arXiv subjects

Yue Yu

Publications and source records attributed to Yue Yu.

At least 307 records · Page 17Linked to original sources

arXiv2023

Quantum Simulation for Partial Differential Equations with Physical Boundary or Interface Conditions

This paper explores the feasibility of quantum simulation for partial differential equations (PDEs) with physical boundary or interface conditions. Semi-discretisation of such problems does not necessarily yield Hamiltonian dynamics and even alters the Hamiltonian structure of the dynamics when boundary and interface conditions are included. This seemingly intractable issue can be resolved by using a recently introduced Schrödingerisation method (Jin et al. 2022) -- it converts any linear PDEs and ODEs with non-Hermitian dynamics to a system of Schrödinger equations, via the so-called warped phase transformation that maps the equation into one higher dimension. We implement this method for several typical problems, including the linear convection equation with inflow boundary conditions and the heat equation with Dirichlet and Neumann boundary conditions. For interface problems, we study the (parabolic) Stefan problem, linear convection, and linear Liouville equations with discontinuous and even measure-valued coefficients. We perform numerical experiments to demonstrate the validity of this approach, which helps to bridge the gap between available quantum algorithms and computational models for classical and quantum dynamics with boundary and interface conditions.

quant-ph↗

arXiv2023

Quantum Simulation for Quantum Dynamics with Artificial Boundary Conditions

Quantum dynamics, typically expressed in the form of a time-dependent Schrödinger equation with a Hermitian Hamiltonian, is a natural application for quantum computing. However, when simulating quantum dynamics that involves the emission of electrons, it is necessary to use artificial boundary conditions (ABC) to confine the computation within a fixed domain. The introduction of ABCs alters the Hamiltonian structure of the dynamics, and existing quantum algorithms can not be directly applied since the evolution is no longer unitary. The current paper utilizes a recently introduced Schrödingerisation method (Jin et al. arXiv:2212.13969 and arXiv:2212.14703) that converts non-Hermitian dynamics to a Schrödinger form, for the artificial boundary problems. We implement this method for three types of ABCs, including the complex absorbing potential technique, perfectly matched layer methods, and Dirichlet-to-Neumann approach. We analyze the query complexity of these algorithms, and perform numerical experiments to demonstrate the validity of this approach. This helps to bridge the gap between available quantum algorithms and computational models for quantum dynamics in unbounded domains.

quant-ph↗

arXiv2023

Theory of the low- and high-field superconducting phases of UTe$_2$

Recent nuclear magnetic resonance (NMR) and calorimetric experiments have observed that UTe$_2$ exhibits a transition between two distinct superconducting phases as a function of magnetic field strength for a field applied along the crystalline $b$-axis. To determine the nature of these phases, we employ a microscopic two-band minimal Hamiltonian with the essential crystal symmetries and structural details. We also adopt anisotropic ferromagnetic exchange terms. We study the resulting pairing symmetries and properties of these low- and high-field phases in mean field theory.

cond-mat.supr-con↗

arXiv2023

Transferability Estimation Based On Principal Gradient Expectation

Transfer learning aims to improve the performance of target tasks by transferring knowledge acquired in source tasks. The standard approach is pre-training followed by fine-tuning or linear probing. Especially, selecting a proper source domain for a specific target domain under predefined tasks is crucial for improving efficiency and effectiveness. It is conventional to solve this problem via estimating transferability. However, existing methods can not reach a trade-off between performance and cost. To comprehensively evaluate estimation methods, we summarize three properties: stability, reliability and efficiency. Building upon them, we propose Principal Gradient Expectation(PGE), a simple yet effective method for assessing transferability. Specifically, we calculate the gradient over each weight unit multiple times with a restart scheme, and then we compute the expectation of all gradients. Finally, the transferability between the source and target is estimated by computing the gap of normalized principal gradients. Extensive experiments show that the proposed metric is superior to state-of-the-art methods on all properties.

cs.CV↗

arXiv2023

Material Properties of Organic Liquids, Ices, and Hazes on Titan

Titan has a diverse range of materials in its atmosphere and on its surface: the simple organics that reside in various phases (gas, liquid, ice) and the solid complex refractory organics that form Titan's haze layers. These materials all actively participate in various physical processes on Titan, and many material properties are found to be important in shaping these processes. Future in-situ exploration on Titan would likely encounter a range of materials, and a comprehensive database to archive the material properties of all possible material candidates will be needed. Here we summarize several important material properties of the organic liquids, ices, and the refractory hazes on Titan that are available in the literature and/or that we have computed. These properties include thermodynamic properties (phase change points, sublimation and vaporization saturation vapor pressure, and latent heat), physical property (density), and surface properties (liquid surface tensions and solid surface energies). We have developed a new database to provide a repository for these data and make them available to the science community. These data can be used as inputs for various theoretical models to interpret current and future remote sensing and in-situ atmospheric and surface measurements on Titan. The material properties of the simple organics may also be applicable to giant planets and icy bodies in the outer solar system, interstellar medium, protoplanetary disks, and exoplanets.

