arXiv subjects

Guang Lin

Publications and source records attributed to Guang Lin.

At least 163 records · Page 9Linked to original sources

arXiv2020

Predicting Mechanical Properties from Microstructure Images in Fiber-reinforced Polymers using Convolutional Neural Networks

Evaluating the mechanical response of fiber-reinforced composites can be extremely time consuming and expensive. Machine learning (ML) techniques offer a means for faster predictions via models trained on existing input-output pairs and have exhibited success in composite research. This paper explores a fully convolutional neural network modified from StressNet, which was originally for lin-ear elastic materials and extended here for a non-linear finite element (FE) simulation to predict the stress field in 2D slices of segmented tomography images of a fiber-reinforced polymer specimen. The network was trained and evaluated on data generated from the FE simulations of the exact microstructure. The testing results show that the trained network accurately captures the characteristics of the stress distribution, especially on fibers, solely from the segmented microstructure images. The trained model can make predictions within seconds in a single forward pass on an ordinary laptop, given the input microstructure, compared to 92.5 hours to run the full FE simulation on a high-performance computing cluster. These results show promise in using ML techniques to conduct fast structural analysis for fiber-reinforced composites and suggest a corollary that the trained model can be used to identify the location of potential damage sites in fiber-reinforced polymers.

cond-mat.mtrl-sci↗

arXiv2020

Spatial Damage Characterization in Self-Sensing Materials via Neural Network-Aided Electrical Impedance Tomography: A Computational Study

Continuous structural health monitoring (SHM) and integrated nondestructive evaluation (NDE) are important for ensuring the safe operation of high-risk engineering structures. Recently, piezoresistive nanocomposite materials have received much attention for SHM and NDE. These materials are self-sensing because their electrical conductivity changes in response to deformation and damage. Combined with electrical impedance tomography (EIT), it is possible to map deleterious effects. However, EIT suffers from important limitations -- it is computationally expensive, provides indistinct information on damage shape, and can miss multiple damages if they are close together. In this article we apply a novel neural network approach to quantify damage metrics such as size, number, and location from EIT data. This network is trained using a simulation routine calibrated to experimental data for a piezoresistive carbon nanofiber-modified epoxy. Our results show that the network can predict the number of damages with 99.2% accuracy, quantify damage size with respect to the averaged radius at an average of 2.46% error, and quantify damage position with respect to the domain length at an average of 0.89% error. These results are an important first step in translating the combination of self-sensing materials and EIT to real-world SHM and NDE.

eess.IV↗

arXiv2020

MFPC-Net: Multi-fidelity Physics-Constrained Neural Process

In this work, we propose a network which can utilize computational cheap low-fidelity data together with limited high-fidelity data to train surrogate models, where the multi-fidelity data are generated from multiple underlying models. The network takes a context set as input (physical observation points, low fidelity solution at observed points) and output (high fidelity solution at observed points) pairs. It uses the neural process to learn a distribution over functions conditioned on context sets and provide the mean and standard deviation at target sets. Moreover, the proposed framework also takes into account the available physical laws that govern the data and imposes them as constraints in the loss function. The multi-fidelity physical constraint network (MFPC-Net) (1) takes datasets obtained from multiple models at the same time in the training, (2) takes advantage of available physical information, (3) learns a stochastic process which can encode prior beliefs about the correlation between two fidelity with a few observations, and (4) produces predictions with uncertainty. The ability of representing a class of functions is ensured by the property of neural process and is achieved by the global latent variables in the neural network. Physical constraints are added to the loss using Lagrange multipliers. An algorithm to optimize the loss function is proposed to effectively train the parameters in the network on an ad hoc basis. Once trained, one can obtain fast evaluations at the entire domain of interest given a few observation points from a new low-and high-fidelity model pair. Particularly, one can further identify the unknown parameters such as permeability fields in elliptic PDEs with a simple modification of the network. Several numerical examples for both forward and inverse problems are presented to demonstrate the performance of the proposed method.

