arXiv subjects

Boya Liu

Publications and source records attributed to Boya Liu.

14 recordsLinked to original sources

arXiv2026

Recovery of time-dependent coefficients for the convection-diffusion equation on conformally transversally anisotropic manifolds from partial data

We study an inverse problem of recovering a time-dependent convection term and density coefficient of the convection-diffusion equation from partial data on a certain type of compact Riemannian manifold of dimension at least three. We prove that the knowledge of a partial input-output operator determines both coefficients uniquely up to a natural gauge. Our geometric setting is conformally transversally anisotropic manifolds, that is, compact Riemannian manifolds with boundary that are conformally embedded into a product of the Euclidean line and a transversal manifold. Additionally, we assume that the attenuated geodesic ray transforms of one-forms and functions are both injective on the transversal manifold.

math.AP↗

arXiv2026

Snatcher: Apple Find My Network Exposes Your Lost Devices To Strangers

Apple's Find My network connects nearly one billion devices to locate missing property via Bluetooth Low Energy (BLE). This paper reveals that insecure BLE advertisements and design tradeoffs allow unauthorized discovery and physical theft of lost Apple devices. We develop Snatcher, an attack and analysis framework implemented fully on Android smartphones without specialized hardware. Snatcher identifies vulnerabilities in unencrypted BLE advertisements, unauthenticated acoustic triggers, and slow MAC address randomization. Through three levels - sound-based direction finding, RSSI-IMU sensor-fusion navigation, and spatial-temporal clustering - our Android-based platform physically tracks and locates lost Apple accessories and devices in real-world tests. Our results highlight a crucial conflict between privacy protection, anti-stalking design, and physical security, urging Apple to strengthen Find My defenses.

cs.CR↗

arXiv2026

Inverse problems for a nonlinear dynamical Schr\"odinger operator with magnetic potential

We study two inverse problems for a nonlinear dynamical Schr\"odinger equation with time-dependent magnetic and electric potentials. Under suitable analyticity assumptions, we show that the associated Dirichlet-to-Neumann map uniquely determines the linear magnetic potential and all coefficients of the nonlinear electric potential. We establish both full-data and partial-data uniqueness results. For the partial data problem, assuming that the coefficients are known in a neighborhood of the boundary, uniqueness is obtained using measurements made on arbitrarily small open subsets of the boundary. In addition, we establish the well-posedness of the forward problem.

math.AP↗

arXiv2025

DevPiolt: Operation Recommendation for IoT Devices at Xiaomi Home

Operation recommendation for IoT devices refers to generating personalized device operations for users based on their context, such as historical operations, environment information, and device status. This task is crucial for enhancing user satisfaction and corporate profits. Existing recommendation models struggle with complex operation logic, diverse user preferences, and sensitive to suboptimal suggestions, limiting their applicability to IoT device operations. To address these issues, we propose DevPiolt, a LLM-based recommendation model for IoT device operations. Specifically, we first equip the LLM with fundamental domain knowledge of IoT operations via continual pre-training and multi-task fine-tuning. Then, we employ direct preference optimization to align the fine-tuned LLM with specific user preferences. Finally, we design a confidence-based exposure control mechanism to avoid negative user experiences from low-quality recommendations. Extensive experiments show that DevPiolt significantly outperforms baselines on all datasets, with an average improvement of 69.5% across all metrics. DevPiolt has been practically deployed in Xiaomi Home app for one quarter, providing daily operation recommendations to 255,000 users. Online experiment results indicate a 21.6% increase in unique visitor device coverage and a 29.1% increase in page view acceptance rates.

cs.AI↗

arXiv2025

On a partial data inverse problem for the semi-linear wave equation

We show that a partial Dirichlet-to-Neumann map, where the measurement set is arbitrarily small, uniquely determines the time-dependent nonlinearity of order three or higher in a semi-linear wave equation up to natural obstructions on a Lorentzian manifold with boundary. In particular, we do not impose any geometric or size restrictions on the measurement set. The proof relies on the technique of higher order linearization combined with the construction of Gaussian beams with reflections on the boundary.

math.AP↗

arXiv2025

A Hyperbolic Inverse Problem for lower order terms on a closed manifold with disjoint data

We study the unique recovery of time-independent lower order terms appearing in the symmetric first order perturbation of the Riemannian wave equation by sending and measuring waves in disjoint open sets of \textit{a priori} known closed Riemannian manifold. In particular, we show that if the set where we capture the waves satisfies a geometric control condition as well as a certain local symmetry condition for the distance functions, then the aforementioned measurement is sufficient to recover the lower order terms up to the natural gauge. For instance, our result holds if the complement of the receiver set is contained in a simple Riemannian manifold.

