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Guodong Zhang

Publications and source records attributed to Guodong Zhang.

50 records · Page 3Linked to original sources
arXiv2019

Computational Design of Finite Strain Auxetic Metamaterials via Topology Optimization and Nonlinear Homogenization

A novel computational framework for designing metamaterials with negative Poisson's ratio over a large strain range is presented in this work by combining the density-based topology optimization together with a mixed stress/deformation driven nonlinear homogenization method. A measure of Poisson's ratio based on the macro deformations is proposed, which is further validated through direct numerical simulations. With the consistent optimization formulations based on nonlinear homogenization, auxetic metamaterial designs with respect to different loading orientations and with different unit cell domains are systematically explored. In addition, the extension to multimaterial auxetic metamaterial designs is also considered, and stable optimization formulations are presented to obtain discrete metamaterial topologies under finite strains. Various new auxetic designs are obtained based on the proposed framework. To validate the performance of optimized designs, a multiscale stability analysis is carried out using the Bloch wave method and rank-one convexity check. As demonstrated, short and/or long wavelength instabilities can occur during the loading process, leading to a change of periodicity of the microstructure, which can affect the performance of an optimized design.

cs.CE↗
arXiv2019

Functional Variational Bayesian Neural Networks

Variational Bayesian neural networks (BNNs) perform variational inference over weights, but it is difficult to specify meaningful priors and approximate posteriors in a high-dimensional weight space. We introduce functional variational Bayesian neural networks (fBNNs), which maximize an Evidence Lower BOund (ELBO) defined directly on stochastic processes, i.e. distributions over functions. We prove that the KL divergence between stochastic processes equals the supremum of marginal KL divergences over all finite sets of inputs. Based on this, we introduce a practical training objective which approximates the functional ELBO using finite measurement sets and the spectral Stein gradient estimator. With fBNNs, we can specify priors entailing rich structures, including Gaussian processes and implicit stochastic processes. Empirically, we find fBNNs extrapolate well using various structured priors, provide reliable uncertainty estimates, and scale to large datasets.

cs.LG↗
arXiv2018

Eigenvalue Corrected Noisy Natural Gradient

Variational Bayesian neural networks combine the flexibility of deep learning with Bayesian uncertainty estimation. However, inference procedures for flexible variational posteriors are computationally expensive. A recently proposed method, noisy natural gradient, is a surprisingly simple method to fit expressive posteriors by adding weight noise to regular natural gradient updates. Noisy K-FAC is an instance of noisy natural gradient that fits a matrix-variate Gaussian posterior with minor changes to ordinary K-FAC. Nevertheless, a matrix-variate Gaussian posterior does not capture an accurate diagonal variance. In this work, we extend on noisy K-FAC to obtain a more flexible posterior distribution called eigenvalue corrected matrix-variate Gaussian. The proposed method computes the full diagonal re-scaling factor in Kronecker-factored eigenbasis. Empirically, our approach consistently outperforms existing algorithms (e.g., noisy K-FAC) on regression and classification tasks.

cs.LG↗
arXiv2018

Three Mechanisms of Weight Decay Regularization

Weight decay is one of the standard tricks in the neural network toolbox, but the reasons for its regularization effect are poorly understood, and recent results have cast doubt on the traditional interpretation in terms of $L_2$ regularization. Literal weight decay has been shown to outperform $L_2$ regularization for optimizers for which they differ. We empirically investigate weight decay for three optimization algorithms (SGD, Adam, and K-FAC) and a variety of network architectures. We identify three distinct mechanisms by which weight decay exerts a regularization effect, depending on the particular optimization algorithm and architecture: (1) increasing the effective learning rate, (2) approximately regularizing the input-output Jacobian norm, and (3) reducing the effective damping coefficient for second-order optimization. Our results provide insight into how to improve the regularization of neural networks.

cs.LG↗
arXiv2018

Ultrafast Bessel beams; advanced tools for laser materials processing

Ultrafast Bessel beams demonstrate a significant capacity of structuring transparent materials with high degree of accuracy and exceptional aspect ratio. The ability to localize energy on the nanometer scale (bypassing the 100 nm milestone) makes them ideal tools for advanced laser nanoscale processing on surfaces and in the bulk. This allows to generate and combine micron and nano-sized features into hybrid structures that show novel functionalities. Their high aspect ratio and the accurate location can equally drive an efficient material modification and processing strategy on large dimensions. We review here the main concepts of generating and using Bessel non-diffractive beams and their remarkable features, discuss general characteristics of their interaction with matter in ablation and material modification regimes, and advocate their use for obtaining hybrid micro and nanoscale structures in two and three dimensions performing complex functions. High throughput applications are indicated. The example list ranges from surface nanostructuring and laser cutting to ultrafast laser welding and the fabrication of three dimensional photonic systems embedded in the volume.

physics.app-ph↗
arXiv2018

Differentiable Compositional Kernel Learning for Gaussian Processes

The generalization properties of Gaussian processes depend heavily on the choice of kernel, and this choice remains a dark art. We present the Neural Kernel Network (NKN), a flexible family of kernels represented by a neural network. The NKN architecture is based on the composition rules for kernels, so that each unit of the network corresponds to a valid kernel. It can compactly approximate compositional kernel structures such as those used by the Automatic Statistician (Lloyd et al., 2014), but because the architecture is differentiable, it is end-to-end trainable with gradient-based optimization. We show that the NKN is universal for the class of stationary kernels. Empirically we demonstrate pattern discovery and extrapolation abilities of NKN on several tasks that depend crucially on identifying the underlying structure, including time series and texture extrapolation, as well as Bayesian optimization.

