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Yiqian Wang

Publications and source records attributed to Yiqian Wang.

At least 19 recordsLinked to original sources
arXiv2026

Can LLMs Discover Scientific Laws in Real and Parallel Worlds?

Scientific equation discovery has long been central to scientific progress, proceeding through iterative cycles of hypothesis generation, observational testing, and refinement under scientific constraints. As LLM capabilities advance and their role in AI for Science expands, it remains an open problem whether they can genuinely discover scientific laws and how this ability should be evaluated. Existing evaluations, however, often either simplify discovery through synthetic settings or reuse published targets that may already be familiar to LLMs. We therefore introduce SCILAWS-BENCH, a benchmark for scientific law discovery built from published research and real scientific data. It comprises 118 problems drawn from 381 scientific papers, covering 291 candidate laws and roughly 8M real data points across six scientific disciplines. Each problem is instantiated in two complementary settings: (1) SCILAWS-REAL asks models to propose laws from fixed real observations and evaluates held-out predictive fit and scientific validity derived from the source literature, and (2) SCILAWS-PARALLEL asks models to actively query residual-calibrated worlds and recover synthesized hidden laws derived from published forms. This two-setting task design preserves each problem's scientific context while separately evaluating fixed-record law discovery and active recovery of a newly synthesized hidden law. We find that predictive fit can diverge from scientific validity, memorization shapes whether models reproduce or move beyond published formulas, and our best-of-N study reveals a selection bottleneck. Our work provides a paper-grounded benchmark and new empirical perspectives for evaluating AI for scientific discovery. Project page: https://yiyihum.github.io/SciLaws-Bench

cs.AI↗
arXiv2025

Order Matters: Rethinking Prompt Construction in In-Context Learning

In-context learning (ICL) enables large language models to perform new tasks by conditioning on a sequence of examples. Most prior work reasonably and intuitively assumes that which examples are chosen has a far greater effect on performance than how those examples are ordered, leading to a focus on example selection. We revisit this assumption and conduct a systematic comparison between the effect of selection and ordering. Through controlled experiments on both classification and generation tasks, using multiple open-source model families (0.5B to 27B parameters) and GPT-5, we find that the variance in performance due to different example orderings is comparable to that from using entirely different example sets. Furthermore, we show that strong orderings can be identified using only a development set, achieving performance close to an oracle that selects the best ordering based on test labels. Our findings highlight the equal and intertwined importance of example selection and ordering in prompt design, calling for a reexamination of the assumptions held in ICL.

cs.CL↗
arXiv2025

Intermittent--synchronization in non-weakly coupled piecewise linear expanding map lattice: a geometric-combinatorics method

The coupled (chaotic) map lattices (CMLs) characterizes the collective dynamics of a spatially distributed system consisting of locally or globally coupled maps. The current research on the dynamic behavior of CMLs is based on the framework of the Perron-Frobenius operator and mainly focuses on weakly-coupled cases. In this paper, a novel geometric-combinatorics method for for non weakly-coupled CMLs is provided on the dynamical behavior of a two-node CMLs with identical piecewise linear expanding maps. We obtain a necessary-sufficient condition for the uniqueness of absolutely continuous invariant measure (ACIM) and for the occurrence of intermittent-synchronization, that is, almost each orbit enters and exits an arbitrarily small neighborhood of the diagonal for an infinite number of times.

math.DS↗
arXiv2025

The Dry Ten Martini Problem for $C^2$ cosine-type quasiperiodic Schrödinger operators

This paper solves ``The Dry Ten Martini Problem'' for $C^2$ cosine-type quasiperiodic Schrödinger operators with large coupling constants and Diophantine frequencies, a model originally introduced by Sinai in 1987 \cite{sinai}. This shows that the analyticity assumption on the potential is not essential for obtaining a dry Cantor spectrum and can be replaced by a certain geometric condition in the low regularity case. In addition, we prove the homogeneity of the spectrum and the absolute continuity of the integrated density of states (IDS).

math-ph↗
arXiv2025

The precise regularity of the Lyapunov exponent for $C^2$ Cos-type quasiperiodic Schrödinger cocycles with large couplings

In this paper, we study the regularity of the Lyapunov exponent for quasiperiodic Schrödinger cocycles with $C^2$ cos-type potentials, large coupling constants, and a fixed Diophantine frequency. We obtain the absolute continuity of the Lyapunov exponent. Moreover, we prove the Lyapunov exponent is $\frac{1}{2}$-Hölder continuous. Furthermore, for any given $r\in (\frac12, 1)$, we can find some energy in the spectrum where the local regularity of the Lyapunov exponent is between $(r-ε)$-Hölder continuity and $(r+ε)$-Hölder continuity.

