arXiv subjects

Hanchun Wang

Publications and source records attributed to Hanchun Wang.

9 recordsLinked to original sources

arXiv2026

Negative Knowledge as Failure-aware Shared Memory for AutoResearch

AI-assisted research systems generate many failed attempts, but those failures rarely become a durable, shared knowledge asset. We propose a negative knowledge memory layer: a curator agent converts each failed attempt into a bounded, typed record in a shared bank, and a downstream research agent explicitly adopts or rejects those records before proposing its next experiment. We evaluate this layer in two settings: same-task retry on ScienceAgentBench and cross-task scientific research on two nonlinear math-physics PDE problems. The negative knowledge layer outperforms vanilla AutoResearch baselines while using fewer tokens; agents with the negative knowledge bank solve new tasks that all baselines fail to solve in PDE systems research. We also show that the previous negative knowledge bank can transfer and enhance AutoResearch on different PDE problems. These results suggest that structured negative knowledge is a knowledge asset that should be explicitly maintained in broader AI-engaged scientific research beyond a memory-compression or debugging aid, alongside positive findings, as a collective infrastructure for scientific memory. Code is available at https://github.com/hch-wang/Negative_Knowledge.

cs.AI↗

arXiv2026

Coupling between Phase Separation and Geometry on a Closed Elastic Curve: Free Energy Minimization and Dynamics

We study the free energy and dynamics of a closed elastic filament (a one-dimensional curve in two dimensions) coupled to a scalar concentration field representing, for example, an absorbed species. The density variable has a tendency to phase-separate whereas the local spontaneous curvature is concentration-dependent. We address analytically and by simulation both the free energy landscape and the dynamics (the latter comprising a coupled Willmore flow and Cahn--Hilliard gradient flow on the full differential geometry of a closed filament), addressing issues that previous work typically sidestepped by restricting to the Monge gauge. Specifically we find that the closure constraint for a deformable filament qualitatively changes the free energy landscape compared with either a rigid closed filament or an open elastic one, admitting metastable and stable states with more than one domain of each type. By numerical global free energy minimization we explore equilibrium morphologies across a wide range of model parameters. For selected parameter values we present fully dynamical results, tracking the time evolution of the various contributions to the free energy and confirming the emergence of both metastable and equilibrium multi-domain morphologies.

cond-mat.soft↗

arXiv2025

Surface Wave Solutions in 1D and 2D for the Broer-Kaup-Boussinesq-Kupershmidt (BKBK) System

The BKBK system is a singular perturbation of the classical shallow water equations which modifies their transport velocity to depend on wave elevation slope. This modification introduces backward diffusion terms proportional to a real parameter $κ$. These terms also make BKBK completely integrable as a Hamiltonian system. Remarkably, when $κ=i/2$ the BKBK system may be transformed into the focusing nonlinear Schrödinger (NLS). Thus, the BKBK system with its real parameter $κ$ is complementary to the traditional modulational approach for water waves. We investigate the Lie algebraic and variational properties of the BKBK system in this paper and we study its solution behaviour in certain computational simulations of regularised versions of the 1D and 2D BKBK systems.

math-ph↗

arXiv2025

Compound Burgers-KdV Soliton Behaviour: Refraction, Reflection and Fusion

We consider a coupled PDE system between the Burgers equation and the KdV equation to model the interactions between `bore'-like structures and wave-like solitons in shallow water. Two derivations of the resulting Burgers-swept KdV system are presented, based on Lie group symmetry and reduced variational principles. Exact compound soliton solutions are obtained, and numerical simulations show that the Burgers and KdV momenta tend toward a balance at which the coupled system reduces to the integrable Gardner equation. The numerical simulations also reveal rich nonlinear solution behaviours that include refraction, reflection, and soliton fusion, before the balance is finally achieved.

