arXiv subjects

Guo Liang

Publications and source records attributed to Guo Liang.

17 recordsLinked to original sources

arXiv2026

Reliable Real-Time Value at Risk Estimation via Quantile Regression Forest with Conformal Calibration

Rapidly evolving market conditions call for real-time risk monitoring, but its online estimation remains challenging. In this paper, we study the online estimation of one of the most widely used risk measures, Value at Risk (VaR). Its accurate and reliable estimation is essential for timely risk control and informed decision-making. We propose to use the quantile regression forest in the offline-simulation-online-estimation (OSOA) framework. Specifically, the quantile regression forest is trained offline to learn the relationship between the online VaR and risk factors, and real-time VaR estimates are then produced online by incorporating observed risk factors. To further ensure reliability, we develop a conformalized estimator that calibrates the online VaR estimates. To the best of our knowledge, we are the first to leverage conformal calibration to estimate real-time VaR reliably based on the OSOA formulation. Theoretical analysis establishes the consistency and coverage validity of the proposed estimators. Numerical experiments confirm the proposed method and demonstrate its effectiveness in practice.

stat.ML↗

arXiv2025

Regular Tree Search for Simulation Optimization

Tackling simulation optimization problems with non-convex objective functions remains a fundamental challenge in operations research. In this paper, we propose a class of random search algorithms, called Regular Tree Search, which integrates adaptive sampling with recursive partitioning of the search space. The algorithm concentrates simulations on increasingly promising regions by iteratively refining a tree structure. A tree search strategy guides sampling decisions, while partitioning is triggered when the number of samples in a leaf node exceeds a threshold that depends on its depth. Furthermore, a specific tree search strategy, Upper Confidence Bounds applied to Trees (UCT), is employed in the Regular Tree Search. We prove global convergence under sub-Gaussian noise, based on assumptions involving the optimality gap, without requiring continuity of the objective function. Numerical experiments confirm that the algorithm reliably identifies the global optimum and provides accurate estimates of its objective value.

math.OC↗

arXiv2025

Enhanced Derivative-Free Optimization Using Adaptive Correlation-Induced Finite Difference Estimators

Gradient-based methods are well-suited for derivative-free optimization (DFO), where finite-difference (FD) estimates are commonly used as gradient surrogates. Traditional stochastic approximation methods, such as Kiefer-Wolfowitz (KW) and simultaneous perturbation stochastic approximation (SPSA), typically utilize only two samples per iteration, resulting in imprecise gradient estimates and necessitating diminishing step sizes for convergence. In this paper, we first explore an efficient FD estimate, referred to as correlation-induced FD estimate, which is a batch-based estimate. Then, we propose an adaptive sampling strategy that dynamically determines the batch size at each iteration. By combining these two components, we develop an algorithm designed to enhance DFO in terms of both gradient estimation efficiency and sample efficiency. Furthermore, we establish the consistency of our proposed algorithm and demonstrate that, despite using a batch of samples per iteration, it achieves the same convergence rate as the KW and SPSA methods. Additionally, we propose a novel stochastic line search technique to adaptively tune the step size in practice. Finally, comprehensive numerical experiments confirm the superior empirical performance of the proposed algorithm.

math.OC↗

arXiv2024

A Correlation-induced Finite Difference Estimator

Finite difference (FD) approximation is a classic approach to stochastic gradient estimation when only noisy function realizations are available. In this paper, we first provide a sample-driven method via the bootstrap technique to estimate the optimal perturbation, and then propose an efficient FD estimator based on correlated samples at the estimated optimal perturbation. Furthermore, theoretical analyses of both the perturbation estimator and the FD estimator reveal that, {\it surprisingly}, the correlation enables the proposed FD estimator to achieve a reduction in variance and, in some cases, a decrease in bias compared to the traditional optimal FD estimator. Numerical results confirm the efficiency of our estimators and align well with the theory presented, especially in scenarios with small sample sizes. Finally, we apply the estimator to solve derivative-free optimization (DFO) problems, and numerical studies show that DFO problems with 100 dimensions can be effectively solved.

stat.ME↗

arXiv2020

Nonlinear guiding of light in tunable food-dye solutions

We provide the first demonstration of nonlinear self-trapping of light in solutions of food coloring dyes, leading to dirt cheap soliton waveguides. The optical self-focusing nonlinearity observed in such solutions is attributed to the optical absorption force acting on dye molecules, as the thermal effect at relatively higher power results in a self-defocusing nonlinearity. We found the nonlinear response increases when the laser wavelength is switched to near the peak absorption for all food dyes tested. Furthermore, the absorption-dependent nonlinearity can be tuned by making purposive samples of different food dyes. In particular, with appropriately mixing of dye solutions, nonlinear response arises for otherwise inactive wavelengths, leading to interaction between two beams of different wavelengths and formation of a coupled soliton-like pair. At milliwatt low power levels, self-trapping achieved at one wavelength in food-dye solutions can serve as low-cost waveguides for optical beams at other wavelengths.

