arXiv subjects

Hongchao Zhang

Publications and source records attributed to Hongchao Zhang.

At least 19 recordsLinked to original sources

arXiv2026

Geometric obstruction to resolving the Hubble tension: orthogonality of scale and shape in distance measurements

We identify a geometric obstruction to resolving the Hubble tension by combining early-time sound-horizon reduction with late-time smooth dark energy. Within $\Lambda$CDM, the BAO--SN matter-density gap $\Delta\Omega_m = 0.037$ is exactly invariant under the sound-horizon rescaling $\alpha \equiv r_s^{\rm mod}/r_s^{\Lambda{\rm CDM}}$, and late-time $w(z)$ deformations cannot eliminate this gap either: reconciling the two datasets requires \emph{opposite} deformations -- phantom ($w < -1$) for BAO, quintessence ($w > -1$) for SN at $z < 0.5$ -- an anti-alignment quantified by $\cos\theta = -0.97$ in $w(z)$ space. A full MCMC analysis of DESI DR2 BAO, Planck plik\_lite, and Pantheon+ bears this out: the optimal $\alpha^* = 0.992$ ($0.8\%$ $r_s$ reduction) brings the joint fit to $H_0 = 70.3 \pm 0.3\;\mathrm{km\,s^{-1}\,Mpc^{-1}}$, still $3.2\sigma$ below SH0ES, with the inter-dataset tension reduced but not removed. The obstruction reflects not a shortage of model freedom but an irreducible disagreement between probes. The deformation space $\{\alpha, \beta_{\rm damp}, w(z)\}$ already spans $93\%$ of the $\Omega_m$ response direction; nonetheless BAO and SN constrain $\Omega_m$ through independent channels and disagree, while the residual $H_0$ deficit, anchored by the local distance ladder, resides in the absolute distance scale that $w(z)$ reshapes but cannot rescale.

astro-ph.CO↗

arXiv2026

Modeling Spectral Energy Shifts in Spatio-Temporal Graph Anomaly Detection

Graph anomaly detection methods aim to distinguish anomalous nodes. While prior methods characterize anomalies through increased variation in the spectral energy distributions, they overlook those that result in decreased variation, i.e., camouflaged anomalies that appear normal. We show that this type of anomaly persists across multiple datasets and remains undetectable by existing spectral approaches. To address this limitation, we propose a node-level spectral energy formulation that is fully compatible with message passing and enables the detection of camouflaged anomalies. Building on this formulation, we introduce an energy-aware graph learning framework that models spectral shifts through energy-driven message passing in both static and time-series graphs. Besides, our unified architecture extends to temporal settings without introducing specialized sequence modules, enabling efficient learning under long sliding windows. Extensive experiments on large-scale benchmarks demonstrate the effectiveness and scalability of our approach.

cs.LG↗

arXiv2026

k-Inductive Neural Barrier Certificates for Unknown Nonlinear Dynamics

While conventional (k=1) discrete-time barrier certificate conditions impose strict safety constraints by requiring the function to be non-increasing at every step, k-inductive barrier certificates relax this by allowing a temporary increase -- up to k-1 times, each within a threshold $ε$ -- while maintaining overall safety, and improving flexibility. This paper leverages neural networks and constructs k-inductive neural barrier certificates (k-NBCs) for (partially) unknown nonlinear systems. While neural networks offer scalability in the design process, they lack formal guarantees, requiring additional approaches such as counterexample-guided inductive synthesis (CEGIS) with satisfiability modulo theories (SMT) for verification. However, the CEGIS-SMT framework requires knowledge of system dynamics, which is unavailable in practical settings. To address this, we leverage the generalization of the Willems et al.'s fundamental lemma, using a single state trajectory, to construct a data-driven representation of (partially) unknown models for SMT verification without sacrificing accuracy. Additionally, CEGIS-SMT further removes the constraint of restricting barrier certificates to specific function classes, such as sum-of-squares, enabling greater flexibility in their design. We validate our approach on three nonlinear case studies with (partially) unknown dynamics.

