arXiv subjects

Peng Xie

Publications and source records attributed to Peng Xie.

At least 37 records · Page 2Linked to original sources

arXiv2026

Data-Driven Reachability Analysis Using Matrix Perturbation Theory

We propose a matrix zonotope perturbation framework that leverages matrix perturbation theory to characterize how noise-induced distortions alter the dynamics within sets of models. The framework derives interpretable Cai-Zhang bounds for matrix zonotopes (MZs) and extends them to constrained matrix zonotopes (CMZs). Motivated by this analysis and the computational burden of CMZ-based reachable-set propagation, we introduce a coefficient-space approximation in which the constrained coefficient space of the CMZ is over-approximated by an unconstrained zonotope. Replacing CMZ-constrained-zonotope (CZ) products with unconstrained MZ-zonotope multiplication yields a simpler and more scalable reachable-set update. Experimental results demonstrate that the proposed method is substantially faster than the standard CMZ approach while producing reachable sets that are less conservative than those obtained with existing MZ-based methods, advancing practical, accurate, and real-time data-driven reachability analysis.

eess.SY↗

arXiv2026

Informed Hybrid Zonotope-based Motion Planning Algorithm

Optimal path planning in nonconvex free spaces poses substantial computational challenges. A common approach formulates such problems as mixed-integer linear programs (MILPs); however, solving general MILPs is computationally intractable and severely limits scalability. To address these limitations, we propose HZ-MP, an informed Hybrid Zonotope-based Motion Planner, which decomposes the obstacle-free space and performs low-dimensional face sampling guided by an ellipsotope heuristic, thereby concentrating exploration on promising transition regions. This structured exploration mitigates the excessive wasted sampling that degrades existing informed planners in narrow-passage or enclosed-goal scenarios. We prove that HZ-MP is probabilistically complete and asymptotically optimal, and demonstrate empirically that it converges to high-quality trajectories within a small number of iterations.

cs.RO↗

arXiv2026

From Points to Sets: Set-Based Safety Verification in the Latent Space

We extend latent representation methods for safety control design to set-valued states. Recent work has shown that barrier functions designed in a learned latent space can transfer safety guarantees back to the original system, but these methods evaluate certificates at single state points, ignoring state uncertainty. A fixed safety margin can partially address this but cannot adapt to the anisotropic and time-varying nature of the uncertainty gap across different safety constraints. We instead represent the system state as a zonotope, propagate it through the encoder to obtain a latent zonotope, and evaluate certificates over the worst case of the entire set. On a 16-dimensional quadrotor suspended-load gate passage task, set-valued evaluation achieves 5/5 collision-free passages, compared to 1/5 for point-based evaluation and 2/5 for a fixed-margin baseline. Set evaluation reports safety in 44.4% of per-head evaluations versus 48.5% for point-based, and this greater conservatism detects 4.1% blind spots where point evaluation falsely certifies safety, enabling earlier corrective control. The safety gap between point and set evaluation varies up to $12\times$ across certificate heads, explaining why no single fixed margin suffices and confirming the need for per-head, per-timestep adaptation, which set evaluation provides by construction.

eess.SY↗

arXiv2026

Data-Driven Reachability Analysis with Optimal Input Design

This paper addresses the conservatism in data-driven reachability analysis for discrete-time linear systems subject to bounded process noise, where the system matrices are unknown and only input--state trajectory data are available. Building on the constrained matrix zonotope (CMZ) framework, two complementary strategies are proposed to reduce conservatism in reachable-set over-approximations. First, the standard Moore--Penrose pseudoinverse is replaced with a row-norm-minimizing right inverse computed via a second-order cone program (SOCP), which directly reduces the size of the resulting model set, yielding tighter generators and less conservative reachable sets. Second, an online A-optimal input design strategy is introduced to improve the informativeness of the collected data and the conditioning of the resulting model set, thereby reducing uncertainty. The proposed framework extends naturally to piecewise affine systems through mode-dependent data partitioning. Numerical results on a five-dimensional stable LTI system and a two-dimensional piecewise affine system demonstrate that combining designed inputs with the row-norm right inverse significantly reduces conservatism compared to a baseline using random inputs and the pseudoinverse, leading to tighter reachable sets for safety verification.

