arXiv subjects

Kaichen Ouyang

Publications and source records attributed to Kaichen Ouyang.

13 recordsLinked to original sources

arXiv2026

SINO: Scale-Invariant Neural Operator

In scientific machine learning, physical fields governed by partial differential equations exhibit low-rank structure and scale invariance. When solving equations on coarse grids, missing information leads to the closure problem: modeling unresolved physics to recover lost dynamics. Although closure terms depend on grid resolution, they represent scale-invariant physical laws. A model truly learning physics should capture these mechanisms with low-rank parameterization rather than memorizing grid-specific patterns. Inspired by this, we propose the Scale-Invariant Neural Operator (SINO), which learns on normalized physical scales via a dual-branch architecture operating in spectral and spatial domains. SINO uses bottleneck MLPs to generate continuous convolution kernels, embedding an explicit low-rank inductive bias that concentrates more than 95 percent of variance in 2-3 modes, as validated by PCA across benchmarks, while drastically reducing parameters. This principled design yields 38 times steeper scaling law exponents than FNO, demonstrating superior parameter efficiency. We compare SINO with traditional models (U-Net, DeepONet), Transformer models (Transolver, Oformer, GK-Transformer), and frequency-domain models (FNO, AMFNO, UFNO) on closure problems spanning externally forced Burgers turbulence, decaying Burgers turbulence, KS turbulence, Kolmogorov-forced NS turbulence, and decaying NS turbulence. Experiments show SINO achieves 1.5-38 times error reduction and 2-23 times parameter efficiency over baselines, with superior scaling laws reflecting exceptional data efficiency from principled low-rank design. Code is available at https://github.com/AI4Science-WestlakeU/SINO.

cs.LG↗

arXiv2026

Random Walk on Bézier Curves for Global Optimization

Balancing exploration and exploitation remains a central challenge in metaheuristic optimization. To address this issue, this paper proposes Bézier Walk Evolution (BWE), a geometry-driven optimization framework that reformulates evolutionary search as adaptive trajectory construction in the decision space. BWE integrates Bézier curve modeling with a distance-aware random walk mechanism to generate topology-guided search trajectories. By adaptively varying the curve order during evolution, the proposed method enables a smooth transition from diversified global exploration to refined local exploitation. Higher-order Bézier curves leverage multiple population-derived control points to enhance search diversity, while lower-order curves generate near-linear trajectories to improve convergence efficiency. This adaptive geometric search mechanism provides an interpretable alternative to conventional nature-inspired designs. Extensive experiments on 41 benchmark functions from the CEC2017 and CEC2022 suites, spanning dimensions from 10 to 100, show that BWE achieves strong overall performance and favorable scalability compared with 7 classical and 6 state-of-the-art optimizers, including L-SHADE and CMA-ES. Additional evaluations on five constrained engineering design problems further demonstrate the practical applicability and robustness of BWE.

cs.NE↗

arXiv2026

TwistNet-2D: Learning Second-Order Channel Interactions via Spiral Twisting for Texture Recognition

Second-order feature statistics are central to texture recognition, yet existing mechanisms exhibit a structural tension: bilinear pooling and Gram matrices capture global channel correlations but discard spatial structure, whereas self-attention models capture cross-position relations through weighted sums rather than explicit pairwise products. We propose TwistNet-2D, a lightweight module that computes local pairwise channel products under directional spatial displacement, jointly encoding where features co-occur and how they interact. The core component, Spiral-Twisted Channel Interaction (STCI), shifts one feature map along a prescribed direction before L2-normalized channel multiplication, capturing cross-position co-occurrence patterns that characterize structured and periodic textures. Four directional heads are aggregated through content-adaptive channel reweighting, and the result is injected via a sigmoid-gated residual path with near-zero initialization. TwistNet-2D adds only approximately 3.5% parameters and approximately 2% FLOPs over ResNet-18. To isolate the contribution of architectural inductive bias from that of transfer learning, all models in this study are trained from scratch without ImageNet pretraining. Under this protocol, TwistNet-2D consistently surpasses parameter-matched baselines and substantially larger ConvNeXt and Swin Transformer backbones across four texture and fine-grained recognition benchmarks, while the multi-head structure produces interpretable, orientation-selective representations that align with classical texture analysis.