eess.SY↗

arXiv2026

Verification and Forward Invariance of Control Barrier Functions for Differential-Algebraic Systems

Differential-algebraic equations (DAEs) arise in power networks, chemical processes, and multibody systems, where algebraic constraints encode physical conservation laws. The safety of such systems is critical, yet safe control is challenging because algebraic constraints restrict allowable state trajectories. Control barrier functions (CBFs) provide computationally efficient safety filters for ordinary differential equation (ODE) systems. However, existing CBF methods are not directly applicable to DAEs due to potential conflicts between the CBF condition and the constraint manifold. This paper introduces DAE-aware CBFs that incorporate the differential-algebraic structure through projected vector fields. We derive conditions that ensure forward invariance of safe sets while preserving algebraic constraints and extend the framework to higher-index DAEs. A systematic verification framework is developed, establishing necessary and sufficient conditions for geometric correctness and feasibility of DAE-aware CBFs. For polynomial systems, sum-of-squares certificates are provided, while for nonpolynomial and neural network candidates, satisfiability modulo theories are used for falsification. The approach is validated on wind turbine and flexible-link manipulator systems.

eess.SY↗

arXiv2026

PACE: A Personalized Adaptive Curriculum Engine for 9-1-1 Call-taker Training

9-1-1 call-taking training requires mastery of over a thousand interdependent skills, covering diverse incident types and protocol-specific nuances. A nationwide labor shortage is already straining training capacity, but effective instruction still demands that trainers tailor objectives to each trainee's evolving competencies. This personalization burden is one that current practice cannot scale. Partnering with Metro Nashville Department of Emergency Communications (MNDEC), we propose PACE (Personalized Adaptive Curriculum Engine), a co-pilot system that augments trainer decision-making by (1) maintaining probabilistic beliefs over trainee skill states, (2) modeling individual learning and forgetting dynamics, and (3) recommending training scenarios that balance acquisition of new competencies with retention of existing ones. PACE propagates evidence over a structured skill graph to accelerate diagnostic coverage and applies contextual bandits to select scenarios that target gaps the trainee is prepared to address. Empirical results show that PACE achieves 19.50% faster time-to-competence and 10.95% higher terminal mastery compared to state-of-the-art frameworks. Co-pilot studies with practicing training officers further demonstrate a 95.45% alignment rate between PACE's and experts' pedagogical judgments on real-world cases. Under estimation, PACE cuts turnaround time to merely 34 seconds from 11.58 minutes, up to 95.08% reduction.

cs.AI↗

arXiv2025

A Generating Polynomial Based Two-Stage Optimization Method for Tensor Rank Decomposition

The tensor rank decomposition, also known as canonical polyadic(CP) or simply tensor decomposition, has a long history in multilinear algebra. However, computing a rank decomposition becomes particularly challenging when the rank lies between its largest and second-largest dimensions. Moreover, for high-order tensor decompositions, a common approach is to first find a decomposition of its flattening order-3 tensor, where a significant gap often exists between the largest and the second-largest dimension, also making this case crucial in practice. For such a case, traditional optimization methods, such as the nonlinear least squares or alternating least squares methods, often fail to produce correct tensor decompositions. There are also direct methods that solve tensor decompositions algebraically. However, these methods usually require the tensor decomposition to be unique and can be computationally expensive, especially when the tensor rank is high. This paper introduces a new generating polynomial (GP) based two-stage algorithm for finding the order-3 nonsymmetric tensor decomposition, even when the tensor decomposition is not unique, assuming the rank does not exceed the largest dimension. The proposed method reformulates the tensor decomposition problem into two sequential optimization problems. Notably, if the first-stage optimization yields a partial solution, it will be effectively utilized in the second stage. We establish the theoretical equivalence between the CP decomposition and the global minimizers of those two-stage optimization problems. Numerical experiments demonstrate that our approach is very efficient and robust, capable of finding tensor decompositions in scenarios where the current state-of-the-art methods often fail.

math.OC↗

arXiv2025

What Prevents Resolving the Hubble Tension through Late-Time Expansion Modifications?

