Huajie Chen, Gero Friesecke
The exact interaction energy of a many-electron system is determined by the electron pair density, which is not well-approximated in standard Kohn-Sham density functional models. Here we study the (complicated but well-defined) exact universal map from density to pair density. We survey how many common functionals, including the most basic version of the LDA (Dirac exchange with no correlation contribution), arise from particular approximations of this map. We develop an algorithm to compute the map numerically, and apply it to one-parameter families {a*rho(a*x)} of one-dimensional homogeneous and inhomogeneous single-particle densities. We observe that the pair density develops remarkable multiscale patterns which strongly depend on both the particle number and the "width" 1/a of the single-particle density. The simulation results are confirmed by rigorous asymptotic results in the limiting regimes a>>1 and a<<1. For one-dimensional homogeneous systems, we show that the whole spectrum of patterns is reproduced surprisingly well by a simple asymptotics-based ansatz which slowly smoothens out the "strictly correlated" a=0 pair density while slowly turning on the a=infty "exchange" terms as a increases. Our findings lend theoretical support to the celebrated semi-empirical idea [Becke93] to mix in a fractional amount of exchange, albeit not to assuming the mixing to be additive and taking the fraction to be a system independent constant.
Huajie Chen, Tianqing Zhu, Yuan Zhao, Bo Liu, Xin Yu, Wanlei Zhou
Image deep steganography (IDS) is a technique that utilizes deep learning to embed a secret image invisibly into a cover image to generate a container image. However, the container images generated by convolutional neural networks (CNNs) are vulnerable to attacks that distort their high-frequency components. To address this problem, we propose a novel method called Low-frequency Image Deep Steganography (LIDS) that allows frequency distribution manipulation in the embedding process. LIDS extracts a feature map from the secret image and adds it to the cover image to yield the container image. The container image is not directly output by the CNNs, and thus, it does not contain high-frequency artifacts. The extracted feature map is regulated by a frequency loss to ensure that its frequency distribution mainly concentrates on the low-frequency domain. To further enhance robustness, an attack layer is inserted to damage the container image. The retrieval network then retrieves a recovered secret image from a damaged container image. Our experiments demonstrate that LIDS outperforms state-of-the-art methods in terms of robustness, while maintaining high fidelity and specificity. By avoiding high-frequency artifacts and manipulating the frequency distribution of the embedded feature map, LIDS achieves improved robustness against attacks that distort the high-frequency components of container images.
Ting Wang, Huajie Chen, Aihui Zhou, Yuzhi Zhou, Daniel Massatt
Incommensurate structures arise from stacking single layers of low-dimensional materials on top of one another with misalignment such as an in-plane twist in orientation. While these structures are of significant physical interest, they pose many theoretical challenges due to the loss of periodicity. In this paper, we characterize the density of states of Schrödinger operators in the weak sense for the incommensurate system and develop novel numerical methods to approximate them. In particular, we (i) justify the thermodynamic limit of the density of states in the real space formulation; and (ii) propose efficient numerical schemes to evaluate the density of states based on planewave approximations and reciprocal space sampling. We present both rigorous analysis and numerical simulations to support the reliability and efficiency of our numerical algorithms.
Yangshuai Wang, Huajie Chen, Mingjie Liao, Christoph Ortner, Hao Wang, Lei Zhang
Hybrid quantum/molecular mechanics models (QM/MM methods) are widely used in material and molecular simulations when MM models do not provide sufficient accuracy but pure QM models are computationally prohibitive. Adaptive QM/MM coupling methods feature on-the-fly classification of atoms during the simulation, allowing the QM and MM subsystems to be updated as needed. In this work, we propose such an adaptive QM/MM method for material defect simulations based on a new residual based it a posteriori error estimator, which provides both lower and upper bounds for the true error. We validate the analysis and illustrate the effectiveness of the new scheme on numerical simulations for material defects.