eess.SY↗

arXiv2026

Bridging Data-Driven Reachability Analysis and Statistical Estimation via Constrained Matrix Convex Generators

Data-driven reachability analysis enables safety verification when first-principles models are unavailable. This requires constructing sets of system models consistent with measured trajectories and noise assumptions. Existing approaches rely on zonotopic or box-based approximations, which do not fit the geometry of common noise distributions such as Gaussian disturbances and can lead to significant conservatism, especially in high-dimensional settings. This paper builds on ellipsotope-based representations to introduce mixed-norm uncertainty sets for data-driven reachability. The highest-density region defines the exact minimum-volume noise confidence set, while Constrained Convex Generators (CCG) and their matrix counterpart (CMCG) provide compatible geometric representations at the noise and parameter level. We show that the resulting CMCG coincides with the maximum-likelihood confidence ellipsoid for Gaussian disturbances, while remaining strictly tighter than constrained matrix zonotopes for mixed bounded-Gaussian noise. For non-convex noise distributions such as Gaussian mixtures, a minimum-volume enclosing ellipsoid provides a tractable convex surrogate. We further prove containment of the CMCG times CCG product and bound the conservatism of the Gaussian-Gaussian interaction. Numerical examples demonstrate substantially tighter reachable sets compared to box-based approximations of Gaussian disturbances. These results enable less conservative safety verification and improve the accuracy of uncertainty-aware control design.

eess.SY↗

arXiv2026

Open3DBench: Open-Source Benchmark for 3D-IC Backend Implementation and PPA Evaluation

This work introduces Open3DBench, an open-source 3D-IC backend implementation benchmark built upon the OpenROAD-flow-scripts framework, enabling comprehensive evaluation of power, performance, area, and thermal metrics. Our proposed flow supports modular integration of 3D partitioning, placement, 3D routing, RC extraction, and thermal simulation, aligning with advanced 3D flows that rely on commercial tools and in-house scripts. We present two foundational 3D placement algorithms: Open3D-Tiling, which emphasizes regular macro placement, and Open3D-DMP, which enhances wirelength optimization through cross-die co-placement with analytical placer DREAMPlace. Experimental results show significant improvements in area (51.19%), wirelength (24.06%), timing (30.84%), and power (5.72%) compared to 2D flows. The results also highlight that better wirelength does not necessarily lead to PPA gain, emphasizing the need of developing PPA-driven methods. Open3DBench offers a standardized, reproducible platform for evaluating 3D EDA methods, effectively bridging the gap between open-source tools and commercial solutions in 3D-IC design.

cs.AR↗

arXiv2026

Synonymous Codon Usage Bias Overrides Phylogeny to Reflect Convergent Frond Architecture in a Rapidly Radiating Fern Family Thelypteridaceae

Convergent evolution provides powerful evidence for natural selection, yet its molecular basis is typically sought in protein-coding amino acid substitutions. Whether adaptive pressures can drive the convergent evolution of synonymous codon usage bias (CUB) to override phylogenetic history remains a fundamental question. Here, we investigate this within the rapidly radiating fern family Thelypteridaceae by establishing a comparative framework that integrates chloroplast phylogenomics with dimensionality reduction of codon usage, morphological data, and divergence time estimation. Our results reveal that chloroplast CUB patterns are strikingly incongruent with the phylogeny of this family. Instead, they partition species into distinct clusters that strongly correlate with a convergently evolved morphological trait, lamina base architecture, a key adaptation whose radiation we date to the early Neogene. This convergent molecular signal is driven by a specific subset of photosynthesis-related genes (ndhJ, psaA, and psbD), which exhibit a high density of type-specific, third-position codon substitutions. These findings demonstrate that CUB can serve as a powerful, quantifiable indicator of adaptive history, revealing a cryptic layer of molecular convergence linked to the regulation of protein synthesis. Our work providing a new framework for uncovering adaptive histories obscured by complex evolutionary processes.

q-bio.PE↗

arXiv2026

Transformer-Accelerated Interpolated Data-Driven Reachability Analysis from Noisy Data

