arXiv subjects

Haitao Liu

Publications and source records attributed to Haitao Liu.

At least 19 recordsLinked to original sources

arXiv2026

Perturbation theory of mesoscale plasmonic waveguide with an analytical treatment of nonclassical electromagnetic boundary condition

The optical modes of mesoscale plasmonic waveguides (MPWs) are significantly affected by nonclassical quantum effects, which can be comprehensively described by the nonclassical electromagnetic boundary condition (NEBC) formulated with the surface-response Feibelman d-parameters. In this paper, a perturbation theory for the nonclassical waveguide modes (NWMs) supported by MPWs under the NEBC is proposed. In this theory, by adopting the classical waveguide modes (CWMs) under the classical electromagnetic boundary condition (CEBC) as the basis functions and treating the NEBC as a first-order perturbation, a general expression of the propagation constant of the NWM with an analytical dependence on the NEBC is derived. This theory transparently reveals the underlying general relation between the nonclassical effects and the propagation properties of the NWMs, thereby providing an effective tool for the understanding and design of MPW devices, as well as for the experimental measurement of the d-parameters.

physics.optics↗

arXiv2026

Minimizing propagated density errors of atomic core-electron for simultaneously accurate bandgaps and lattice constants in closed-shell Copper semiconductors

Density functional theory struggles to accurately determine electron density of atoms, whose error is inevitably encoded into the pseudopotential and propagated into solid-state calculations. However, little is known about how this affects accuracy nor how to remedy it. In this work, through a systematic study of the effect of Cu atomic density on bandgap and lattice constants of over 50 Cu-containing simple closed-shell semiconductors, we find that core-electron density can drastically affect nuclear attraction to valence electrons and subsequent charge distribution and energy position of Cu 3$d$ electrons. The error can be eliminated at its source by employing modified Hartree-Fock pseudopotentials for Cu core while retaining (semi-)local functionals for valence electrons. This real-space partitioning approach leads to simultaneous high-accuracy in bandgap and lattice constants across the entire material class.

cond-mat.mtrl-sci↗

arXiv2026

Impact of mode completeness on the accuracy of the coupling theory of quasinormal modes: a strict numerical demonstration

The coupling theory of quasinormal modes (QNMs) for a coupled system of generally lossy and dispersive optical nanoresonators has been established in a rigorous manner based on the first principle of Maxwell's equations [Phys. Rev. B 102, 045430 (2020)], and can achieve superior computational efficiency and physical intuitiveness compared with full-wave numerical methods if a small set of modes can achieve a high accuracy. The QNMs suffer from an exponential divergence of far field and can form a complete basis inside but not outside the resonator. In the QNM coupling theory (QCT), it is required that the QNMs of each resonator form a complete basis in expanding the scattered field both inside and outside the resonator, which can be achieved by using regularized QNMs (RQNMs). However, a strict numerical demonstration of the impact of the mode completeness of RQNMs on the accuracy of QCT by using a virtually complete basis of RQNMs is still absent. In this paper, we will provide such a numerical demonstration along with an improvement of the QCT and some theoretical demonstrations on a rigorous incorporation of RQNMs into the QCT. The RQNMs are obtained by introducing an equivalent surface current (ESC) encircling the resonator (called ESC-RQNMs) or the perfectly matched layer (PML) surrounding the computational domain (called PML-RQNMs). The numerical example is selected as two one-dimensional resonators of slabs in the extreme coupling case of direct contact, for which a virtually complete basis of RQNMs can be solved either analytically (for ESC-RQNMs) or numerically (for PML-RQNMs). The results show that by using a virtually complete basis of RQNMs, the QCT can achieve a high accuracy in predicting both the source-free eigenmodes and the source-excited scattered field of the coupled system, which is not true if using the incomplete basis of not-regularized QNMs (i.e., physical QNMs).