Huajie Chen, Mingjie Liao, Hao Wang, Yangshuai Wang, Lei Zhang
QM (quantum mechenics) and MM (molecular mechenics) coupling methods are widely used in simulations of crystalline defects. In this paper, we construct a residual based a posteriori error indicator for QM/MM coupling approximations. We prove the reliability of the error indicator (upper bound of the true approximation error) and develop some sampling techniques for its efficient calculation. Based on the error indicator and Dörfler marking strategy, we design an adaptive QM/MM algorithm for crystalline defects and demonstrate the efficiency with some numerical experiments.
Xuanyu Liu, Huajie Chen, Christoph Ortner
The minimum energy path (MEP) describes the mechanism of reaction, and the energy barrier along the path can be used to calculate the reaction rate in thermal systems. The nudged elastic band (NEB) method is one of the most commonly used schemes to compute MEPs numerically. It approximates an MEP by a discrete set of configuration images, where the discretization size determines both computational cost and accuracy of the simulations. In this paper, we consider a discrete MEP to be a stationary state of the NEB method and prove an optimal convergence rate of the discrete MEP with respect to the number of images. Numerical simulations for the transitions of some several proto-typical model systems are performed to support the theory.
Huajie Chen, Tianqing Zhu, Chi Liu, Shui Yu, Wanlei Zhou
In recent years, there has been significant advancement in the field of model watermarking techniques. However, the protection of image-processing neural networks remains a challenge, with only a limited number of methods being developed. The objective of these techniques is to embed a watermark in the output images of the target generative network, so that the watermark signal can be detected in the output of a surrogate model obtained through model extraction attacks. This promising technique, however, has certain limits. Analysis of the frequency domain reveals that the watermark signal is mainly concealed in the high-frequency components of the output. Thus, we propose an overwriting attack that involves forging another watermark in the output of the generative network. The experimental results demonstrate the efficacy of this attack in sabotaging existing watermarking schemes for image-processing networks, with an almost 100% success rate. To counter this attack, we devise an adversarial framework for the watermarking network. The framework incorporates a specially designed adversarial training step, where the watermarking network is trained to defend against the overwriting network, thereby enhancing its robustness. Additionally, we observe an overfitting phenomenon in the existing watermarking method, which can render it ineffective. To address this issue, we modify the training process to eliminate the overfitting problem.
Huajie Chen, Christoph Ortner, Yangshuai Wang
We develop and analyze a framework for consistent QM/MM (quantum/classic) hybrid models of crystalline defects, which admits general atomistic interactions including traditional off-the-shell interatomic potentials as well as state of art "machine-learned interatomic potentials". We (i) establish an a priori error estimate for the QM/MM approximations in terms of matching conditions between the MM and QM models, and (ii) demonstrate how to use these matching conditions to construct practical machine learned MM potentials specifically for QM/MM simulations.
Yukuan Hu, Huajie Chen, Xin Liu
In this work, we construct a novel numerical method for solving the multi-marginal optimal transport problems with Coulomb cost. This type of optimal transport problems arises in quantum physics and plays an important role in understanding the strongly correlated quantum systems. With a Monge-like ansatz, the orginal high-dimensional problems are transferred into mathematical programmings with generalized complementarity constraints, and thus the curse of dimensionality is surmounted. However, the latter ones are themselves hard to deal with from both theoretical and practical perspective. Moreover in the presence of nonconvexity, brute-force searching for global solutions becomes prohibitive as the problem size grows large. To this end, we propose a global optimization approach for solving the nonconvex optimization problems, by exploiting an efficient proximal block coordinate descent local solver and an initialization subroutine based on hierarchical grid refinements. We provide numerical simulations on some typical physical systems to show the efficiency of our approach. The results match well with both theoretical predictions and physical intuitions, and give the first visualization of optimal transport maps for some two dimensional systems.