astro-ph.EP↗

arXiv2023

The Solar Upper Transition Region Imager (SUTRI) onboard the SATech-01 satellite

The Solar Upper Transition Region Imager (SUTRI) onboard the Space Advanced Technology demonstration satellite (SATech-01), which was launched to a sun-synchronous orbit at a height of 500 km in July 2022, aims to test the on-orbit performance of our newly developed Sc-Si multi-layer reflecting mirror and the 2kx2k EUV CMOS imaging camera and to take full-disk solar images at the Ne VII 46.5 nm spectral line with a filter width of 3 nm. SUTRI employs a Ritchey-Chretien optical system with an aperture of 18 cm. The on-orbit observations show that SUTRI images have a field of view of 41.6'x41.6' and a moderate spatial resolution of 8" without an image stabilization system. The normal cadence of SUTRI images is 30 s and the solar observation time is about 16 hours each day because the earth eclipse time accounts for about 1/3 of SATech-01's orbit period. Approximately 15 GB data is acquired each day and made available online after processing. SUTRI images are valuable as the Ne VII 46.5 nm line is formed at a temperature regime of 0.5 MK in the solar atmosphere, which has rarely been sampled by existing solar imagers. SUTRI observations will establish connections between structures in the lower solar atmosphere and corona, and advance our understanding of various types of solar activity such as flares, filament eruptions, coronal jets and coronal mass ejections.

astro-ph.SR↗

arXiv2023

Stochastic Clustered Federated Learning

Federated learning is a distributed learning framework that takes full advantage of private data samples kept on edge devices. In real-world federated learning systems, these data samples are often decentralized and Non-Independently Identically Distributed (Non-IID), causing divergence and performance degradation in the federated learning process. As a new solution, clustered federated learning groups federated clients with similar data distributions to impair the Non-IID effects and train a better model for every cluster. This paper proposes StoCFL, a novel clustered federated learning approach for generic Non-IID issues. In detail, StoCFL implements a flexible CFL framework that supports an arbitrary proportion of client participation and newly joined clients for a varying FL system, while maintaining a great improvement in model performance. The intensive experiments are conducted by using four basic Non-IID settings and a real-world dataset. The results show that StoCFL could obtain promising cluster results even when the number of clusters is unknown. Based on the client clustering results, models trained with StoCFL outperform baseline approaches in a variety of contexts.

cs.LG↗

arXiv2023

Neighborhood-Regularized Self-Training for Learning with Few Labels

Training deep neural networks (DNNs) with limited supervision has been a popular research topic as it can significantly alleviate the annotation burden. Self-training has been successfully applied in semi-supervised learning tasks, but one drawback of self-training is that it is vulnerable to the label noise from incorrect pseudo labels. Inspired by the fact that samples with similar labels tend to share similar representations, we develop a neighborhood-based sample selection approach to tackle the issue of noisy pseudo labels. We further stabilize self-training via aggregating the predictions from different rounds during sample selection. Experiments on eight tasks show that our proposed method outperforms the strongest self-training baseline with 1.83% and 2.51% performance gain for text and graph datasets on average. Our further analysis demonstrates that our proposed data selection strategy reduces the noise of pseudo labels by 36.8% and saves 57.3% of the time when compared with the best baseline. Our code and appendices will be uploaded to https://github.com/ritaranx/NeST.

cs.LG↗

arXiv2023

Two Sides of the Same Coin: Exploiting the Impact of Identifiers in Neural Code Comprehension

Previous studies have demonstrated that neural code comprehension models are vulnerable to identifier naming. By renaming as few as one identifier in the source code, the models would output completely irrelevant results, indicating that identifiers can be misleading for model prediction. However, identifiers are not completely detrimental to code comprehension, since the semantics of identifier names can be related to the program semantics. Well exploiting the two opposite impacts of identifiers is essential for enhancing the robustness and accuracy of neural code comprehension, and still remains under-explored. In this work, we propose to model the impact of identifiers from a novel causal perspective, and propose a counterfactual reasoning-based framework named CREAM. CREAM explicitly captures the misleading information of identifiers through multi-task learning in the training stage, and reduces the misleading impact by counterfactual inference in the inference stage. We evaluate CREAM on three popular neural code comprehension tasks, including function naming, defect detection and code classification. Experiment results show that CREAM not only significantly outperforms baselines in terms of robustness (e.g., +37.9% on the function naming task at F1 score), but also achieve improved results on the original datasets (e.g., +0.5% on the function naming task at F1 score).