nlin.PS↗

arXiv2025

Robust Probabilistic Model Checking with Continuous Reward Domains

Probabilistic model checking traditionally verifies properties on the expected value of a measure of interest. This restriction may fail to capture the quality of service of a significant proportion of a system's runs, especially when the probability distribution of the measure of interest is poorly represented by its expected value due to heavy-tail behaviors or multiple modalities. Recent works inspired by distributional reinforcement learning use discrete histograms to approximate integer reward distribution, but they struggle with continuous reward space and present challenges in balancing accuracy and scalability. We propose a novel method for handling both continuous and discrete reward distributions in Discrete Time Markov Chains using moment matching with Erlang mixtures. By analytically deriving higher-order moments through Moment Generating Functions, our method approximates the reward distribution with theoretically bounded error while preserving the statistical properties of the true distribution. This detailed distributional insight enables the formulation and robust model checking of quality properties based on the entire reward distribution function, rather than restricting to its expected value. We include a theoretical foundation ensuring bounded approximation errors, along with an experimental evaluation demonstrating our method's accuracy and scalability in practical model-checking problems.

cs.AI↗

arXiv2024

Universal Topology Refinement for Medical Image Segmentation with Polynomial Feature Synthesis

Although existing medical image segmentation methods provide impressive pixel-wise accuracy, they often neglect topological correctness, making their segmentations unusable for many downstream tasks. One option is to retrain such models whilst including a topology-driven loss component. However, this is computationally expensive and often impractical. A better solution would be to have a versatile plug-and-play topology refinement method that is compatible with any domain-specific segmentation pipeline. Directly training a post-processing model to mitigate topological errors often fails as such models tend to be biased towards the topological errors of a target segmentation network. The diversity of these errors is confined to the information provided by a labelled training set, which is especially problematic for small datasets. Our method solves this problem by training a model-agnostic topology refinement network with synthetic segmentations that cover a wide variety of topological errors. Inspired by the Stone-Weierstrass theorem, we synthesize topology-perturbation masks with randomly sampled coefficients of orthogonal polynomial bases, which ensures a complete and unbiased representation. Practically, we verified the efficiency and effectiveness of our methods as being compatible with multiple families of polynomial bases, and show evidence that our universal plug-and-play topology refinement network outperforms both existing topology-driven learning-based and post-processing methods. We also show that combining our method with learning-based models provides an effortless add-on, which can further improve the performance of existing approaches.

eess.IV↗

arXiv2024

Collisions of Burgers Bores with Nonlinear Waves

This paper treats nonlinear wave current interactions in their simplest form, as an overtaking collision. In one spatial dimension, the paper investigates the collision interaction formulated as an initial value problem of a Burgers bore overtaking solutions of two types of nonlinear wave equations, Korteweg de Vries (KdV) and nonlinear Schrodinger (NLS). The bore wave state arising after the overtaking Burgers-KdV collision in numerical simulations is found to depend qualitatively on the balance between nonlinearity and dispersion in the KdV equation. The Burgers-KdV system is also made stochastic by following the stochastic advection by Lie transport approach (SALT).

physics.flu-dyn↗

arXiv2023

RESenv: A Realistic Earthquake Simulation Environment based on Unreal Engine

Earthquakes have a significant impact on societies and economies, driving the need for effective search and rescue strategies. With the growing role of AI and robotics in these operations, high-quality synthetic visual data becomes crucial. Current simulation methods, mostly focusing on single building damages, often fail to provide realistic visuals for complex urban settings. To bridge this gap, we introduce an innovative earthquake simulation system using the Chaos Physics System in Unreal Engine. Our approach aims to offer detailed and realistic visual simulations essential for AI and robotic training in rescue missions. By integrating real seismic waveform data, we enhance the authenticity and relevance of our simulations, ensuring they closely mirror real-world earthquake scenarios. Leveraging the advanced capabilities of Unreal Engine, our system delivers not only high-quality visualisations but also real-time dynamic interactions, making the simulated environments more immersive and responsive. By providing advanced renderings, accurate physical interactions, and comprehensive geological movements, our solution outperforms traditional methods in efficiency and user experience. Our simulation environment stands out in its detail and realism, making it a valuable tool for AI tasks such as path planning and image recognition related to earthquake responses. We validate our approach through three AI-based tasks: similarity detection, path planning, and image segmentation.

cs.CE↗

arXiv2021

The Golden Ratio and Hydrodynamics

There are useful and useless golden ratios. The useful one helps in traffic. The useless and rather mysterious one arises in hydrodynamics of point vortices, which we discuss in detail.

math.DS↗