math.AP↗

arXiv2025

H\"older stability of an inverse spectral problem for the magnetic Schr\"odinger operator on a simple manifold

We show that on a simple Riemannian manifold, the electric potential and the solenoidal part of the magnetic potential appearing in the magnetic Schr\"odinger operator can be recovered H\"older stably from the boundary spectral data. This data contains the eigenvalues and the Neumann traces of the corresponding sequence of Dirichlet eigenfunctions of the operator. Our proof contains two parts, which we present in the reverse order. (1) We show that the boundary spectral data can be stably obtained from the Dirichlet-to-Neumann map associated with the respective initial boundary value problem for a hyperbolic equation, whose leading order terms are a priori known. (2) We construct geometric optics solutions to the hyperbolic equation, which reduce the stable recovery of the lower order terms to the stable inversion of the geodesic ray transform of one-forms and functions.

math.AP↗

arXiv2024

Stable determination of the first order perturbation of the biharmonic operator from partial data

We consider an inverse boundary value problem for the biharmonic operator with the first order perturbation in a bounded domain of dimension three or higher. Assuming that the first and the zeroth order perturbations are known in a neighborhood of the boundary, we establish log-type stability estimates for these perturbations from a partial Dirichlet-to-Neumann map. Specifically, measurements are taken only on an arbitrarily small open subsets of the boundary.

math.AP↗

arXiv2023

Stability estimates for an inverse boundary value problem for biharmonic operators with first order perturbation from partial data

In this paper we study an inverse boundary value problem for the biharmonic operator with first order perturbation. Our geometric setting is that of a bounded simply connected domain in the Euclidean space of dimension three or higher. Assuming that the inaccessible portion of the boundary is flat, and we have knowledge of the Dirichlet-to-Neumann map on the complement, we prove logarithmic type stability estimates for both the first and the zeroth order perturbation of the biharmonic operator.

math.AP↗

arXiv2023

Recovery of a time-dependent potential in hyperbolic equations on conformally transversally anisotropic manifolds

We study an inverse problem of determining a time-dependent potential appearing in the wave equation in conformally transversally anisotropic manifolds of dimension three or higher. These are compact Riemannian manifolds with boundary that are conformally embedded in a product of the real line and a transversal manifold. Under the assumption of the attenuated geodesic ray transform being injective on the transversal manifold, we prove the unique determination of time-dependent potentials from the knowledge of a certain partial Cauchy data set.

math.AP↗

arXiv2023

Partial data inverse problem for hyperbolic equation with time-dependent damping coefficient and potential

We study an inverse problem of determining a time-dependent damping coefficient and potential appearing in the wave equation in a compact Riemannian manifold of dimension three or higher. More specifically, we are concerned with the case of conformally transversally anisotropic manifolds, or in other words, compact Riemannian manifolds with boundary conformally embedded in a product of the Euclidean line and a transversal manifold. With an additional assumption of the attenuated geodesic ray transform being injective on the transversal manifold, we prove that the knowledge of a certain partial Cauchy data set determines time-dependent damping coefficient and potential uniquely.

math.AP↗

arXiv2022

Three travel time inverse problems on simple Riemannian manifolds

We provide new proofs based on the Myers-Steenrod theorem to confirm that travel time data, travel time difference data and the broken scattering relations determine a simple Riemannian metric on a disc up to the natural gauge of a boundary fixing diffeomorphism. Our method of the proof leads to a Lipschitz-type stability estimate for the first two data sets in the class of simple metrics.

math.DG↗

arXiv2020

Stability estimates in a partial data inverse boundary value problem for biharmonic operators at high frequencies

We study the inverse boundary value problems of determining a potential in the Helmholtz type equation for the perturbed biharmonic operator from the knowledge of the partial Cauchy data set. Our geometric setting is that of a domain whose inaccessible portion of the boundary is contained in a hyperplane, and we are given the Cauchy data set on the complement. The uniqueness and logarithmic stability for this problem were established in [37] and [7], respectively. We establish stability estimates in the high frequency regime, with an explicit dependence on the frequency parameter, under mild regularity assumptions on the potentials, sharpening those of [7].

math.AP↗

arXiv2018

Global identifiability of low regularity fluid parameters in acoustic tomography of moving fluid

We are concerned with inverse boundary problems for first order perturbations of the Laplacian, which arise as model operators in the acoustic tomography of a moving fluid. We show that the knowledge of the Dirichlet--to--Neumann map on the boundary of a bounded domain in $\mathbb{R}^n$, $n\ge 3$, determines the first order perturbation of low regularity up to a natural gauge transformation, which sometimes is trivial. As an application, we recover the fluid parameters of low regularity from boundary measurements, sharpening the regularity assumptions in the recent results of [1] and [3]. In particular, we allow some fluid parameters to be discontinuous.

math.AP↗