Data-driven reachability analysis provides guaranteed outer approximations of reachable sets from input-state measurements, yet each propagation step requires a matrix-zonotope multiplication whose cost grows with the horizon length, limiting scalability. We observe that data-driven propagation is inherently step-size sensitive, in the sense that set-valued operators at different discretization resolutions yield non-equivalent reachable sets at the same physical time, a property absent in model-based propagation. Exploiting this multi-resolution structure, we propose Interpolated Reachability Analysis (IRA), which computes a sparse chain of coarse anchor sets sequentially and reconstructs fine-resolution intermediate sets in parallel across coarse intervals. We derive a fully data-driven coarse-noise over-approximation that removes the need for continuous-time system knowledge, prove deterministic outer-approximation guarantees for all interpolated sets, and establish conditional tightness relative to the fine-resolution chain. To replace the remaining matrix-zonotope multiplications in the fine phase, we further develop Transformer-Accelerated IRA (TA-IRA), where an encoder-decoder Transformer is calibrated via split conformal prediction to provide finite-sample pointwise and path-wise coverage certificates. Numerical experiments on a five-dimensional linear system confirm the theoretical guarantees and demonstrate significant computational savings.

eess.SY↗

arXiv2026

Transformer-Enhanced Data-Driven Output Reachability with Conformal Coverage Guarantees

This paper considers output reachability analysis for linear time-invariant systems with unknown state-space matrices and unknown observation map, given only noisy input-output measurements. The Cayley--Hamilton theorem is applied to eliminate the latent state algebraically, producing an autoregressive input-output model whose parameter uncertainty is enclosed in a matrix zonotope. Set-valued propagation of this model yields output reachable sets with deterministic containment guarantees under a bounded aggregated residual assumption. The conservatism inherent in the lifted matrix-zonotope product is then mitigated by a decoder-only Transformer trained on labels obtained through directional contraction of the formal envelope via an exterior non-reachability certificate. Split conformal prediction restores distribution-free coverage at both per-step and trajectory levels without access to the true reachable-set hull. The framework is validated on a five-dimensional system with multiple unknown observation matrices.

eess.SY↗

arXiv2026

Data-Driven Reachability Analysis via Diffusion Models with PAC Guarantees

We present a data-driven framework for reachability analysis of nonlinear dynamical systems that requires no explicit model. A denoising diffusion probabilistic model learns the time-evolving state distribution of a dynamical system from trajectory data alone. The predicted reachable set takes the form of a sublevel set of a nonconformity score derived from the reconstruction error, with the threshold calibrated via the Learn Then Test procedure so that the probability of excluding a reachable state is bounded with high probability. Experiments on three nonlinear systems, a forced Duffing oscillator, a planar quadrotor, and a high-dimensional reaction-diffusion system, confirm that the empirical miss rate remains below the Probably Approximately Correct (PAC) bound while scaling to state dimensions beyond the reach of classical grid-based and polynomial methods.

eess.SY↗

arXiv2026

Certified Set Convergence for Piecewise Affine Systems via Neural Lyapunov Functions

Safety-critical control of piecewise affine (PWA) systems under bounded additive disturbances requires guarantees not for individual states but for entire state sets simultaneously: a single control action must steer every state in the set toward a target, even as sets crossing mode boundaries split and evolve under distinct affine dynamics. Certifying such set convergence via neural Lyapunov functions couples the Lipschitz constants of the value function and the policy, yet certified bounds for expressive networks exceed true values by orders of magnitude, creating a certification barrier. We resolve this through a three-stage pipeline that decouples verification from the policy. A value function from Hamilton-Jacobi backward reachability, trained via reinforcement learning, is the Lyapunov candidate. A permutation-invariant Deep Sets controller, distilled via regret minimization, produces a common action. Verification propagates zonotopes through the value network, yielding verified Lyapunov upper bounds over entire sets without bounding the policy Lipschitz constant. On four benchmarks up to dimension six, including systems with per-mode operator norms exceeding unity, the framework certifies set convergence with positive margin on every system. A spectrally constrained local certificate completes the terminal guarantee, and the set-actor is the only tested method to achieve full strict set containment, at constant-time online cost.