physics.comp-ph↗

arXiv2020

An adaptive Hessian approximated stochastic gradient MCMC method

Bayesian approaches have been successfully integrated into training deep neural networks. One popular family is stochastic gradient Markov chain Monte Carlo methods (SG-MCMC), which have gained increasing interest due to their scalability to handle large datasets and the ability to avoid overfitting. Although standard SG-MCMC methods have shown great performance in a variety of problems, they may be inefficient when the random variables in the target posterior densities have scale differences or are highly correlated. In this work, we present an adaptive Hessian approximated stochastic gradient MCMC method to incorporate local geometric information while sampling from the posterior. The idea is to apply stochastic approximation to sequentially update a preconditioning matrix at each iteration. The preconditioner possesses second-order information and can guide the random walk of a sampler efficiently. Instead of computing and saving the full Hessian of the log posterior, we use limited memory of the sample and their stochastic gradients to approximate the inverse Hessian-vector multiplication in the updating formula. Moreover, by smoothly optimizing the preconditioning matrix, our proposed algorithm can asymptotically converge to the target distribution with a controllable bias under mild conditions. To reduce the training and testing computational burden, we adopt a magnitude-based weight pruning method to enforce the sparsity of the network. Our method is user-friendly and is scalable to standard SG-MCMC updating rules by implementing an additional preconditioner. The sparse approximation of inverse Hessian alleviates storage and computational complexities for large dimensional models. The bias introduced by stochastic approximation is controllable and can be analyzed theoretically. Numerical experiments are performed on several problems.

math.NA↗

arXiv2020

Multifidelity Data Fusion via Gradient-Enhanced Gaussian Process Regression

We propose a data fusion method based on multi-fidelity Gaussian process regression (GPR) framework. This method combines available data of the quantity of interest (QoI) and its gradients with different fidelity levels, namely, it is a Gradient-enhanced Cokriging method (GE-Cokriging). It provides the approximations of both the QoI and its gradients simultaneously with uncertainty estimates. We compare this method with the conventional multi-fidelity Cokriging method that does not use gradients information, and the result suggests that GE-Cokriging has a better performance in predicting both QoI and its gradients. Moreover, GE-Cokriging even shows better generalization result in some cases where Cokriging performs poorly due to the singularity of the covariance matrix. We demonstrate the application of GE-Cokriging in several practical cases including reconstructing the trajectories and velocity of an underdamped oscillator with respect to time simultaneously, and investigating the sensitivity of power factor of a load bus with respect to varying power inputs of a generator bus in a large scale power system. We also show that though GE-Cokriging method requires a little bit higher computational cost than Cokriging method, the result of accuracy comparison shows that this cost is usually worth it.

cs.CE↗

arXiv2020

Gaussian Process Assisted Active Learning of Physical Laws

In many areas of science and engineering, discovering the governing differential equations from the noisy experimental data is an essential challenge. It is also a critical step in understanding the physical phenomena and prediction of the future behaviors of the systems. However, in many cases, it is expensive or time-consuming to collect experimental data. This article provides an active learning approach to estimate the unknown differential equations accurately with reduced experimental data size. We propose an adaptive design criterion combining the D-optimality and the maximin space-filling criterion. In contrast to active learning for other regression models, the D-optimality here requires the unknown solution of the differential equations and derivatives of the solution. We estimate the Gaussian process (GP) regression models from the available experimental data and use them as the surrogates of these unknown solution functions. The derivatives of the estimated GP models are derived and used to substitute the derivatives of the solution. Variable selection-based regression methods are used to learn the differential equations from the experimental data. Through multiple case studies, we demonstrate the proposed approach outperforms the D-optimality and the maximin space-filling design alone in terms of model accuracy and data economy.

stat.ME↗

arXiv2020

Peri-Net-Pro: The neural processes with quantified uncertainty for crack patterns