physics.optics↗

arXiv2025

Pseudopotentials, an overlooked source and remedy of DFT errors

First-principles calculations rely heavily on pseudopotentials, yet their impact on accuracy is hardly addressed. In this work, we show that most pseudopotentials to date introduce errors, which manifest themselves as errors of atomic energy levels, leading to a $de facto$ deviation from the Hohenberg-Kohn theorem. We consider the atomic-level adjusted pseudopotentials, whose interplay with exchange-correlation functional provides a pragmatic correction that balances accuracy and efficiency. We benchmark our theory with bandgap calculation for 54 semiconductors containing monovalent Cu. The results, compared to those from conventional studies, not only remove all erroneous metal predictions for 11 compounds, but also reduce the mean relative error from 80\% to 20\%. Overall accuracy even exceeds those of standard hybrid functionals and GW methods.

cond-mat.mtrl-sci↗

arXiv2025

Fourier modal method and coordinate transformation method under nonclassical electromagnetic boundary condition for the electromagnetism of mesoscale metallic nanostructures

The optical response of mesoscale metallic nanostructures (MMNSs) with feature sizes down to extreme nanometer scales is largely affected by the nonclassical quantum effects, which can be comprehensively described by the nonclassical electromagnetic boundary condition (NEBC) incorporating surface-response Feibelman d-parameters. Here we report the Fourier modal method (FMM) and the coordinate transformation method (C method) under the NEBC, which are built up by incorporating the NEBC into a recently reported 3D-C method [Opt. Express 29, 1516 (2021)] that is applicable to the general three-dimensional (3D) photonic structures with curved boundaries. The validity and accuracy of the proposed method are confirmed numerically through a comparison with other full-wave method incorporating the NEBC. The present work marries the NEBC and the well-developed modal methods of FMM and C method, thus bringing the advantages of these modal methods in physical intuitiveness and computational efficiency to the electromagnetic modeling of nonclassical quantum effects in the MMNSs.

physics.optics↗

arXiv2025

Are there type-III multiferroics?

Multiferroics are known to be classified into two types. However, type-I lacks sufficient magnetoelectric coupling and type-II lacks sufficient electric polarization, making both practically difficult. In this work, we explore the possibility of type-III multiferroics, where the origins of ferroelectricity and magnetism are highly intertwined but not causally related, with a combination of strong magnetoelectric coupling and large polarization. Our first-principles calculations predict that monolayer TiCdO$_{4}$ is such a type-III ferroelectric-ferromagnetic multiferroics with both electronic and magnetic orders originating from competing electron populations on oxygen atoms. It shows an electric polarization of 50 $μ$C/m$^{2}$ while the maximum linear and quadratic magnetoelectric response are as high as 35000 ps/m and 1.59 $\times$ 10$^{-14}$ s/A, respectively. Our study opens up new perspectives for the discovery and design of much-anticipated multiferroics that can be used for cross-modulation.

cond-mat.mtrl-sci↗

arXiv2025

Local perfect chirality at reflection-zeros away from exceptional points in optical whispering gallery microcavity

Recently, a local and imperfect chirality of the resonant eigenmode at the exceptional point (EP) has been reported in the optical whispering gallery microcavity system perturbed by two strong nanoscatterers [Phys. Rev. A 108, L041501 (2023)]. Here, we discover a local perfect chirality of the resonant eigenmode away from the EP in the parameter space of the strongly perturbed microcavity system. By considering the multiple scattering process of the azimuthally propagating modes (APMs) at the nanoscatterers with a first-principles-based model, the local perfect chirality is predicted to result from the unidirectional reflectionlessness, i.e., the reflection-zero (R-zero) of the APMs at the two nanoscatterers. Numerical results and model predictions consistently show that the structural parameters of the R-zero typically deviate from those of the EP, which means that the pair of split resonant eigenmodes at the R-zero have different complex resonance frequencies and electromagnetic fields. In general, only one of the pair of split eigenmodes exhibits a local perfect chirality within the local azimuthal range divided by the two nanoscatterers. With the decrease of the two nanoscatterers' sizes or their relative azimuthal angle, the R-zero tends to coincide with the EP.