cs.LG↗
arXiv2018

Noisy Natural Gradient as Variational Inference

Variational Bayesian neural nets combine the flexibility of deep learning with Bayesian uncertainty estimation. Unfortunately, there is a tradeoff between cheap but simple variational families (e.g.~fully factorized) or expensive and complicated inference procedures. We show that natural gradient ascent with adaptive weight noise implicitly fits a variational posterior to maximize the evidence lower bound (ELBO). This insight allows us to train full-covariance, fully factorized, or matrix-variate Gaussian variational posteriors using noisy versions of natural gradient, Adam, and K-FAC, respectively, making it possible to scale up to modern-size ConvNets. On standard regression benchmarks, our noisy K-FAC algorithm makes better predictions and matches Hamiltonian Monte Carlo's predictive variances better than existing methods. Its improved uncertainty estimates lead to more efficient exploration in active learning, and intrinsic motivation for reinforcement learning.

cs.LG↗
arXiv2017

Numerical approximations of the Cahn-Hilliard and Allen-Cahn Equations with general nonlinear potential using the Invariant Energy Quadratization approach

In this paper, we carry out stability and error analyses for two first-order, semi-discrete time stepping schemes, which are based on the newly developed Invariant Energy Quadratization approach, for solving the well-known Cahn-Hilliard and Allen-Cahn equations with general nonlinear bulk potentials. Some reasonable sufficient conditions about boundedness and continuity of the nonlinear functional are given in order to obtain optimal error estimates. These conditions are naturally satisfied by two commonly used nonlinear potentials including the double-well potential and regularized logarithmic Flory-Huggins potential. The well-posedness, unconditional energy stabilities and optimal error estimates of the numerical schemes are proved rigorously.

math.NA↗
arXiv2017

Stability and convergence analysis of A linear, fully decoupled and unconditionally energy stable scheme for magneto-hydrodynamic equations

In this paper, we consider numerical approximations for solving the nonlinear magneto-hydrodynamical system, that couples the Navier-Stokes equations and Maxwell equations together. A challenging issue to solve this model numerically is about the time marching problem, i.e., how to develop suitable temporal discretizations for the nonlinear terms in order to preserve the energy stability at the discrete level. We solve this issue in this paper by developing a linear, fully decoupled, first order time-stepping scheme, by combining the projection method and some subtle implicit-explicit treatments for nonlinear coupling terms. We further prove that the scheme is unconditional energy stable and derive the optimal error estimates rigorously. Various numerical experiments are implemented to demonstrate the stability and the accuracy in simulating some benchmark simulations, including the Kelvin-Helmholtz shear instability and the magnetic-frozen phenomenon in the lid-driven cavity.

math.NA↗
arXiv2017

Deformable Convolutional Networks

Convolutional neural networks (CNNs) are inherently limited to model geometric transformations due to the fixed geometric structures in its building modules. In this work, we introduce two new modules to enhance the transformation modeling capacity of CNNs, namely, deformable convolution and deformable RoI pooling. Both are based on the idea of augmenting the spatial sampling locations in the modules with additional offsets and learning the offsets from target tasks, without additional supervision. The new modules can readily replace their plain counterparts in existing CNNs and can be easily trained end-to-end by standard back-propagation, giving rise to deformable convolutional networks. Extensive experiments validate the effectiveness of our approach on sophisticated vision tasks of object detection and semantic segmentation. The code would be released.

cs.CV↗
arXiv2016

Error estimates for structure-preserving discretization of the incompressible MHD system

In this paper, we carry out the error analysis for the structure-preserving discretization of the incompressible MHD system. This system, as a coupled system of Navier-Stokes equations and Maxwell's equations, is nonlinear. We use its energy estimate and the underlying physical structure to facilitate the error analysis. Under certain CFL conditions, we prove the optimal order of convergence. To support the theoretical results, we also present numerical tests.

math.NA↗
arXiv2004

Applicability of Gaussian Noise Approximation for Optically Pre-Amplified DPSK Receivers with Balanced Detection

This letter presents a comparison of exact probability density function with the Gaussian noise approximation in optically pre-amplified DPSK receivers with optical Mach-Zehnder interferometer demodulation (MZI) and balanced detection, including the impact of phase noise. It is found that the Gaussian noise approximation significantly over-estimates ASE-ASE beat noise in DPSK receivers with balanced detection particularly when phase noise is negligible, compared to IM/DD receivers, ASE- amplified spontaneous emission. However, the Gaussian noise approximation is still applicable for DPSK receivers with balanced detection and the measured 3-dB advantage is predicted by the Gaussian noise distribution.

physics.optics↗
arXiv2004

Quantum Limited DPSK Receivers with Optical Mach-Zehnder Interferometer Demodulation

We present an analysis of quantum-limited DPSK receivers with optical Mach-Zehnder interferometer (MZI) demodulation. It is shown for the first time that the quantum limits for DPSK/MZI receivers with single-port and balanced detections exactly differ from 3-dB in receiver sensitivity, obtained by both Poisson and Gaussian noise statistics.

physics.optics↗