Wenyuan Wu

Yu Wang, Wenyuan Wu, Bican Xia

A special homotopy continuation method, as a combination of the polyhedral homotopy and the linear product homotopy, is proposed for computing all the isolated solutions to a special class of polynomial systems. The root number bound of this method is between the total degree bound and the mixed volume bound and can be easily computed. The new algorithm has been implemented as a program called LPH using C++. Our experiments show its efficiency compared to the polyhedral or other homotopies on such systems. As an application, the algorithm can be used to find witness points on each connected component of a real variety.

Wenqiang Yang, Wenyuan Wu, Robert M. Corless

Solving initial value problems and boundary value problems of Linear Ordinary Differential Equations (ODEs) plays an important role in many applications. There are various numerical methods and solvers to obtain approximate solutions represented by points. However, few work about optimal solution to minimize the residual can be found in the literatures. In this paper, we first use Hermit cubic spline interpolation at mesh points to represent the solution, then we define the residual error as the square of the L2 norm of the residual obtained by substituting the interpolation solution back to ODEs. Thus, solving ODEs is reduced to an optimization problem in curtain solution space which can be solved by conjugate gradient method with taking advantages of sparsity of the corresponding matrix. The examples of IVP and BVP in the paper show that this method can find a solution with smaller global error without additional mesh points.

Xiaolin Qin, Wenyuan Wu, Yong Feng et al.

This paper deals with the structural analysis problem of dynamic lumped process high-index DAE models. We consider two methods for index reduction of such models by differentiation: Pryce's method and the symbolic differential elimination algorithm rifsimp. Discussion and comparison of these methods are given via a class of fundamental process simulation examples. In particular, the efficiency of the Pryce method is illustrated as a function of the number of tanks in process design.

Rui Li, Wenyuan Wu, Weijie Miao

Fully homomorphic encryption (FHE) supports only additions and multiplications, so FHE-only neural-network inference typically replaces ReLU with polynomials fitted over empirical activation intervals. Such interval fitting often requires higher-degree polynomials to control activation error, incurring homomorphic evaluation costs, while classification is determined by the final logit decision. We revisit ReLU replacement from a decision-aware perspective: given a trained single-hidden-layer ReLU MLP and a specified calibration set, can an HE-friendly low-degree polynomial replace ReLU without retraining while preserving calibration-set decisions? We focus on quadratic replacement, the lowest-degree choice that retains a genuine per-unit nonlinearity. For calibration sets positive-margin separable in the lifted space, we formulate quadratic replacement as a linear separation problem, yielding necessary and sufficient conditions for calibration-lossless replacement and a constructive algorithm for the coefficients. When the positive-margin condition fails -- typically due to a few misclassified calibration samples -- we extend the same geometric framework via reduced convex hulls and Lagrangian-dual soft-margin relaxations, which bound the influence of any single sample, converting the problem into smaller convex quadratic programs that yield approximately feasible coefficients with high empirical agreement on calibration-set decisions. In particular, at the maximal weight cap $μ=1$, the reduced-convex-hull relaxation reduces to the convex-hull separation of the strictly separable case; the relaxation thus continuously extends the exact theory. Under CKKS, the quadratic replacement matches plaintext top-1 accuracy on multiple benchmarks, running 3.7--4.1$\times$ faster than Remez-7 in the activation module and 1.18--1.68$\times$ faster end-to-end.

Zhenyi Ji, Wenyuan Wu, Yi Li et al.

In this paper, based on the homotopy continuation method and the interval Newton method, an efficient algorithm is introduced to isolate the real roots of semi-algebraic system. Tests on some random examples and a variety of problems including transcendental functions arising in many applications show that the new algorithm reduces the cost substantially compared with the traditional symbolic approaches.

Yanliang Huang, Peng Xie, Zhen Zhang et al.

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.

Yanliang Huang, Peng Xie, Wenyuan Wu et al.

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.

Wenyuan Wu, Wenqiang Yang

Solving Linear Ordinary Differential Equations (ODEs) plays an important role in many applications. There are various numerical methods and solvers to obtain approximate solutions. However, few work about global error estimation can be found in the literature. In this paper, we first give a definition of the residual, based on the piecewise Hermit interpolation, which is a kind of the backward-error of ODE solvers. It indicates the reliability and quality of numerical solution. Secondly, the global error between the exact solution and an approximate solution is the forward error and a bound of it can be given by using the backward-error. The examples in the paper show that our estimate works well for a large class of ODE models.

Yong Feng, Wenyuan Wu, Jingzhong Zhang

Factorization of polynomials is one of the foundations of symbolic computation. Its applications arise in numerous branches of mathematics and other sciences. However, the present advanced programming languages such as C++ and J++, do not support symbolic computation directly. Hence, it leads to difficulties in applying factorization in engineering fields. In this paper, we present an algorithm which use numerical method to obtain exact factors of a bivariate polynomial with rational coefficients. Our method can be directly implemented in efficient programming language such C++ together with the GNU Multiple-Precision Library. In addition, the numerical computation part often only requires double precision and is easily parallelizable.

Likang Peng, Chao Su, Wenyuan Wu et al.