physics.optics↗

arXiv2025

Generative Multi-Form Bayesian Optimization

Many real-world problems, such as airfoil design, involve optimizing a black-box expensive objective function over complex structured input space (e.g., discrete space or non-Euclidean space). By mapping the complex structured input space into a latent space of dozens of variables, a two-stage procedure labeled as generative model based optimization (GMO) in this paper, shows promise in solving such problems. However, the latent dimension of GMO is hard to determine, which may trigger the conflicting issue between desirable solution accuracy and convergence rate. To address the above issue, we propose a multi-form GMO approach, namely generative multi-form optimization (GMFoO), which conducts optimization over multiple latent spaces simultaneously to complement each other. More specifically, we devise a generative model which promotes positive correlation between latent spaces to facilitate effective knowledge transfer in GMFoO. And further, by using Bayesian optimization (BO) as the optimizer, we propose two strategies to exchange information between these latent spaces continuously. Experimental results are presented on airfoil and corbel design problems and an area maximization problem as well to demonstrate that our proposed GMFoO converges to better designs on a limited computational budget.

cs.CE↗

arXiv2025

Co-Learning Bayesian Optimization

Bayesian optimization (BO) is well known to be sample-efficient for solving black-box problems. However, the BO algorithms can sometimes get stuck in suboptimal solutions even with plenty of samples. Intrinsically, such suboptimal problem of BO can attribute to the poor surrogate accuracy of the trained Gaussian process (GP), particularly that in the regions where the optimal solutions locate. Hence, we propose to build multiple GP models instead of a single GP surrogate to complement each other and thus resolving the suboptimal problem of BO. Nevertheless, according to the bias-variance tradeoff equation, the individual prediction errors can increase when increasing the diversity of models, which may lead to even worse overall surrogate accuracy. On the other hand, based on the theory of Rademacher complexity, it has been proved that exploiting the agreement of models on unlabeled information can help to reduce the complexity of the hypothesis space, and therefore achieving the required surrogate accuracy with fewer samples. Such value of model agreement has been extensively demonstrated for co-training style algorithms to boost model accuracy with a small portion of samples. Inspired by the above, we propose a novel BO algorithm labeled as co-learning BO (CLBO), which exploits both model diversity and agreement on unlabeled information to improve the overall surrogate accuracy with limited samples, and therefore achieving more efficient global optimization. Through tests on five numerical toy problems and three engineering benchmarks, the effectiveness of proposed CLBO has been well demonstrated.

cs.LG↗

arXiv2024

A way to identify whether a DFT gap is from right reasons or error cancellations: The case of copper chalcogenides

Gap opening remains elusive in copper chalcogenides (Cu$_{2}X$, $X$ = S, Se and Te), not least because Hubbard + $U$, hybrid functional and ${GW}$ methods have also failed. In this work, we elucidate that their failure originates from a severe underestimation of the 4$s$-3$d$ orbital splitting of the Cu atom, which leads to a band-order inversion in the presence of an anionic crystal field. As a result, the Fermi energy is pinned due to symmetry, yielding an invariant zero gap. Utilizing the hybrid pseudopotentials to correct the underestimation on the atomic side opens up gaps of experimental magnitude in Cu$_{2}X$, suggesting their predominantly electronic nature. Our work not only clarifies the debate about the Cu$_{2}X$ gap, but also provides a way to identify which of the different methods really captures the physical essence and which is the result of error cancellation.

cond-mat.mtrl-sci↗

arXiv2024

ALI-DPFL: Differentially Private Federated Learning with Adaptive Local Iterations

Federated Learning (FL) is a distributed machine learning technique that allows model training among multiple devices or organizations by sharing training parameters instead of raw data. However, adversaries can still infer individual information through inference attacks (e.g. differential attacks) on these training parameters. As a result, Differential Privacy (DP) has been widely used in FL to prevent such attacks. We consider differentially private federated learning in a resource-constrained scenario, where both privacy budget and communication rounds are constrained. By theoretically analyzing the convergence, we can find the optimal number of local DPSGD iterations for clients between any two sequential global updates. Based on this, we design an algorithm of Differentially Private Federated Learning with Adaptive Local Iterations (ALI-DPFL). We experiment our algorithm on the MNIST, FashionMNIST and Cifar10 datasets, and demonstrate significantly better performances than previous work in the resource-constraint scenario. Code is available at https://github.com/cheng-t/ALI-DPFL.

cs.LG↗

arXiv2024

DP-DCAN: Differentially Private Deep Contrastive Autoencoder Network for Single-cell Clustering