cs.CV↗

arXiv2026

Dogfight Search: A Swarm-Based Optimization Algorithm for Complex Engineering Optimization and Mountainous Terrain Path Planning

Dogfight is a tactical behavior of cooperation between fighters. Inspired by this, this paper proposes a novel metaphor-free metaheuristic algorithm called Dogfight Search (DoS). Unlike traditional algorithms, DoS draws algorithmic framework from the inspiration, but its search mechanism is constructed based on the displacement integration equations in kinematics. Through experimental validation on CEC2017 and CEC2022 benchmark test functions, 10 real-world constrained optimization problems and mountainous terrain path planning tasks, DoS significantly outperforms 7 advanced competitors in overall performance and ranks first in the Friedman ranking. Furthermore, this paper compares the performance of DoS with 3 SOTA algorithms on the CEC2017 and CEC2022 benchmark test functions. The results show that DoS continues to maintain its lead, demonstrating strong competitiveness. The source code of DoS is available at https://ww2.mathworks.cn/matlabcentral/fileexchange/183519-dogfight-search.

cs.AI↗

arXiv2026

Physics-Informed Evolution: An Evolutionary Framework for Solving Quantum Control Problems Involving the Schrödinger Equation

Physics-informed Neural Networks (PINNs) show that embedding physical laws directly into the learning objective can significantly enhance the efficiency and physical consistency of neural network solutions. Similar to optimizing loss functions in machine learning, evolutionary algorithms iteratively optimize objective functions by simulating natural selection processes. Inspired by this principle, we ask a natural question: can physical information be similarly embedded into the fitness function of evolutionary algorithms? In this work, we propose Physics-informed Evolution (PIE), a novel framework that incorporates physical information derived from governing physical laws into the evolutionary fitness landscape, thereby extending Physics-informed artificial intelligence methods from machine learning to the broader domain of evolutionary computation. As a concrete instantiation, we apply PIE to quantum control problems governed by the Schrödinger equation, where the goal is to find optimal control fields that drive quantum systems from initial states to desired target states. We validate PIE on three representative quantum control benchmarks: state preparation in V-type three-level systems, entangled state generation in superconducting quantum circuits, and two-atom cavity QED systems. Within the PIE framework, we systematically compare the performance of ten single-objective and five multi-objective evolutionary algorithms. Experimental results demonstrate that by embedding physical information into the fitness function, PIE effectively guides evolutionary search, yielding control fields with high fidelity, low state deviation, and robust performance across different scenarios. Our findings further suggest that the Physics-informed principle extends naturally beyond neural network training to the broader domain of evolutionary computation.

quant-ph↗

arXiv2026

Wasserstein Evolution : Evolutionary Optimization as Phase Transition

Evolutionary algorithms (EAs) serve as powerful black-box optimizers inspired by biological evolution. However, most existing EAs predominantly focus on heuristic operators such as crossover and mutation, while usually overlooking underlying physical interpretability such as statistical mechanics and thermosdynamics. This theoretical void limits the principled understanding of algorithmic dynamics, hindering the systematic design of evolutionary search beyond ad-hoc heuristics. To bridge this gap, we first point out that evolutionary optimization can be conceptually reframed as a physical phase transition process. Building on this perspective, we establish the theoretical grounds by modeling the optimization dynamics as a Wasserstein gradient flow of free energy. Consequently, a robust and interpretable solver named Wasserstein Evolution (WE) is proposed. WE mathematically frames the trade-off between exploration and exploitation as a competition between potential gradient forces and entropic forces. This formulation guarantees convergence to the Boltzmann distribution, thereby minimizing free energy and maximizing entropy, which promotes highly diverse solutions. Extensive experiments on complex multimodal and physical potential functions demonstrate that WE achieves superior diversity and stability compared to established baselines.