This paper uses the peridynamic theory, which is well-suited to crack studies, to predict the crack patterns in a moving disk and classify them according to the modes and finally perform regression analysis. In that way, the crack patterns are obtained according to each mode by Molecular Dynamic (MD) simulation using the peridynamics. Image classification and regression studies are conducted through Convolutional Neural Networks (CNNs) and the neural processes. First, we increased the amount and quality of the data using peridynamics, which can theoretically compensate for the problems of the finite element method (FEM) in generating crack pattern images. Second, we did the case study for the PMB, LPS, and VES models that were obtained using the peridynamic theory. Case studies were performed to classify the images using CNNs and determine the PMB, LBS, and VES models' suitability. Finally, we performed the regression analysis for the images of the crack patterns with neural processes to predict the crack patterns. In the regression problem, by representing the results of the variance according to the epochs, it can be confirmed that the result of the variance is decreased by increasing the epoch numbers through the neural processes. The most critical point of this study is that the neural processes make an accurate prediction even if there are missing or insufficient training data.

cs.CE↗

arXiv2020

Multi-Fidelity Gaussian Process based Empirical Potential Development for Si:H Nanowires

In material modeling, the calculation speed using the empirical potentials is fast compared to the first principle calculations, but the results are not as accurate as of the first principle calculations. First principle calculations are accurate but slow and very expensive to calculate. In this work, first, the H-H binding energy and H$_2$-H$_2$ interaction energy are calculated using the first principle calculations which can be applied to the Tersoff empirical potential. Second, the H-H parameters are estimated. After fitting H-H parameters, the mechanical properties are obtained. Finally, to integrate both the low-fidelity empirical potential data and the data from the high-fidelity first-principle calculations, the multi-fidelity Gaussian process regression is employed to predict the H-H binding energy and the H$_2$-H$_2$ interaction energy. Numerical results demonstrate the accuracy of the developed empirical potentials.

physics.comp-ph↗

arXiv2020

RotEqNet: Rotation-Equivariant Network for Fluid Systems with Symmetric High-Order Tensors

In the recent application of scientific modeling, machine learning models are largely applied to facilitate computational simulations of fluid systems. Rotation symmetry is a general property for most symmetric fluid systems. However, in general, current machine learning methods have no theoretical way to guarantee rotational symmetry. By observing an important property of contraction and rotation operation on high-order symmetric tensors, we prove that the rotation operation is preserved via tensor contraction. Based on this theoretical justification, in this paper, we introduce Rotation-Equivariant Network (RotEqNet) to guarantee the property of rotation-equivariance for high-order tensors in fluid systems. We implement RotEqNet and evaluate our claims through four case studies on various fluid systems. The property of error reduction and rotation-equivariance is verified in these case studies. Results from the comparative study show that our method outperforms conventional methods, which rely on data augmentation.

cs.CE↗

arXiv2020

An Adaptive Empirical Bayesian Method for Sparse Deep Learning

We propose a novel adaptive empirical Bayesian method for sparse deep learning, where the sparsity is ensured via a class of self-adaptive spike-and-slab priors. The proposed method works by alternatively sampling from an adaptive hierarchical posterior distribution using stochastic gradient Markov Chain Monte Carlo (MCMC) and smoothly optimizing the hyperparameters using stochastic approximation (SA). We further prove the convergence of the proposed method to the asymptotically correct distribution under mild conditions. Empirical applications of the proposed method lead to the state-of-the-art performance on MNIST and Fashion MNIST with shallow convolutional neural networks and the state-of-the-art compression performance on CIFAR10 with Residual Networks. The proposed method also improves resistance to adversarial attacks.

stat.ML↗

arXiv2020

Improving Simulation Efficiency of MCMC for Inverse Modeling of Hydrologic Systems with a Kalman-Inspired Proposal Distribution