Single-cell RNA sequencing (scRNA-seq) is important to transcriptomic analysis of gene expression. Recently, deep learning has facilitated the analysis of high-dimensional single-cell data. Unfortunately, deep learning models may leak sensitive information about users. As a result, Differential Privacy (DP) is increasingly used to protect privacy. However, existing DP methods usually perturb whole neural networks to achieve differential privacy, and hence result in great performance overheads. To address this challenge, in this paper, we take advantage of the uniqueness of the autoencoder that it outputs only the dimension-reduced vector in the middle of the network, and design a Differentially Private Deep Contrastive Autoencoder Network (DP-DCAN) by partial network perturbation for single-cell clustering. Since only partial network is added with noise, the performance improvement is obvious and twofold: one part of network is trained with less noise due to a bigger privacy budget, and the other part is trained without any noise. Experimental results of six datasets have verified that DP-DCAN is superior to the traditional DP scheme with whole network perturbation. Moreover, DP-DCAN demonstrates strong robustness to adversarial attacks.

cs.LG↗

arXiv2024

Stable phases of freestanding monolayer TiO$_2$: The emergence of out-of-plane ferroelectricity

Despite being successfully synthesized [Zhang $et$ $al.$, Nat. Mater. \textbf{20}, 1073 (2021)], the monolayer structure of stable hexagonal TiO$_2$ is unknown, and it is not even clear whether it can exist in a freestanding form. Through first-principles calculations, we have identified two previously uncharted stable structures, namely, distorted 1$\times$$\sqrt{3}$ 1T-TiO$_2$ and $\sqrt{3}$$\times$$\sqrt{3}$ 1T-TiO$_2$, both of which are energetically more favourable than commonly adopted 1H and 1T phases. Here structural distortions are characterized by the out-of-plane shifts of Ti atoms due to the pseudo-Jahn-Teller interactions, which break one and all two inversion symmetries of 1T configuration. As a consequence, the 1$\times$$\sqrt{3}$ 1T remains centrosymmetric while the $\sqrt{3}$$\times$$\sqrt{3}$ 1T exhibits out-of-plane ferroelectricity. Electronic structure calculations show that both two are wide-bandgap semiconductors with bandgaps larger than their bulk counterparts. Our study not only deepens the understanding of structural instability in wide-gap semiconductors but also adds a new member to the rare family of two-dimensional out-of-plane ferroelectrics.

cond-mat.mtrl-sci↗

arXiv2023

Truncated Laplace and Gaussian mechanisms of RDP

The Laplace mechanism and the Gaussian mechanism are primary mechanisms in differential privacy, widely applicable to many scenarios involving numerical data. However, due to the infinite-range random variables they generate, the Laplace and Gaussian mechanisms may return values that are semantically impossible, such as negative numbers. To address this issue, we have designed the truncated Laplace mechanism and Gaussian mechanism. For a given truncation interval [a, b], the truncated Gaussian mechanism ensures the same Renyi Differential Privacy (RDP) as the untruncated mechanism, regardless of the values chosen for the truncation interval [a, b]. Similarly, the truncated Laplace mechanism, for specified interval [a, b], maintains the same RDP as the untruncated mechanism. We provide the RDP expressions for each of them. We believe that our study can further enhance the utility of differential privacy in specific applications.

cs.CR↗

arXiv2022

Robust Motion Averaging for Multi-view Registration of Point Sets Based Maximum Correntropy Criterion

As an efficient algorithm to solve the multi-view registration problem,the motion averaging (MA) algorithm has been extensively studied and many MA-based algorithms have been introduced. They aim at recovering global motions from relative motions and exploiting information redundancy to average accumulative errors. However, one property of these methods is that they use Guass-Newton method to solve a least squares problem for the increment of global motions, which may lead to low efficiency and poor robustness to outliers. In this paper, we propose a novel motion averaging framework for the multi-view registration with Laplacian kernel-based maximum correntropy criterion (LMCC). Utilizing the Lie algebra motion framework and the correntropy measure, we propose a new cost function that takes all constraints supplied by relative motions into account. Obtaining the increment used to correct the global motions, can further be formulated as an optimization problem aimed at maximizing the cost function. By virtue of the quadratic technique, the optimization problem can be solved by dividing into two subproblems, i.e., computing the weight for each relative motion according to the current residuals and solving a second-order cone program problem (SOCP) for the increment in the next iteration. We also provide a novel strategy for determining the kernel width which ensures that our method can efficiently exploit information redundancy supplied by relative motions in the presence of many outliers. Finally, we compare the proposed method with other MA-based multi-view registration methods to verify its performance. Experimental tests on synthetic and real data demonstrate that our method achieves superior performance in terms of efficiency, accuracy and robustness.