cs.NE↗

arXiv2025

OPAL: Operator-Programmed Algorithms for Landscape-Aware Black-Box Optimization

Black-box optimization often relies on evolutionary and swarm algorithms whose performance is highly problem dependent. We view an optimizer as a short program over a small vocabulary of search operators and learn this operator program separately for each problem instance. We instantiate this idea in Operator-Programmed Algorithms (OPAL), a landscape-aware framework for continuous black-box optimization that uses a small design budget with a standard differential evolution baseline to probe the landscape, builds a $k$-nearest neighbor graph over sampled points, and encodes this trajectory with a graph neural network. A meta-learner then maps the resulting representation to a phase-wise schedule of exploration, restart, and local search operators. On the CEC~2017 test suite, a single meta-trained OPAL policy is statistically competitive with state-of-the-art adaptive differential evolution variants and achieves significant improvements over simpler baselines under nonparametric tests. Ablation studies on CEC~2017 justify the choices for the design phase, the trajectory graph, and the operator-program representation, while the meta-components add only modest wall-clock overhead. Overall, the results indicate that operator-programmed, landscape-aware per-instance design is a practical way forward beyond ad hoc metaphor-based algorithms in black-box optimization.

cs.NE↗

arXiv2025

Twisted Convolutional Networks (TCNs): Enhancing Feature Interactions for Non-Spatial Data Classification

Twisted Convolutional Networks (TCNs) are proposed as a novel deep learning architecture for classifying one-dimensional data with arbitrary feature order and minimal spatial relationships. Unlike conventional Convolutional Neural Networks (CNNs) that rely on structured feature sequences, TCNs explicitly combine subsets of input features through theoretically grounded multiplicative and pairwise interaction mechanisms to create enriched representations. This feature combination strategy, formalized through polynomial feature expansions, captures high-order feature interactions that traditional convolutional approaches miss. We provide a comprehensive mathematical framework for TCNs, demonstrating how the twisted convolution operation generalizes standard convolutions while maintaining computational tractability. Through extensive experiments on five benchmark datasets from diverse domains (medical diagnostics, political science, synthetic data, chemometrics, and healthcare), we show that TCNs achieve statistically significant improvements over CNNs, Residual Networks (ResNet), Graph Neural Networks (GNNs), DeepSets, and Support Vector Machine (SVM). The performance gains are validated through statistical testing. TCNs also exhibit superior training stability and generalization capabilities, highlighting their robustness for non-spatial data classification tasks.

cs.CV↗

arXiv2025

Learn from Global Correlations: Enhancing Evolutionary Algorithm via Spectral GNN

Evolutionary algorithms (EAs) simulate natural selection but have two main limitations: (1) they rarely update individuals based on global correlations, limiting comprehensive learning; (2) they struggle with balancing exploration and exploitation, where excessive exploitation causes premature convergence, and excessive exploration slows down the search. Moreover, EAs often depend on manual parameter settings, which can disrupt the exploration-exploitation balance. To address these issues, we propose Graph Neural Evolution (GNE), a novel EA framework. GNE represents the population as a graph, where nodes represent individuals, and edges capture their relationships, enabling global information usage. GNE utilizes spectral graph neural networks (GNNs) to decompose evolutionary signals into frequency components, applying a filtering function to fuse these components. High-frequency components capture diverse global information, while low-frequency ones capture more consistent information. This explicit frequency filtering strategy directly controls global-scale features through frequency components, overcoming the limitations of manual parameter settings and making the exploration-exploitation control more interpretable and manageable. Tests on nine benchmark functions (e.g., Sphere, Rastrigin, Rosenbrock) show that GNE outperforms classical (GA, DE, CMA-ES) and advanced algorithms (SDAES, RL-SHADE) under various conditions, including noise-corrupted and optimal solution deviation scenarios. GNE achieves solutions several orders of magnitude better (e.g., 3.07e-20 mean on Sphere vs. 1.51e-07).

cs.NE↗

arXiv2025

A Benchmark Suite for Multi-Objective Optimization in Battery Thermal Management System Design