We demonstrate that Type Ia supernovae (SNe Ia) observations impose the critical constraint for resolving the Hubble tension through late-time expansion modifications. Applying the Fisher-bias optimization framework to cosmic chronometers (CC), baryon acoustic oscillations (BAO) from DESI DR2, Planck CMB, and Pantheon+ data, we find that: (i) deformations in $H(z \lesssim 3)$ (via $w(z)$ reconstruction) can reconcile tensions between CC, Planck, DESI BAO, and SH0ES measurements while maintaining or improving fit quality ($Δχ^2 < 0$ relative to $Λ$CDM); (ii) In the neighborhood of Planck best-fit $Λ$CDM model, no cosmologically viable solutions targeting $H_0 \gtrsim 69$ satisfy SNe Ia constraints. MCMC validation confirms the maximum achievable $H_0 = 69.09\pm0.30$ ($χ^2_{\rm BF} \approx χ^2_{Λ\rm CDM}$) across all data combinations, indicating that the conflict between late-time $w(z)$ modifications and SNe Ia observations prevents complete resolution of the Hubble tension.

astro-ph.CO↗

arXiv2025

Stochastic Neural Control Barrier Functions

Control Barrier Functions (CBFs) are utilized to ensure the safety of control systems. CBFs act as safety filters in order to provide safety guarantees without compromising system performance. These safety guarantees rely on the construction of valid CBFs. Due to their complexity, CBFs can be represented by neural networks, known as neural CBFs (NCBFs). Existing works on the verification of the NCBF focus on the synthesis and verification of NCBFs in deterministic settings, leaving the stochastic NCBFs (SNCBFs) less studied. In this work, we propose a verifiably safe synthesis for SNCBFs. We consider the cases of smooth SNCBFs with twice-differentiable activation functions and SNCBFs that utilize the Rectified Linear Unit or ReLU activation function. We propose a verification-free synthesis framework for smooth SNCBFs and a verification-in-the-loop synthesis framework for both smooth and ReLU SNCBFs. and we validate our frameworks in three cases, namely, the inverted pendulum, Darboux, and the unicycle model.

eess.SY↗

arXiv2025

Safe Control for Nonlinear Systems Under Faults and Attacks Via Control Barrier Functions

Safety is one of the most important properties of control systems. Sensor faults and attacks and actuator failures may cause errors in the sensor measurements and system dynamics, which leads to erroneous control inputs and hence safety violations. In this paper, we improve the robustness against sensor faults and actuator failures by proposing a class of Fault-Tolerant Control Barrier Functions (FT-CBFs) for nonlinear systems. Our approach maintains a set of state estimators according to fault patterns and incorporates CBF-based linear constraints for each state estimator. We then propose a framework for joint safety and stability by integrating FT-CBFs with Control Lyapunov Functions. With a similar philosophy of utilizing redundancy, we proposed High order CBF-based approach to ensure safety when actuator failures occur. We propose a sum-of-squares (SOS) based approach to verify the feasibility of FT-CBFs for both sensor faults and actuator failures. We evaluate our approach via two case studies, namely, a wheeled mobile robot (WMR) system in the presence of a sensor attack and a Boeing 747 lateral control system under actuator failures.

eess.SY↗

arXiv2025

Giant Orbital Torque-driven Picosecond Switching in Magnetic Tunnel Junctions

Orbital Hall effect was recently discovered as a novel pathway for driving magnetic moment. However, the integration of orbital Hall effect in magnetic memories suffers from low orbital-to-spin conversion efficiency and incompatibility with magnetic tunnel junctions. Here we demonstrate an orbital Hall effect-driven magnetic tunnel junction based on Ru/W bilayer, where the Ru layer possesses a strong orbital Hall conductivity and the {\alpha}-W layer features an orbital-to-spin conversion efficiency exceeding 90% because of the large orbit-spin diffusivity. By harnessing the giant orbital torque, we achieve a 28.7-picosecond switching and a five to eight-fold reduction in driving voltages over conventional spin-orbit torque magnetic memories. Our work bridges the critical gap between orbital effects and magnetic memory applications, significantly advancing the field of spintronics and orbitronics.