physics.optics↗

arXiv2019

Experimental observation of anisotropic diffraction induced by orbital angular momentum

We reveal for the first time a direct relationship between the diffraction of optical beams and their carrying orbital angular momentum (OAM). We experimentally demonstrate a novel phenomenon that the anisotropic diffraction can be induced by the OAM, predicted by us [Opt. Express, \textbf{26}, 8084 (2018)], via the propagations of the elliptic beams with the OAM in linearly and both-linearly-and-nonlinearly isotropic media, respectively. In the former case, when its carrying OAM equals the so-called critical OAM, the spiraling elliptic Gaussian beam (fundamental eigenmode) is observed in the free space, where only the eigenmode with cylindrical-symmetry is supposed to exist for the beam without the OAM. In the latter case, the spiraling elliptic soliton, predicted by Desyatnikov et al. [Phys. Rev. Lett, \textbf{104}, 053902 (2010)], is observed to stably propagate in a cylindrical lead glass. The power-controllable rotation of such an elliptic beam is also experimentally demonstrated.

physics.optics↗

arXiv2019

Optical force-induced nonlinearity and self-guiding of light in human red blood cell suspensions

Osmotic conditions play an important role in the cell properties of human red blood cells (RBCs), which are crucial for the pathological analysis of some blood diseases such as malaria. Over the past decades, numerous efforts have mainly focused on the study of the RBC biomechanical properties that arise from the unique deformability of erythrocytes. Here, we demonstrate nonlinear optical effects from human RBCs suspended in different osmotic solutions. Specifically, we observe self-trapping and scattering-resistant nonlinear propagation of a laser beam through RBC suspensions under all three osmotic conditions, where the strength of the optical nonlinearity increases with osmotic pressure on the cells. This tunable nonlinearity is attributed to optical forces, particularly the forward scattering and gradient forces. Interestingly, in aged blood samples (with lysed cells), a notably different nonlinear behavior is observed due to the presence of free hemoglobin. We use a theoretical model with an optical force-mediated nonlocal nonlinearity to explain the experimental observations. Our work on light self-guiding through scattering bio-soft-matter may introduce new photonic tools for noninvasive biomedical imaging and medical diagnosis.

physics.optics↗

arXiv2018

Anisotropic diffraction induced by orbital angular momentum during propagations of optical beams

It is demonstrated that the orbital angular momentum (OAM) carried by the elliptic beam without the phase-singularity can induce the anisotropic diffraction (AD). The quantitative relation between the OAM and its induced AD is analytically obtained by a comparison of two different kinds of (1+2)-dimensional beam propagations: the linear propagations of the elliptic beam without the OAM in an anisotropic medium and that with the OAM in an isotropic one. In the former case, the optical beam evolves as the fundamental mode of the eigenmodes when its ellipticity is the square root of the anisotropic parameter defined in the paper; while in the latter case, the fundamental mode exists only when the OAM carried by the optical beam equals a specific one called a critical OAM. The OAM always enhances the beam-expanding in the major-axis direction and weakens that in the minor-axis direction no matter the sign of the OAM, and the larger the OAM, the stronger the AD induced by it. Besides, the OAM can also make the elliptic beam rotate, and the absolute value of the rotation angle is no larger than $π/2$ during the propagation.

physics.optics↗

arXiv2015

Transition between self-focusing and self-defocusing in nonlocally nonlinear media

We reveal the relevance between the nonlocality and the focusing/defocusing states in nonlocally nonlinear media, and predict a novel phenomenon that the self-focusing/self-defocusing property of the optical beam in the nonlocally nonlinear medium with a sine-oscillation response function depends on its degree of nonlocality. The transition from the focusing nonlinearity to the defocusing nonlinearity of the nonlinear refractive index will happen when the degree of nonlocality of the system goes cross a critical value, and vise verse. Bright and dark soliton solutions are obtained, respectively, in the focusing state and in the defocusing state, and their stabilities are also discussed. It is mentioned that such a phenomenon might be experimentally realized in the nematic liquid crystal with negative dielectric anisotropy or in the quadratic nonlinear medium.

physics.optics↗

arXiv2015

Application of the Hamiltonian formulation to nonlinear light-envelope propagations

A new approach, which is based on the new canonical equations of Hamilton found by us recently, is presented to analytically obtain the approximate solution of the nonlocal nonlinear Schrödinger equation (NNLSE). The approximate analytical soliton solution of the NNLSE can be obtained, and the stability of the soliton can be analytically analysed in the simple way as well, all of which are consistent with the results published earlier. For the single light-envelope propagated in nonlocal nonlinear media modeled by the NNLSE, the Hamiltonian of the system can be constructed, which is the sum of the generalized kinetic energy and the generalized potential. The extreme point of the generalized potential corresponds to the soliton solution of the NNLSE. The soliton is stable when the generalized potential has the minimum, and unstable otherwise. In addition, the rigorous proof of the equivalency between the NNLSE and the Euler-Lagrange equation is given on the premise of the response function with even symmetry.