Huajie Chen, Xingao Gong, Lianhua He, Zhang Yang, Aihui Zhou
In this paper, we study finite dimensional approximations of Kohn-Sham models, which are widely used in electronic structure calculations. We prove the convergence of the finite dimensional approximations and derive the a priori error estimates for ground state energies and solutions. We also provide numerical simulations for several molecular systems that support our theory.
Huajie Chen, Faizan Q. Nazar, Christoph Ortner
We develop a rigorous framework for modelling the geometry equilibration of crystalline defects. We formulate the equilibration of crystal defects as a variational problems on a discrete energy space and establish qualitatively sharp far-field decay estimates for the equilibrium configuration. This work extends Ehrlacher, Ortner, Shapeev (2016) by admitting infinite-range interaction which in particular includes some quantum chemistry based interatomic potentials.
Huajie Chen, Tianqing Zhu, Lefeng Zhang, Bo Liu, Derui Wang, Wanlei Zhou, Minhui Xue
Model extraction attacks currently pose a non-negligible threat to the security and privacy of deep learning models. By querying the model with a small dataset and usingthe query results as the ground-truth labels, an adversary can steal a piracy model with performance comparable to the original model. Two key issues that cause the threat are, on the one hand, accurate and unlimited queries can be obtained by the adversary; on the other hand, the adversary can aggregate the query results to train the model step by step. The existing defenses usually employ model watermarking or fingerprinting to protect the ownership. However, these methods cannot proactively prevent the violation from happening. To mitigate the threat, we propose QUEEN (QUEry unlEarNing) that proactively launches counterattacks on potential model extraction attacks from the very beginning. To limit the potential threat, QUEEN has sensitivity measurement and outputs perturbation that prevents the adversary from training a piracy model with high performance. In sensitivity measurement, QUEEN measures the single query sensitivity by its distance from the center of its cluster in the feature space. To reduce the learning accuracy of attacks, for the highly sensitive query batch, QUEEN applies query unlearning, which is implemented by gradient reverse to perturb the softmax output such that the piracy model will generate reverse gradients to worsen its performance unconsciously. Experiments show that QUEEN outperforms the state-of-the-art defenses against various model extraction attacks with a relatively low cost to the model accuracy. The artifact is publicly available at https://anonymous.4open.science/r/queen implementation-5408/.
Huajie Chen, Tianqing Zhu, Yuchen Zhong, Yang Zhang, Shang Wang, Feng He, Lefeng Zhang, Jialiang Shen, Minghao Wang, Wanlei Zhou
Dataset distillation compresses a large real dataset into a small synthetic one, enabling models trained on the synthetic data to achieve performance comparable to those trained on the real data. Although synthetic datasets are assumed to be privacy-preserving, we show that existing distillation methods can cause severe privacy leakage because synthetic datasets implicitly encode the weight trajectories of the distilled model, they become over-informative and exploitable by adversaries. To expose this risk, we introduce the Information Revelation Attack (IRA) against state-of-the-art distillation techniques. Experiments show that IRA accurately predicts both the distillation algorithm and model architecture, and can successfully infer membership and recover sensitive samples from the real dataset.
Jack Thomas, Huajie Chen, Christoph Ortner
We show that the local density of states (LDOS) of a wide class of tight-binding models has a weak body-order expansion. Specifically, we prove that the resulting body-order expansion for analytic observables such as the electron density or the energy has an exponential rate of convergence both at finite Fermi-temperature as well as for insulators at zero Fermi-temperature. We discuss potential consequences of this observation for modelling the potential energy landscape, as well as for solving the electronic structure problem.