Bayesian analysis is widely used in science and engineering for real-time forecasting, decision making, and to help unravel the processes that explain the observed data. These data are some deterministic and/or stochastic transformations of the underlying parameters. A key task is then to summarize the posterior distribution of these parameters. When models become too difficult to analyze analytically, Monte Carlo methods can be used to approximate the target distribution. Of these, Markov chain Monte Carlo (MCMC) methods are particularly powerful. Such methods generate a random walk through the parameter space and, under strict conditions of reversibility and ergodicity, will successively visit solutions with frequency proportional to the underlying target density. This requires a proposal distribution that generates candidate solutions starting from an arbitrary initial state. The speed of the sampled chains converging to the target distribution deteriorates rapidly, however, with increasing parameter dimensionality. In this paper, we introduce a new proposal distribution that enhances significantly the efficiency of MCMC simulation for highly parameterized models. This proposal distribution exploits the cross-covariance of model parameters, measurements and model outputs, and generates candidate states much alike the analysis step in the Kalman filter. We embed the Kalman-inspired proposal distribution in the DREAM algorithm during burn-in, and present several numerical experiments with complex, high-dimensional or multi-modal target distributions. Results demonstrate that this new proposal distribution can greatly improve simulation efficiency of MCMC. Specifically, we observe a speed-up on the order of 10-30 times for groundwater models with more than one-hundred parameters.

math.OC↗

arXiv2019

Bayesian inverse regression for dimension reduction with small datasets

We consider supervised dimension reduction problems, namely to identify a low dimensional projection of the predictors $\-x$ which can retain the statistical relationship between $\-x$ and the response variable $y$. We follow the idea of the sliced inverse regression (SIR) and the sliced average variance estimation (SAVE) type of methods, which is to use the statistical information of the conditional distribution $π(\-x|y)$ to identify the dimension reduction (DR) space. In particular we focus on the task of computing this conditional distribution without slicing the data. We propose a Bayesian framework to compute the conditional distribution where the likelihood function is obtained using the Gaussian process regression model. The conditional distribution $π(\-x|y)$ can then be computed directly via Monte Carlo sampling. We then can perform DR by considering certain moment functions (e.g. the first or the second moment) of the samples of the posterior distribution. With numerical examples, we demonstrate that the proposed method is especially effective for small data problems.

stat.CO↗

arXiv2019

Inverse modeling of hydrologic parameters in CLM4 via generalized polynomial chaos in the Bayesian framework

In this study, the applicability of generalized polynomial chaos (gPC) expansion for land surface model parameter estimation is evaluated. We compute the (posterior) distribution of the critical hydrological parameters that are subject to great uncertainty in the community land model (CLM). The unknown parameters include those that have been identified as the most influential factors on the simulations of surface and subsurface runoff, latent and sensible heat fluxes, and soil moisture in CLM4.0. We setup the inversion problem this problem in the Bayesian framework in two steps: (i) build a surrogate model expressing the input-output mapping, and (ii) compute the posterior distributions of the input parameters. Development of the surrogate model is done with a Bayesian procedure, based on the variable selection methods that use gPC expansions. Our approach accounts for bases selection uncertainty and quantifies the importance of the gPC terms, and hence all the input parameters, via the associated posterior probabilities.

stat.AP↗

arXiv2019

Efficient Deep Learning Techniques for Multiphase Flow Simulation in Heterogeneous Porous Media

We present efficient deep learning techniques for approximating flow and transport equations for both single phase and two-phase flow problems. The proposed methods take advantages of the sparsity structures in the underlying discrete systems and can be served as efficient alternatives to the system solvers at the full order. In particular, for the flow problem, we design a network with convolutional and locally connected layers to perform model reductions. Moreover, we employ a custom loss function to impose local mass conservation constraints. This helps to preserve the physical property of velocity solution which we are interested in learning. For the saturation problem, we propose a residual type of network to approximate the dynamics. Our main contribution here is the design of custom sparsely connected layers which take into account the inherent sparse interaction between the input and output. After training, the approximated feed-forward map can be applied iteratively to predict solutions in the long range. Our trained networks, especially in two-phase flow where the maps are nonlinear, show their great potential in accurately approximating the underlying physical system and improvement in computational efficiency. Some numerical experiments are performed and discussed to demonstrate the performance of our proposed techniques.

