat conductivity in a nano-material, and we numerically verify the break down of the Fourier's law.

math.NA↗