eess.SY↗

arXiv2026

Conformalized Data-Driven Reachability Analysis with PAC Guarantees

Data-driven reachability analysis computes over-approximations of reachable sets directly from noisy data. Existing deterministic methods require either known noise bounds or system-specific structural parameters such as Lipschitz constants. We propose Conformalized Data-Driven Reachability (CDDR), a framework that provides Probably Approximately Correct (PAC) coverage guarantees through the Learn Then Test (LTT) calibration procedure, requiring only that calibration and test trajectories be independently and identically distributed. CDDR is developed for three settings: linear time-invariant (LTI) systems with unknown process noise distributions, LTI systems with bounded measurement noise, and general nonlinear systems including non-Lipschitz dynamics. Experiments on a 5-dimensional LTI system under Gaussian and heavy-tailed Student-t noise and on a 2-dimensional non-Lipschitz system with fractional damping demonstrate that CDDR achieves valid coverage where deterministic methods do not provide formal guarantees. Under anisotropic noise, a normalized score function reduces the reachable set volume while preserving the PAC guarantee.

eess.SY↗

arXiv2026

Data-Driven Reachability Analysis for Piecewise Affine Systems

Hybrid systems play a crucial role in modeling real-world applications where discrete and continuous dynamics interact, including autonomous vehicles, power systems, and traffic networks. Safety verification for these systems requires determining whether system states can enter unsafe regions under given initial conditions and uncertainties, a question directly addressed by reachability analysis. However, hybrid systems present unique difficulties because their state space is divided into multiple regions with distinct dynamic models, causing traditional data-driven methods to produce inadequate over-approximations of reachable sets at region boundaries where dynamics change abruptly. This paper introduces a novel approach using hybrid zonotopes for data-driven reachability analysis of piecewise affine systems. Our method addresses the boundary transition problem by developing computational algorithms that calculate the family of set models guaranteed to contain the true system trajectories. Additionally, we extend and evaluate three methods for set-based estimation that account for input-output data with measurement noise.

eess.SY↗

arXiv2025

Dispersion-Aware Modeling Framework for Parallel Optical Computing

Optical computing represents a groundbreaking technology that leverages the unique properties of photons, with innate parallelism standing as its most compelling advantage. Parallel optical computing like cascaded Mach-Zehnder interferometers (MZIs) based offers powerful computational capabilities but also introduces new challenges, particularly concerning dispersion due to the introduction of new frequencies. In this work, we extend existing theories of cascaded MZI systems to develop a generalized model tailored for wavelength-multiplexed parallel optical computing. Our comprehensive model incorporates component dispersion characteristics into a wavelength-dependent transfer matrix framework and is experimentally validated. We propose a computationally efficient compensation strategy that reduces global dispersion error within a 40 nm range from 0.22 to 0.039 using edge-spectrum calibration. This work establishes a fundamental framework for dispersion-aware model and error correction in MZI-based parallel optical computing chips, advancing the reliability of multi-wavelength photonic processors.

physics.optics↗

arXiv2025

Roundabout Constrained Convex Generators: A Unified Framework for Multiply-Connected Reachable Sets

This paper introduces Roundabout Constrained Convex Generators (RCGs), a set representation framework for modeling multiply connected regions in control and verification applications. The RCG representation extends the constrained convex generators framework by incorporating an inner exclusion zone, creating sets with topological holes that naturally arise in collision avoidance and safety-critical control problems. We present two equivalent formulations: a set difference representation that provides geometric intuition and a unified parametric representation that facilitates computational implementation. The paper establishes closure properties under fundamental operations, including linear transformations, Minkowski sums, and intersections with convex generator sets. We derive special cases, including roundabout zonotopes and roundabout ellipsotopes, which offer computational advantages for specific norm selections. The framework maintains compatibility with existing optimization solvers while enabling the representation of non-convex feasible regions that were previously challenging to model efficiently.