nlin.PS↗

arXiv2014

Spiraling elliptic breathers in saturable nonlinear media with linear anisotropy

We have introduced a class of spiraling elliptic breathers in saturable nonlinear media with linear anisotropy. Two kinds of evolution behaviors of the breathers, rotating and pendulum-like librating, are both predicted by the variational approach, and confirmed by the numerical simulation.The spiraling elliptic breathers can rotate even though they have no initial orbital angular momentum (OAM). Due to the linear anisotropy of the media, the OAM is no longer conserved. Therefore, the angular velocity is found to be not a constant but a periodic function of the propagation distance. When the linear anisotropy is large enough, the spiraling elliptic breathers can librate like the pendulum. The spiraling elliptic breathers exist in the media with not only the saturable nonlinearity but also the nonlocal nonlinearity, as a matter of fact, they are universal in the nonlinear media with the linear anisotropy.

nlin.PS↗

arXiv2014

Application of canonical Hamiltonian formulation to nonlinear light-envelope propagations

We first point out it is conditional to apply the variational approach to the nonlocal nonlinear Schrödinger equation (NNLSE), that is, the response function must be an even function. Different from the variational approach, the canonical Hamiltonian formulation for the first-order differential system are used to deal with the problems of the nonlinear light-envelope propagations. The Hamiltonian of the system modeled by the NNLSE is obtained, which can be expressed as the sum of the generalized kinetic energy and the generalized potential. The solitons correspond to extreme points of the generalized potential. The stabilities of solitons in both local and nonlocal nonlinear media are also investigated by the analysis of the generalized potential. They are stable when the potential has minimum, and unstable otherwise.

nlin.PS↗

arXiv2013

Canonical equations of Hamilton for the nonlinear Schrödinger equation

We define two different systems of mathematical physics: the second-order differential system (SODS) and the first-order differential system (FODS). The Newton's second law of motion and the nonlinear Schrödinger equation (NLSE) are the exemplary SODS and FODS, respectively. We obtain a new kind of canonical equations of Hamilton (CEH), which are of some kind of symmetry in form and are formally different with the conventional CEH without symmetry [H. Goldstein, C. Poole, J. Safko, Classical Mechanics, third ed., Addison-Wesley, 2001]. We also prove that the number of the CEHs is equal to the number of the generalized coordinates for the FODS, but twice the number of the generalized coordinates for the SODS. We show that the FODS can only be expressed by the new CEH, but do not by the conventional CEH, while the SODS can be done by both the new and the conventional CEHs. As an example, we prove that the nonlinear Schrödinger equation can be expressed with the new CEH in a consistent way.

physics.class-ph↗

arXiv2012

Canonical equations of Hamilton with beautiful symmetry

The Hamiltonian formulation plays the essential role in constructing the framework of modern physics. In this paper, a new form of canonical equations of Hamilton with the complete symmetry is obtained, which are valid not only for the first-order differential system, but also for the second-order differential system. The conventional form of the canonical equations without the symmetry [Goldstein et al., Classical Mechanics, 3rd ed, Addison-Wesley, 2001] are only for the second-order differential system. It is pointed out for the first time that the number of the canonical equations for the first-order differential system is half of that for the second-order differential system. The nonlinear Schrödinger equation, a universal first-order differential system, can be expressed with the new canonical equations in a consistent way.

physics.class-ph↗

arXiv2012

A variational approach to Schroedinger equation with parity-time symmetry Gaussian complex potential

A variational technique is established to deal with the Schrodinger equation with parity-time(PT) symmetric Gaussian complex potential. The method is extended to the linear and self-focusing and defocusing nonlinear cases. Some unusual properties in PT systems such as transverse power flow and PT breaking points can be analyzed by this method. Following numerical simulations, the analytical results are in good agreement with the numerical results.

nlin.PS↗

arXiv2011

Spiraling elliptic solitons in nonlocal nonlinear media without anisotropy

The optical spatial solitons with ellipse-shaped spots have generally been considered to be a result of either linear or nonlinear anisotropy. In this paper, we introduce a class of spiraling elliptic solitons in the nonlocal nonlinear media without both linear and nonlinear anisotropy. The spiraling elliptic solitons carry the orbital angular momentum, which plays a key role in the formation of such solitons, and are stable for any degree of nonlocality except the local case when the response function of the material is Gaussian function. The formation of such solitons can be attributable to the effective anisotropic diffraction (linear anisotropy) resulting from the orbital angular momentum. Our variational analytical result is confirmed by direct numerical simulation of the nonlocal nonlinear Schrodinger equation.

nlin.PS↗

arXiv2011

Spiraling elliptic solitons in generic nonlocal nonlinear media

We have introduced a class of spiraling elliptic solitons in generic nonlocal nonlinear media. The spiraling elliptic solitons carry the orbital angular momentum. This class solitons are stable for any degree of nonlocality except for the local case when the response function of the material is Gaussian function.

nlin.PS↗