cs.SE↗

arXiv2023

MetaNO: How to Transfer Your Knowledge on Learning Hidden Physics

Gradient-based meta-learning methods have primarily been applied to classical machine learning tasks such as image classification. Recently, PDE-solving deep learning methods, such as neural operators, are starting to make an important impact on learning and predicting the response of a complex physical system directly from observational data. Since the data acquisition in this context is commonly challenging and costly, the call of utilization and transfer of existing knowledge to new and unseen physical systems is even more acute. Herein, we propose a novel meta-learning approach for neural operators, which can be seen as transferring the knowledge of solution operators between governing (unknown) PDEs with varying parameter fields. Our approach is a provably universal solution operator for multiple PDE solving tasks, with a key theoretical observation that underlying parameter fields can be captured in the first layer of neural operator models, in contrast to typical final-layer transfer in existing meta-learning methods. As applications, we demonstrate the efficacy of our proposed approach on PDE-based datasets and a real-world material modeling problem, illustrating that our method can handle complex and nonlinear physical response learning tasks while greatly improving the sampling efficiency in unseen tasks.

cs.LG↗

arXiv2023

INO: Invariant Neural Operators for Learning Complex Physical Systems with Momentum Conservation

Neural operators, which emerge as implicit solution operators of hidden governing equations, have recently become popular tools for learning responses of complex real-world physical systems. Nevertheless, the majority of neural operator applications has thus far been data-driven, which neglects the intrinsic preservation of fundamental physical laws in data. In this paper, we introduce a novel integral neural operator architecture, to learn physical models with fundamental conservation laws automatically guaranteed. In particular, by replacing the frame-dependent position information with its invariant counterpart in the kernel space, the proposed neural operator is by design translation- and rotation-invariant, and consequently abides by the conservation laws of linear and angular momentums. As applications, we demonstrate the expressivity and efficacy of our model in learning complex material behaviors from both synthetic and experimental datasets, and show that, by automatically satisfying these essential physical laws, our learned neural operator is not only generalizable in handling translated and rotated datasets, but also achieves state-of-the-art accuracy and efficiency as compared to baseline neural operator models.

cs.LG↗

arXiv2023

Towards a unified nonlocal, peridynamics framework for the coarse-graining of molecular dynamics data with fractures

Molecular dynamics (MD) has served as a powerful tool for designing materials with reduced reliance on laboratory testing. However, the use of MD directly to treat the deformation and failure of materials at the mesoscale is still largely beyond reach. Herein, we propose a learning framework to extract a peridynamic model as a mesoscale continuum surrogate from MD simulated material fracture datasets. Firstly, we develop a novel coarse-graining method, to automatically handle the material fracture and its corresponding discontinuities in MD displacement dataset. Inspired by the Weighted Essentially Non-Oscillatory scheme, the key idea lies at an adaptive procedure to automatically choose the locally smoothest stencil, then reconstruct the coarse-grained material displacement field as piecewise smooth solutions containing discontinuities. Then, based on the coarse-grained MD data, a two-phase optimization-based learning approach is proposed to infer the optimal peridynamics model with damage criterion. In the first phase, we identify the optimal nonlocal kernel function from datasets without material damage, to capture the material stiffness properties. Then, in the second phase, the material damage criterion is learnt as a smoothed step function from the data with fractures. As a result, a peridynamics surrogate is obtained. Our peridynamics surrogate model can be employed in further prediction tasks with different grid resolutions from training, and hence allows for substantial reductions in computational cost compared with MD. We illustrate the efficacy of the proposed approach with several numerical tests for single layer graphene. Our tests show that the proposed data-driven model is robust and generalizable: it is capable in modeling the initialization and growth of fractures under discretization and loading settings that are different from the ones used during training.

cond-mat.mtrl-sci↗

arXiv2022

Quantum simulation of partial differential equations via Schrodingerisation: technical details

We study a new method - called Schrodingerisation introduced in [Jin, Liu, Yu, arXiv: 2212.13969] - for solving general linear partial differential equations with quantum simulation. This method converts linear partial differential equations into a `Schrodingerised' or Hamiltonian system, using a new and simple transformation called the warped phase transformation. Here we provide more in-depth technical discussions and expand on this approach in a more detailed and pedagogical way. We apply this to more examples of partial differential equations, including heat, convection, Fokker-Planck, linear Boltzmann and Black-Scholes equations. This approach can also be extended to Schrodingerise general linear partial differential equations, including the Vlasov-Fokker-Planck equation and the Liouville representation equation for nonlinear ordinary differential equations.