cond-mat.mtrl-sci↗

arXiv2025

Decentralized Conjugate Gradient and Memoryless BFGS Methods

This paper proposes a new decentralized conjugate gradient (NDCG) method and a decentralized memoryless BFGS (DMBFGS) method for the nonconvex and strongly convex decentralized optimization problem, respectively, of minimizing a finite sum of continuously differentiable functions over a fixed-connected undirected network. Gradient tracking techniques are applied in these two methods to enhance their convergence properties and the numerical stability. In particular, we show global convergence of NDCG with constant stepsize for general nonconvex smooth decentralized optimization. Our new DMBFGS method uses a scaled memoryless BFGS technique and only requires gradient information to approximate second-order information of the component functions in the objective. We also establish global convergence and linear convergence rate of DMBFGS with constant stepsize for strongly convex smooth decentralized optimization. Our numerical results show that NDCG and DMBFGS are very efficient in terms of both iteration and communication cost compared with other state-of-the-art methods for solving smooth decentralized optimization.

math.OC↗

arXiv2024

SEEV: Synthesis with Efficient Exact Verification for ReLU Neural Barrier Functions

Neural Control Barrier Functions (NCBFs) have shown significant promise in enforcing safety constraints on nonlinear autonomous systems. State-of-the-art exact approaches to verifying safety of NCBF-based controllers exploit the piecewise-linear structure of ReLU neural networks, however, such approaches still rely on enumerating all of the activation regions of the network near the safety boundary, thus incurring high computation cost. In this paper, we propose a framework for Synthesis with Efficient Exact Verification (SEEV). Our framework consists of two components, namely (i) an NCBF synthesis algorithm that introduces a novel regularizer to reduce the number of activation regions at the safety boundary, and (ii) a verification algorithm that exploits tight over-approximations of the safety conditions to reduce the cost of verifying each piecewise-linear segment. Our simulations show that SEEV significantly improves verification efficiency while maintaining the CBF quality across various benchmark systems and neural network structures. Our code is available at https://github.com/HongchaoZhang-HZ/SEEV.

eess.SY↗

arXiv2024

Who is Responsible? Explaining Safety Violations in Multi-Agent Cyber-Physical Systems

Multi-agent cyber-physical systems are present in a variety of applications. Agent decision-making can be affected due to errors induced by uncertain, dynamic operating environments or due to incorrect actions taken by an agent. When an erroneous decision that leads to a violation of safety is identified, assigning responsibility to individual agents is a key step toward preventing future accidents. Current approaches to carrying out such investigations require human labor or high degree of familiarity with operating environments. Automated strategies to assign responsibility can achieve a significant reduction in human effort and associated cognitive burden. In this paper, we develop an automated procedure to assign responsibility for safety violations to actions of any single agent in a principled manner. We base our approach on reasoning about safety violations in road safety. Given a safety violation, we use counterfactual reasoning to create alternative scenarios, showing how different outcomes could have occurred if certain actions had been replaced by others. We introduce the degree of responsibility (DoR) metric for each agent. The DoR, using the Shapley value, quantifies each agent's contribution to the safety violation, providing a basis to explain and justify decisions. We also develop heuristic techniques and methods based on agent interaction structures to improve scalability as agent numbers grow. We examine three safety violation cases from the National Highway Traffic Safety Administration (NHTSA). We run experiments using CARLA urban driving simulator. Results show the DoR improves the explainability of decisions and accountability for agent actions and their consequences.

eess.SY↗

arXiv2024

A Decentralized Primal-Dual Method with Quasi-Newton Tracking

This paper considers the decentralized optimization problem of minimizing a finite sum of strongly convex and twice continuously differentiable functions over a fixed-connected undirected network. A fully decentralized primal-dual method(DPDM) and its generalization(GDPDM), which allows for multiple primal steps per iteration, are proposed. In our methods, both primal and dual updates use second-order information obtained by quasi-Newton techniques which only involve matrix-vector multiplication. Specifically, the primal update applies a Jacobi relaxation step using the BFGS approximation for both computation and communication efficiency. The dual update employs a new second-order correction step. We show that the decentralized local primal updating direction on each node asymptotically approaches the centralized quasi-Newton direction. Under proper choice of parameters, GDPDM including DPDM has global linear convergence for solving strongly convex decentralized optimization problems. Our numerical results show both GDPDM and DPDM are very efficient compared with other state-of-the-art methods for solving decentralized optimization.