Beilei Liu, Huajie Chen, Geneviève Dusson, Jun Fang, Xingyu Gao
We propose an adaptive planewave method for eigenvalue problems in electronic structure calculations. The method combines a priori convergence rates and accurate a posteriori error estimates into an effective way of updating the energy cut-off for planewave discretizations, for both linear and nonlinear eigenvalue problems. The method is error controllable for linear eigenvalue problems in the sense that for a given required accuracy, an energy cut-off for which the solution matches the target accuracy can be reached efficiently. Further, the method is particularly promising for nonlinear eigenvalue problems in electronic structure calculations as it shall reduce the cost of early iterations in self-consistent algorithms. We present some numerical experiments for both linear and nonlinear eigenvalue problems. In particular, we provide electronic structure calculations for some insulator and metallic systems simulated with Kohn--Sham density functional theory (DFT) and the projector augmented wave (PAW) method, illustrating the efficiency and potential of the algorithm.
Yuzhi Zhou, Huajie Chen, Aihui Zhou
We propose a novel numerical algorithm for computing the electronic structure related eigenvalue problem of incommensurate systems. Unlike the conventional practice that approximates the system by a large commensurate supercell, our algorithm directly discretizes the eigenvalue problem under the framework of a plane wave method. The emerging ergodicity and the interpretation from higher dimensions give rise to many unique features compared to what we have been familiar with in the periodic system. The numerical results of 1D and 2D quantum eigenvalue problems are presented to show the reliability and efficiency of our scheme. Furthermore, the extension of our algorithm to full Kohn-Sham density functional theory calculations are discussed.
Xue Quan, Huajie Chen
The Wigner localization is an electron phase at low densities when the electrons are sharply localized around equilibrium positions. The simulation of the Wigner localization phenomenon requires careful treatment of the many-body correlations, as the electron-electron interaction dominates the system. This work proposes a numerical algorithm to study the electron ground states of the Wigner molecules. The main features of our algorithm are three-fold: (i) a finite element discretization of the one-body space such that the sharp localization can be captured; (ii) a good initial state obtained by exploiting the strongly correlated limit; and (iii) a selected configuration interaction method by choosing the Slater determinants from (stochastic) gradients. Numerical experiments for some typical one-dimensional quantum wires and two-dimensional circular quantum dots are provided to show the efficiency of our algorithm.
Huajie Chen, Xiaoying Dai, Xingao Gong, Lianhua He, Aihui Zhou
The Kohn-Sham equation is a powerful, widely used approach for computation of ground state electronic energies and densities in chemistry, materials science, biology, and nanosciences. In this paper, we study the adaptive finite element approximations for the Kohn-Sham model. Based on the residual type a posteriori error estimators proposed in this paper, we introduce an adaptive finite element algorithm with a quite general marking strategy and prove the convergence of the adaptive finite element approximations. Using D{\" o}rfler's marking strategy, we then get the convergence rate and quasi-optimal complexity. We also carry out several typical numerical experiments that not only support our theory,but also show the robustness and efficiency of the adaptive finite element computations in electronic structure calculations.
Huajie Chen, Jianfeng Lu, Christoph Ortner
We consider a tight binding model for localised crystalline defects with electrons in the canonical ensemble (finite electronic temperature) and nuclei positions relaxed according to the Born--Oppenheimer approximation. We prove that the limit model as the computational domain size grows to infinity is formulated in the grand-canonical ensemble for the electrons. The Fermi-level for the limit model is fixed at a homogeneous crystal level, independent of the defect or electron number in the sequence of finite-domain approximations. We quantify the rates of convergence for the nuclei configuration and for the Fermi-level.
Huajie Chen, Gero Friesecke, Christian B. Mendl
In this paper, we study numerical discretizations to solve density functional models in the "strictly correlated electrons" (SCE) framework. Unlike previous studies our work is not restricted to radially symmetric densities. In the SCE framework, the exchange-correlation functional encodes the effects of the strong correlation regime by minimizing the pairwise Coulomb repulsion, resulting in an optimal transport problem. We give a mathematical derivation of the self-consistent Kohn-Sham-SCE equations, construct an efficient numerical discretization for this type of problem for N = 2 electrons, and apply it to the H2 molecule in its dissociating limit. Moreover, we prove that the SCE density functional model is correct for the H2 molecule in its dissociating limit.