math.NA↗

arXiv2019

Bayesian identification of discontinuous fields with an ensemble-based variable separation multiscale method

This work presents a multiscale model reduction approach to discontinuous fields identification problems in the framework of Bayesian inference. An ensemble-based variable separation (VS) method is proposed to approximate multiscale basis functions used to build a coarse model. The variable-separation expression is constructed for stochastic multiscale basis functions based on the random field, which is treated Gauss process as prior information. To this end, multiple local inhomogeneous Dirichlet boundary condition problems are required to be solved, and the ensemble-based method is used to obtain variable separation forms for the corresponding local functions. The local functions share the same interpolate rule for different physical basis functions in each coarse block. This approach significantly improves the efficiency of computation. We obtain the variable separation expression of multiscale basis functions, which can be used to the models with different boundary conditions and source terms, once the expression constructed. The proposed method is applied to discontinuous field identification problems where the hybrid of total variation and Gaussian (TG) densities are imposed as the penalty. We give a convergence analysis of the approximate posterior to the reference one with respect to the Kullback-Leibler (KL) divergence under the hybrid prior. The proposed method is applied to identify discontinuous structures in permeability fields. Two patterns of discontinuous structures are considered in numerical examples: separated blocks and nested blocks.

math.NA↗

arXiv2019

Reinforcement Learning for Traffic Control with Adaptive Horizon

This paper proposes a reinforcement learning approach for traffic control with the adaptive horizon. To build the controller for the traffic network, a Q-learning-based strategy that controls the green light passing time at the network intersections is applied. The controller includes two components: the regular Q-learning controller that controls the traffic light signal, and the adaptive controller that continuously optimizes the action space for the Q-learning algorithm in order to improve the efficiency of the Q-learning algorithm. The regular Q-learning controller uses the control cost function as a reward function to determine the action to choose. The adaptive controller examines the control cost and updates the action space of the controller by determining the subset of actions that are most likely to obtain optimal results and shrinking the action space to that subset. Uncertainties in traffic influx and turning rate are introduced to test the robustness of the controller under a stochastic environment. Compared with those with model predictive control (MPC), the results show that the proposed Q-learning-based controller outperforms the MPC method by reaching a stable solution in a shorter period and achieves lower control costs. The proposed Q-learning-based controller is also robust under 30% traffic demand uncertainty and 15% turning rate uncertainty.

eess.SY↗

arXiv2019

On the anticipative nonlinear filtering problem and its stability

In this paper, we consider an anticipative nonlinear filtering problem, in which the observation noise is correlated with the past of the signal. This new signal-observation model has its applications in both finance models with insider trading and in engineering. We derive a new equation for the filter in this context, analyzing both the nonlinear and the linear cases. We also handle the case of a finite filter with Volterra type observation. The performance of our algorithm is presented through numerical experiments.

math.PR↗

arXiv2018

Latent Transformations for Object View Points Synthesis

We propose a fully-convolutional conditional generative model, the latent transformation neural network (LTNN), capable of view synthesis using a light-weight neural network suited for real-time applications. In contrast to existing conditional generative models which incorporate conditioning information via concatenation, we introduce a dedicated network component, the conditional transformation unit (CTU), designed to learn the latent space transformations corresponding to specified target views. In addition, a consistency loss term is defined to guide the network toward learning the desired latent space mappings, a task-divided decoder is constructed to refine the quality of generated views, and an adaptive discriminator is introduced to improve the adversarial training process. The generality of the proposed methodology is demonstrated on a collection of three diverse tasks: multi-view reconstruction on real hand depth images, view synthesis of real and synthetic faces, and the rotation of rigid objects. The proposed model is shown to exceed state-of-the-art results in each category while simultaneously achieving a reduction in the computational demand required for inference by 30% on average.

cs.CV↗