Synthetic Benchmark Problems (SBPs) are commonly used to evaluate the performance of metaheuristic algorithms. However, these SBPs often contain various unrealistic properties, potentially leading to underestimation or overestimation of algorithmic performance. While several benchmark suites comprising real-world problems have been proposed for various types of metaheuristics, a notable gap exists for Constrained Multi-objective Optimization Problems (CMOPs) derived from practical engineering applications, particularly in the domain of Battery Thermal Management System (BTMS) design. To address this gap, this study develops and presents a specialized benchmark suite for multi-objective optimization in BTMS. This suite comprises a diverse collection of real-world constrained problems, each defined via accurate surrogate models based on recent research to efficiently represent complex thermal-fluid interactions. The primary goal of this benchmark suite is to provide a practical and relevant testing ground for evolutionary algorithms and optimization methods focused on energy storage thermal management. Future work will involve establishing comprehensive baseline results using state-of-the-art algorithms, conducting comparative analyses, and developing a standardized ranking scheme to facilitate robust performance assessment.

cs.NE↗

arXiv2025

Why Flow Matching is Particle Swarm Optimization?

This paper preliminarily investigates the duality between flow matching in generative models and particle swarm optimization (PSO) in evolutionary computation. Through theoretical analysis, we reveal the intrinsic connections between these two approaches in terms of their mathematical formulations and optimization mechanisms: the vector field learning in flow matching shares similar mathematical expressions with the velocity update rules in PSO; both methods follow the fundamental framework of progressive evolution from initial to target distributions; and both can be formulated as dynamical systems governed by ordinary differential equations. Our study demonstrates that flow matching can be viewed as a continuous generalization of PSO, while PSO provides a discrete implementation of swarm intelligence principles. This duality understanding establishes a theoretical foundation for developing novel hybrid algorithms and creates a unified framework for analyzing both methods. Although this paper only presents preliminary discussions, the revealed correspondences suggest several promising research directions, including improving swarm intelligence algorithms based on flow matching principles and enhancing generative models using swarm intelligence concepts.

cs.NE↗

arXiv2025

Consciousness as a Jamming Phase

This paper develops a neural jamming phase diagram that interprets the emergence of consciousness in large language models as a critical phenomenon in high-dimensional disordered systems.By establishing analogies with jamming transitions in granular matter and other complex systems, we identify three fundamental control parameters governing the phase behavior of neural networks: temperature, volume fraction, and stress.The theory provides a unified physical explanation for empirical scaling laws in artificial intelligence, demonstrating how computational cooling, density optimization, and noise reduction collectively drive systems toward a critical jamming surface where generalized intelligence emerges. Remarkably, the same thermodynamic principles that describe conventional jamming transitions appear to underlie the emergence of consciousness in neural networks, evidenced by shared critical signatures including divergent correlation lengths and scaling exponents.Our work explains neural language models' critical scaling through jamming physics, suggesting consciousness is a jamming phase that intrinsically connects knowledge components via long-range correlations.

cond-mat.dis-nn↗

arXiv2025

Rethinking Over-Smoothing in Graph Neural Networks: A Perspective from Anderson Localization

Graph Neural Networks (GNNs) have shown great potential in graph data analysis due to their powerful representation capabilities. However, as the network depth increases, the issue of over-smoothing becomes more severe, causing node representations to lose their distinctiveness. This paper analyzes the mechanism of over-smoothing through the analogy to Anderson localization and introduces participation degree as a metric to quantify this phenomenon. Specifically, as the depth of the GNN increases, node features homogenize after multiple layers of message passing, leading to a loss of distinctiveness, similar to the behavior of vibration modes in disordered systems. In this context, over-smoothing in GNNs can be understood as the expansion of low-frequency modes (increased participation degree) and the localization of high-frequency modes (decreased participation degree). Based on this, we systematically reviewed the potential connection between the Anderson localization behavior in disordered systems and the over-smoothing behavior in Graph Neural Networks. A theoretical analysis was conducted, and we proposed the potential of alleviating over-smoothing by reducing the disorder in information propagation.

cs.LG↗