math.OC↗

arXiv2024

Verification and Synthesis of Compatible Control Lyapunov and Control Barrier Functions

Safety and stability are essential properties of control systems. Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs) are powerful tools to ensure safety and stability respectively. However, previous approaches typically verify and synthesize the CBFs and CLFs separately, satisfying their respective constraints, without proving that the CBFs and CLFs are compatible with each other, namely at every state, there exists control actions within the input limits that satisfy both the CBF and CLF constraints simultaneously. Ignoring the compatibility criteria might cause the CLF-CBF-QP controller to fail at runtime. There exists some recent works that synthesized compatible CLF and CBF, but relying on nominal polynomial or rational controllers, which is just a sufficient but not necessary condition for compatibility. In this work, we investigate verification and synthesis of compatible CBF and CLF independent from any nominal controllers. We derive exact necessary and sufficient conditions for compatibility, and further formulate Sum-Of-Squares programs for the compatibility verification. Based on our verification framework, we also design a nominal-controller-free synthesis method, which can effectively expands the compatible region, in which the system is guaranteed to be both safe and stable. We evaluate our method on a non-linear toy problem, and also a 3D quadrotor to demonstrate its scalability. The code is open-sourced at \url{https://github.com/hongkai-dai/compatible_clf_cbf}.

eess.SY↗

arXiv2024

NAND-like SOT-MRAM-based Approximate Storage for Error-Tolerant Applications

We demonstrate approximate storage based on NAND-like spin-orbit torque (SOT) MRAM, through "device-modeling-architecture" explorations. We experimentally achieve down to 1E-5 level selectivity. Selectivity and low-power solutions are established by numerical calculation workflow. System-level power consumption is evaluated in the 512 KB last-level cache according to 5 quality levels. Error-tolerant applications, such as image processing, alleviate the demand for selectivity down to the 5E-2 level, leading to 54% ~ 61% energy-saving. Our proposal paves the novel and suitable path for high-density and low-power NAND-like SOT-MRAM.

physics.app-ph↗

arXiv2024

Learning a Formally Verified Control Barrier Function in Stochastic Environment

Safety is a fundamental requirement of control systems. Control Barrier Functions (CBFs) are proposed to ensure the safety of the control system by constructing safety filters or synthesizing control inputs. However, the safety guarantee and performance of safe controllers rely on the construction of valid CBFs. Inspired by universal approximatability, CBFs are represented by neural networks, known as neural CBFs (NCBFs). This paper presents an algorithm for synthesizing formally verified continuous-time neural Control Barrier Functions in stochastic environments in a single step. The proposed training process ensures efficacy across the entire state space with only a finite number of data points by constructing a sample-based learning framework for Stochastic Neural CBFs (SNCBFs). Our methodology eliminates the need for post hoc verification by enforcing Lipschitz bounds on the neural network, its Jacobian, and Hessian terms. We demonstrate the effectiveness of our approach through case studies on the inverted pendulum system and obstacle avoidance in autonomous driving, showcasing larger safe regions compared to baseline methods.

cs.RO↗

arXiv2024

On the improved dynamics approach in loop quantum black holes

In this paper, we consider the Böhmer-Vandersloot (BV) model of loop quantum black holes obtained from the improved dynamics approach. We adopt the Saini-Singh gauge, in which it was found analytically that the BV spacetime is geodesically complete. We show that black/white hole horizons do not exist in this geodesically complete spacetime. Instead, there exists only an infinite number of transition surfaces, which always separate trapped regions from anti-trapped ones. Comments on the improved dynamics approach adopted in other models of loop quantum black holes are also given.

gr-qc↗