cs.CV↗

arXiv2022

Imperfect chirality at exceptional points in optical whispering-gallery microcavities

Non-Hermitian systems have attracted considerable attention for their broad impacts on various physical platforms and peculiar applications. In non-Hermitian systems, both eigenvalues and eigenstates simultaneously coalesce at exceptional points (EPs). As one of the remarkable features of EPs, the field chirality is commonly considered perfect, which is utilized as an intriguing feature to control wave propagation and regarded as a criterion of EP. However, in this work, we discover an imperfect chirality of eigenmodes at the EPs in an optical whispering gallery mode (WGM) microcavity perturbed by two strong nanoscatterers. This counterintuitive phenomenon originates from a strong frequency-dependence of the scattering between the counterpropagating waves at an "effective scatterer", which could be explained by a first-principle-based model considering a dynamic multiple-scattering process of the azimuthally propagating modes. We find that the generally imperfect chirality at the EP tends to be globally perfect with the decrease of the scattering effect induced by the nanoscatterers. Furthermore, the chirality also becomes locally perfect with the decrease of the relative azimuthal angle between the two strong nanoscatterers. This work provides a new understanding of the general properties of chirality at EPs. It will benefit the potential applications enabled by the chirality features of non-Hermitian systems at EPs.

physics.optics↗

arXiv2022

Learning Multi-Task Gaussian Process Over Heterogeneous Input Domains

Multi-task Gaussian process (MTGP) is a well-known non-parametric Bayesian model for learning correlated tasks effectively by transferring knowledge across tasks. But current MTGPs are usually limited to the multi-task scenario defined in the same input domain, leaving no space for tackling the heterogeneous case, i.e., the features of input domains vary over tasks. To this end, this paper presents a novel heterogeneous stochastic variational linear model of coregionalization (HSVLMC) model for simultaneously learning the tasks with varied input domains. Particularly, we develop the stochastic variational framework with Bayesian calibration that (i) takes into account the effect of dimensionality reduction raised by domain mappings in order to achieve effective input alignment; and (ii) employs a residual modeling strategy to leverage the inductive bias brought by prior domain mappings for better model inference. Finally, the superiority of the proposed model against existing LMC models has been extensively verified on diverse heterogeneous multi-task cases and a practical multi-fidelity steam turbine exhaust problem.

stat.ML↗

arXiv2022

Deep Probabilistic Time Series Forecasting using Augmented Recurrent Input for Dynamic Systems

The demand of probabilistic time series forecasting has been recently raised in various dynamic system scenarios, for example, system identification and prognostic and health management of machines. To this end, we combine the advances in both deep generative models and state space model (SSM) to come up with a novel, data-driven deep probabilistic sequence model. Specifically, we follow the popular encoder-decoder generative structure to build the recurrent neural networks (RNN) assisted variational sequence model on an augmented recurrent input space, which could induce rich stochastic sequence dependency. Besides, in order to alleviate the inconsistency issue of the posterior between training and predicting as well as improving the mining of dynamic patterns, we (i) propose using a lagged hybrid output as input for the posterior at next time step, which brings training and predicting into alignment; and (ii) further devise a generalized auto-regressive strategy that encodes all the historical dependencies for the posterior. Thereafter, we first investigate the methodological characteristics of the proposed deep probabilistic sequence model on toy cases, and then comprehensively demonstrate the superiority of our model against existing deep probabilistic SSM models through extensive numerical experiments on eight system identification benchmarks from various dynamic systems. Finally, we apply our sequence model to a real-world centrifugal compressor forecasting problem, and again verify its outstanding performance by quantifying the time series predictive distribution.

cs.LG↗