math.DS↗
arXiv2023

Deep learning network to correct axial and coronal eye motion in 3D OCT retinal imaging

Optical Coherence Tomography (OCT) is one of the most important retinal imaging technique. However, involuntary motion artifacts still pose a major challenge in OCT imaging that compromises the quality of downstream analysis, such as retinal layer segmentation and OCT Angiography. We propose deep learning based neural networks to correct axial and coronal motion artifacts in OCT based on a single volumetric scan. The proposed method consists of two fully-convolutional neural networks that predict Z and X dimensional displacement maps sequentially in two stages. The experimental result shows that the proposed method can effectively correct motion artifacts and achieve smaller error than other methods. Specifically, the method can recover the overall curvature of the retina, and can be generalized well to various diseases and resolutions.

eess.IV↗
arXiv2022

An objective vortex identification method

Generally, the vortex structures should be independent of the observers who are moving, especially when their coordinates are non-inertial, which may result in confusions in communications between researchers. The property that not being influenced by the choice of coordinate is called objective. Mostly, researchers would like to gather data in the inertial coordinate because most physical laws are valid in the inertial coordinate. As a result, how to transfer the observations in a non-inertial coordinate to those in an inertial coordinate raises interest. In this paper, methods are provided to obtain velocity and velocity gradient tensor in an inertial coordinate from the non-inertial observations based on one known zero-vorticity point which can be chosen from physical fact such as the point is located in the inviscid region.Further, objective vortex structure can be calculated from the objective velocity or velocity gradient tensor. With Liutex chosen as the indicator of the vortex, two numerical examples are used to test the proposed methods. The results show that the methods perform very well and the relative error is extremely small.

physics.flu-dyn↗
arXiv2020

Liutex-based Modified Navier-Stokes Equation

The Navier-Stokes (NS) partial differential equations, as the governing equation of fluid dynamics, are based on particles with zero volume. In such a condition, conservation law of moment of momentum is automatically satisfied, and thus NS equations only contain conservation of mass, momentum and energy. Because of the difficulty to get an analytical solution of NS equations, scientists develop finite element method (FEM) and finite volume method (FVM) to obtain approximate solutions. However, these methods are dependent on the size of finite volumes, which is not zero. Considering the size of the finite volume, conservation law of moment of momentum is no longer automatically satisfied and it is necessary to develop a new control equation to take effect of momentum into account. In this paper, new relations of reciprocal shear stresses are derived from conservation law of moment of momentum, and so are new constitutive relations and modified NS equations. The Liutex based NS equation may be the universal governing equations for both laminar and turbulent flow which is dominated by vortices and conservation of moment of momentum must be satisfied.

physics.flu-dyn↗
arXiv2018

Physical meaning of vorticity based on the RS decomposition and an explicit formula for the Liutex vector

In the present study, the physical meaning of vorticity is revisited based on the RS decomposition proposed by Liu et al. in the framework of Liutex (previously named Rortex), a vortex vector field with information of both rotation axis and swirling strength [ C. Liu et al., "Rortex-A new vortex vector definition and vorticity tensor and vector decomposition", Phys. Fluids 30, 035103 (2018)]. It is demonstrated that the vorticity in the direction of rotational axis is twice the spatial mean angular velocity in the small neighborhood around the considered point while the imaginary part of the complex eigenvalue (λ_ci) of the velocity gradient tensor (if exist) is the pseudo-time average angular velocity of a trajectory moving circularly or spirally around the axis. In addition, an explicit expression of the Liutex vector in terms of the eigenvalues and eigenvectors of velocity gradient is obtained for the first time from above understanding, which can further, though mildly, accelerate the calculation and give more physical comprehension of the Liutex vector.

physics.flu-dyn↗
arXiv2017

Multi-speaker Recognition in Cocktail Party Problem

This paper proposes an original statistical decision theory to accomplish a multi-speaker recognition task in cocktail party problem. This theory relies on an assumption that the varied frequencies of speakers obey Gaussian distribution and the relationship of their voiceprints can be represented by Euclidean distance vectors. This paper uses Mel-Frequency Cepstral Coefficients to extract the feature of a voice in judging whether a speaker is included in a multi-speaker environment and distinguish who the speaker should be. Finally, a thirteen-dimension constellation drawing is established by mapping from Manhattan distances of speakers in order to take a thorough consideration about gross influential factors.