Cross-modal hashing (CMH) facilitates efficient retrieval across different modalities (e.g., image and text) by encoding data into compact binary representations. While recent methods have achieved remarkable performance, they often rely heavily on fully annotated datasets, which are costly and labor-intensive to obtain. In real-world scenarios, particularly in multi-label datasets, label noise is prevalent and severely degrades retrieval performance. Moreover, existing CMH approaches typically overlook the partial semantic overlaps inherent in multi-label data, limiting their robustness and generalization. To tackle these challenges, we propose a novel framework named Semantic-Consistent Bidirectional Contrastive Hashing (SCBCH). The framework comprises two complementary modules: (1) Cross-modal Semantic-Consistent Classification (CSCC), which leverages cross-modal semantic consistency to estimate sample reliability and reduce the impact of noisy labels; (2) Bidirectional Soft Contrastive Hashing (BSCH), which dynamically generates soft contrastive sample pairs based on multi-label semantic overlap, enabling adaptive contrastive learning between semantically similar and dissimilar samples across modalities. Extensive experiments on four widely-used cross-modal retrieval benchmarks validate the effectiveness and robustness of our method, consistently outperforming state-of-the-art approaches under noisy multi-label conditions.

Wenqiang Yang, Wenyuan Wu, Yong Feng et al.

Simulation and modeling are essential in product development, integrated into the design and manufacturing process to enhance efficiency and quality. They are typically represented as complex nonlinear differential algebraic equations. The growing diversity of product requirements demands multi-task optimization, a key challenge in simulation modeling research. A dual physics-informed neural network architecture has been proposed to decouple constraints and objective functions in parametric differential algebraic equation optimization problems. Theoretical analysis shows that introducing a relaxation variable with a global error bound ensures solution equivalence between the network and optimization problem. A genetic algorithm-enhanced training framework for physics-informed neural networks improves training precision and efficiency, avoiding redundant solving of differential algebraic equations. This approach enables generalization for multi-task objectives with a single, training maintaining real-time responsiveness to product requirements.

Wenyuan Wu, Peng Xie, Zhen Zhang et al.

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.

Zhen Zhang, Ahmad Hafez, Peng Xie et al.

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.

Zhen Zhang, Peng Xie, Wenyuan Wu et al.

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.

Wenyuan Wu, Zheng Liu, Yong Chen et al.

In recent years, the rapid development of deep neural networks has brought increased attention to the security and robustness of these models. While existing adversarial attack algorithms have demonstrated success in improving adversarial transferability, their performance remains suboptimal due to a lack of consideration for the discrepancies between target and source models. To address this limitation, we propose a novel method, Inverse Knowledge Distillation (IKD), designed to enhance adversarial transferability effectively. IKD introduces a distillation-inspired loss function that seamlessly integrates with gradient-based attack methods, promoting diversity in attack gradients and mitigating overfitting to specific model architectures. By diversifying gradients, IKD enables the generation of adversarial samples with superior generalization capabilities across different models, significantly enhancing their effectiveness in black-box attack scenarios. Extensive experiments on the ImageNet dataset validate the effectiveness of our approach, demonstrating substantial improvements in the transferability and attack success rates of adversarial samples across a wide range of models.

Peng Xie, Yanlinag Huang, Wenyuan Wu et al.

Motion planning through narrow passages remains a core challenge: sampling-based planners rarely place samples inside these narrow but critical regions, and even when samples land inside a passage, the straight-line connections between them run close to obstacle boundaries and are frequently rejected by collision checking. Decomposition-based planners resolve both issues by partitioning free space into convex cells -- every passage is captured exactly as a cell boundary, and any path within a cell is collision-free by construction. However, the number of candidate corridors through the cell graph grows combinatorially with environment complexity, creating a bottleneck in corridor selection. We present GNN-DIP, a framework that addresses this by integrating a Graph Neural Network (GNN) with a two-phase Decomposition-Informed Planner (DIP). The GNN predicts portal scores on the cell adjacency graph to bias corridor search toward near-optimal regions while preserving completeness. In 2D, Constrained Delaunay Triangulation (CDT) with the Funnel algorithm yields exact shortest paths within corridors; in 3D, Slab convex decomposition with portal-face sampling provides near-optimal path evaluation. Benchmarks on 2D narrow-passage scenarios, 3D bottleneck environments with up to 246 obstacles, and dynamic 2D settings show that GNN-DIP achieves 99--100% success rates with 2--280 times speedup over sampling-based baselines.

Wenyuan Wu, Jasmin Heierli, Max Meisterhans et al.

The advent of increasingly powerful language models has raised expectations for language-based interactions. However, controlling these models is a challenge, emphasizing the need to be able to investigate the feasibility and value of their application. We present PROMISE, a framework that facilitates the development of complex language-based interactions with information systems. Its use of state machine modeling concepts enables model-driven, dynamic prompt orchestration across hierarchically nested states and transitions. This improves the control of the behavior of language models and thus enables their effective and efficient use. In this technical report we show the benefits of PROMISE in the context of application scenarios within health information systems and demonstrate its ability to handle complex interactions. We also include code examples and present default user interfaces available as part of PROMISE.