quant-ph↗

arXiv2022

Quantum simulation of partial differential equations via Schrodingerisation

We present a simple new way - called Schrodingerisation - to simulate general linear partial differential equations via quantum simulation. Using a simple new transform, referred to as the warped phase transformation, any linear partial differential equation can be recast into a system of Schrodinger's equations - in real time - in a straightforward way. This can be seen directly on the level of the dynamical equations without more sophisticated methods. This approach is not only applicable to PDEs for classical problems but also those for quantum problems - like the preparation of quantum ground states, Gibbs states and the simulation of quantum states in random media in the semiclassical limit.

quant-ph↗

arXiv2022

EDoG: Adversarial Edge Detection For Graph Neural Networks

Graph Neural Networks (GNNs) have been widely applied to different tasks such as bioinformatics, drug design, and social networks. However, recent studies have shown that GNNs are vulnerable to adversarial attacks which aim to mislead the node or subgraph classification prediction by adding subtle perturbations. Detecting these attacks is challenging due to the small magnitude of perturbation and the discrete nature of graph data. In this paper, we propose a general adversarial edge detection pipeline EDoG without requiring knowledge of the attack strategies based on graph generation. Specifically, we propose a novel graph generation approach combined with link prediction to detect suspicious adversarial edges. To effectively train the graph generative model, we sample several sub-graphs from the given graph data. We show that since the number of adversarial edges is usually low in practice, with low probability the sampled sub-graphs will contain adversarial edges based on the union bound. In addition, considering the strong attacks which perturb a large number of edges, we propose a set of novel features to perform outlier detection as the preprocessing for our detection. Extensive experimental results on three real-world graph datasets including a private transaction rule dataset from a major company and two types of synthetic graphs with controlled properties show that EDoG can achieve above 0.8 AUC against four state-of-the-art unseen attack strategies without requiring any knowledge about the attack type; and around 0.85 with knowledge of the attack type. EDoG significantly outperforms traditional malicious edge detection baselines. We also show that an adaptive attack with full knowledge of our detection pipeline is difficult to bypass it.

cs.LG↗

arXiv2022

Multi-task Joint Strategies of Self-supervised Representation Learning on Biomedical Networks for Drug Discovery

Self-supervised representation learning (SSL) on biomedical networks provides new opportunities for drug discovery. However, how to effectively combine multiple SSL models is still challenging and has been rarely explored. Therefore, we propose multi-task joint strategies of self-supervised representation learning on biomedical networks for drug discovery, named MSSL2drug. We design six basic SSL tasks inspired by various modality features including structures, semantics, and attributes in heterogeneous biomedical networks. Importantly, fifteen combinations of multiple tasks are evaluated by a graph attention-based multi-task adversarial learning framework in two drug discovery scenarios. The results suggest two important findings. (1) Combinations of multimodal tasks achieve the best performance compared to other multi-task joint models. (2) The local-global combination models yield higher performance than random two-task combinations when there are the same size of modalities. Therefore, we conjecture that the multimodal and local-global combination strategies can be treated as the guideline of multi-task SSL for drug discovery.

cs.LG↗

arXiv2022

Unified Implementation of Finite Element Methods involving Jumps and Averages in Matlab

We provide unified implementations of the finite element methods involving jumps and averages in Maltab by combing the use of the software package varFEM, including the adaptive finite element methods for the Poisson equation and the $C^0$ interior penalty methods for the biharmonic equation. The design ideas can be extended to other Galerkin-based methods, for example, the discontinuous Galerkin methods and the virtual element methods.

math.NA↗

arXiv2022

Polynomial Distributions and Transformations

Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of systems rather than to assume polynomials for only approximating known or empirically estimated distributions. Polynomial distributions offer a great modeling flexibility, and often, also mathematical tractability. However, unlike canonical distributions, polynomial functions may have non-negative values in the interval of support for some parameter values, the number of their parameters is usually much larger than for canonical distributions, and the interval of support must be finite. In particular, polynomial distributions are defined here assuming three forms of polynomial function. The transformation of polynomial distributions and fitting a histogram to a polynomial distribution are considered. The key properties of polynomial distributions are derived in closed-form. A piecewise polynomial distribution construction is devised to ensure that it is non-negative over the support interval. Finally, the problems of estimating parameters of polynomial distributions and generating polynomially distributed samples are also studied.

cs.IT↗