eess.AS↗
arXiv2017

Intermittent behaviors in weakly coupled map lattices

In this paper, we study intermittent behaviors of coupled piecewise-expanding map lattices with two nodes and a weak coupling. We show that the successive phase transition between ordered and disordered phases occurs for almost every orbit. That is, we prove $\liminf_{n\rightarrow \infty}| x_1(n)-x_2(n)|=0$ and $\limsup_{n\rightarrow \infty}| x_1(n)-x_2(n)|\ge c_0>0$, where $x_1(n), x_2(n)$ correspond to the coordinates of two nodes at the iterative step $n$. We also prove the same conclusion for weakly coupled tent-map lattices with any multi-nodes.

math.DS↗
arXiv2015

Quasi-Periodic Schrödinger Cocycles with Positive Lyapunov Exponent are not Open in the Smooth Topology

One knows that the set of quasi-periodic Schrödinger cocycles with positive Lyapunov exponent is open and dense in the analytic topology. In this paper, we construct cocycles with positive Lyapunov exponent which can be approximated by ones with zero Lyapunov exponent in the space of ${\cal C}^ l$ ($1 \le l\le \infty$) smooth quasi-periodic cocycles. As a consequence, the set of quasi-periodic Schrödinger cocycles with positive Lyapunov exponent is not ${\cal C}^ l$ open.

math.DS↗
arXiv2014

Cantor spectrum for a class of $C^2$ quasiperiodic Schrödinger operators

We show that for a class of $C^2$ quasiperiodic potentials and for any Diophantine frequency, the spectrum of the corresponding Schrödinger operators is Cantor. Our approach is of purely dynamical systems, which depends on a detailed analysis of asymptotic stable and unstable directions. We also apply it to general $\mathrm{SL}(2,\mathbb R)$ cocycles, and obtain that uniform hyperbolic systems form a open and dense set in some one-parameter family.

math.DS↗
arXiv2013

Uniform Positivity and Continuity of Lyapunov Exponents for a Class of $C^2$ Quasiperiodic Schrödinger Cocycles 

We show that for a class of $C^2$ quasiperiodic potentials and for any Diophantine frequency, the Lyapunov exponents of the corresponding Schrödinger cocycles are uniformly positive and weak Hölder continuous as function of energies. As a corollary, we also obtain that the corresponding integrated density of states (IDS) is weak Hölder continous. Our approach is of purely dynamical systems, which depends on a detailed analysis of asymptotic stable and unstable directions. We also apply it to more general $\mathrm{SL}(2,\mathbb R)$ cocycles, which in turn can be applied to get uniform positivity and continuity of Lyapuonv exponents around unique nondegenerate extremal points of any smooth potential, and to a certain class of $C^2$ Szeg\H o cocycles.

math.DS↗
arXiv2013

Boundedness of semilinear Duffing equations at resonance with oscillating nonlinearities

In this paper, we prove the boundedness of all the solutions for the equation $\ddot{x}+n^2x+g(x)+ψ'(x)=p(t)$ with the Lazer-Leach condition on $g$ and $p$, where $n\in \mathbb{N^+}$, $p(t)$ and $ψ'(x)$ are periodic and $g(x)$ is bounded. For the critical situation that $\big |\int_0^{2π}p(t)e^{int}dt \big|=2\big|g(+\infty)-g(-\infty)\big|$, we also prove a sufficient and necessary condition for the boundedness if $ψ'(x)\equiv0$.

math.DS↗
arXiv2013

Examples of Discontinuity of Lyapunov Exponent in Smooth Quasi-Periodic Cocycles

We study the regularity of the Lyapunov exponent for quasi-periodic cocycles $(T_ω, A)$ where $T_ω$ is an irrational rotation $x\to x+ 2πω$ on $\SS^1$ and $A\in {\cal C}^l(\SS^1, SL(2,\mathbb{R}))$, $0\le l\le \infty$. For any fixed $l=0, 1, 2, \cdots, \infty$ and any fixed $ω$ of bounded-type, we construct $D_{l}\in {\cal C}^l(\SS^1, SL(2,\mathbb{R}))$ such that the Lyapunov exponent is not continuous at $D_{l}$ in ${\cal C}^l$-topology. We also construct such examples in a smaller Schrödinger class.

math.DS↗