math.OC↗

arXiv2025

Testing and Fault Tolerance Techniques for CNT-Based FPGAs

As the semiconductor manufacturing process technology node shrinks into the nanometer-scale, the CMOS-based Field Programmable Gate Arrays (FPGAs) face big challenges in scalability of performance and power consumption. Multi-walled Carbon Nanotube (MWCNT) serves as a promising candidate for Cu interconnects thanks to the superior conductivity. Moreover, Carbon Nanotube Field Transistor (CNFET) also emerges as a prospective alternative to the conventional CMOS device because of high power efficiency and large noise margin. The combination of MWCNT and CNFET enables the promising CNT-based FPGAs. However, the MWCNT interconnects exhibit significant process variations due to immature fabrication process, leading to delay faults. Also, the non-ideal CNFET fabrication process may generate a few metallic CNTs (m-CNTs), rendering correlated faulty blocks. In this article, we propose a ring oscillator (RO) based testing technique to detect delay faults due to the process variation of MWCNT interconnects. Furthermore, we propose an effective testing technique for the carry chains in CLBs, and an improved circuit design based on the lookup table (LUT) is applied to speed up the fault testing of CNT-based FPGAs. In addition, we propose a testing algorithm to detect m-CNTs in CLBs. Finally, we propose a redundant spare row sharing architecture to improve the yield of CNT-based FPGA further. Experimental results show that the test time for a 6-input LUT can be reduced by 35.49% compared with conventional testing, and the proposed algorithm can achieve a high test coverage with little overhead. The proposed redundant architecture can repair the faulty segment effectively and efficiently.

cs.AR↗

arXiv2025

Hybrid Polynomial Zonotopes: A Set Representation for Reachability Analysis in Hybrid Nonaffine Systems

Reachability analysis for hybrid nonaffine systems remains computationally challenging, as existing set representations--including constrained, polynomial, and hybrid zonotopes--either lose tightness under high-order nonaffine maps or suffer exponential blow-up after discrete jumps. This paper introduces Hybrid Polynomial Zonotope (HPZ), a novel set representation that combines the mode-dependent generator structure of hybrid zonotopes with the algebraic expressiveness of polynomial zonotopes. HPZs compactly encode non-convex reachable states across modes by attaching polynomial exponents to each hybrid generator, enabling precise capture of high-order state-input couplings without vertex enumeration. We develop a comprehensive library of HPZ operations, including Minkowski sum, linear transformation, and intersection. Theoretical analysis and computational experiments demonstrate that HPZs achieve superior tightness preservation and computational efficiency compared to existing approaches for hybrid system reachability analysis.

eess.SY↗

arXiv2025

SwitchLingua: The First Large-Scale Multilingual and Multi-Ethnic Code-Switching Dataset

Code-switching (CS) is the alternating use of two or more languages within a conversation or utterance, often influenced by social context and speaker identity. This linguistic phenomenon poses challenges for Automatic Speech Recognition (ASR) systems, which are typically designed for a single language and struggle to handle multilingual inputs. The growing global demand for multilingual applications, including Code-Switching ASR (CSASR), Text-to-Speech (CSTTS), and Cross-Lingual Information Retrieval (CLIR), highlights the inadequacy of existing monolingual datasets. Although some code-switching datasets exist, most are limited to bilingual mixing within homogeneous ethnic groups, leaving a critical need for a large-scale, diverse benchmark akin to ImageNet in computer vision. To bridge this gap, we introduce \textbf{LinguaMaster}, a multi-agent collaboration framework specifically designed for efficient and scalable multilingual data synthesis. Leveraging this framework, we curate \textbf{SwitchLingua}, the first large-scale multilingual and multi-ethnic code-switching dataset, including: (1) 420K CS textual samples across 12 languages, and (2) over 80 hours of audio recordings from 174 speakers representing 18 countries/regions and 63 racial/ethnic backgrounds, based on the textual data. This dataset captures rich linguistic and cultural diversity, offering a foundational resource for advancing multilingual and multicultural research. Furthermore, to address the issue that existing ASR evaluation metrics lack sensitivity to code-switching scenarios, we propose the \textbf{Semantic-Aware Error Rate (SAER)}, a novel evaluation metric that incorporates semantic information, providing a more accurate and context-aware assessment of system performance.

cs.CL↗