arXiv subjects

Lu Lu

Publications and source records attributed to Lu Lu.

At least 199 records · Page 11Linked to original sources

arXiv2021

Physics-informed neural networks with hard constraints for inverse design

Inverse design arises in a variety of areas in engineering such as acoustic, mechanics, thermal/electronic transport, electromagnetism, and optics. Topology optimization is a major form of inverse design, where we optimize a designed geometry to achieve targeted properties and the geometry is parameterized by a density function. This optimization is challenging, because it has a very high dimensionality and is usually constrained by partial differential equations (PDEs) and additional inequalities. Here, we propose a new deep learning method -- physics-informed neural networks with hard constraints (hPINNs) -- for solving topology optimization. hPINN leverages the recent development of PINNs for solving PDEs, and thus does not rely on any numerical PDE solver. However, all the constraints in PINNs are soft constraints, and hence we impose hard constraints by using the penalty method and the augmented Lagrangian method. We demonstrate the effectiveness of hPINN for a holography problem in optics and a fluid problem of Stokes flow. We achieve the same objective as conventional PDE-constrained optimization methods based on adjoint methods and numerical PDE solvers, but find that the design obtained from hPINN is often simpler and smoother for problems whose solution is not unique. Moreover, the implementation of inverse design with hPINN can be easier than that of conventional methods.

physics.comp-ph↗

arXiv2020

Operator learning for predicting multiscale bubble growth dynamics

Simulating and predicting multiscale problems that couple multiple physics and dynamics across many orders of spatiotemporal scales is a great challenge that has not been investigated systematically by deep neural networks (DNNs). Herein, we develop a framework based on operator regression, the so-called deep operator network (DeepONet), with the long term objective to simplify multiscale modeling by avoiding the fragile and time-consuming "hand-shaking" interface algorithms for stitching together heterogeneous descriptions of multiscale phenomena. To this end, as a first step, we investigate if a DeepONet can learn the dynamics of different scale regimes, one at the deterministic macroscale and the other at the stochastic microscale regime with inherent thermal fluctuations. Specifically, we test the effectiveness and accuracy of DeepONet in predicting multirate bubble growth dynamics, which is described by a Rayleigh-Plesset (R-P) equation at the macroscale and modeled as a stochastic nucleation and cavitation process at the microscale by dissipative particle dynamics (DPD). Taken together, our findings demonstrate that DeepONets can be employed to unify the macroscale and microscale models of the multirate bubble growth problem, hence providing new insight into the role of operator regression via DNNs in tackling realistic multiscale problems and in simplifying modeling with heterogeneous descriptions.

physics.comp-ph↗

arXiv2020

DeepM&Mnet for hypersonics: Predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators

In high-speed flow past a normal shock, the fluid temperature rises rapidly triggering downstream chemical dissociation reactions. The chemical changes lead to appreciable changes in fluid properties, and these coupled multiphysics and the resulting multiscale dynamics are challenging to resolve numerically. Using conventional computational fluid dynamics (CFD) requires excessive computing cost. Here, we propose a totally new efficient approach, assuming that some sparse measurements of the state variables are available that can be seamlessly integrated in the simulation algorithm. We employ a special neural network for approximating nonlinear operators, the DeepONet, which is used to predict separately each individual field, given inputs from the rest of the fields of the coupled multiphysics system. We demonstrate the effectiveness of DeepONet by predicting five species in the non-equilibrium chemistry downstream of a normal shock at high Mach numbers as well as the velocity and temperature fields. We show that upon training, DeepONets can be over five orders of magnitude faster than the CFD solver employed to generate the training data and yield good accuracy for unseen Mach numbers within the range of training. Outside this range, DeepONet can still predict accurately and fast if a few sparse measurements are available. We then propose a composite supervised neural network, DeepM&Mnet, that uses multiple pre-trained DeepONets as building blocks and scattered measurements to infer the set of all seven fields in the entire domain of interest. Two DeepM&Mnet architectures are tested, and we demonstrate the accuracy and capacity for efficient data assimilation. DeepM&Mnet is simple and general: it can be employed to construct complex multiphysics and multiscale models and assimilate sparse measurements using pre-trained DeepONets in a "plug-and-play" mode.

physics.comp-ph↗

arXiv2020

DeepM&Mnet: Inferring the electroconvection multiphysics fields based on operator approximation by neural networks

Electroconvection is a multiphysics problem involving coupling of the flow field with the electric field as well as the cation and anion concentration fields. For small Debye lengths, very steep boundary layers are developed, but standard numerical methods can simulate the different regimes quite accurately. Here, we use electroconvection as a benchmark problem to put forward a new data assimilation framework, the DeepM&Mnet, for simulating multiphysics and multiscale problems at speeds much faster than standard numerical methods using pre-trained neural networks (NNs). We first pre-train DeepONets that can predict independently each field, given general inputs from the rest of the fields of the coupled system. DeepONets can approximate nonlinear operators and are composed of two sub-networks, a branch net for the input fields and a trunk net for the locations of the output field. DeepONets, which are extremely fast, are used as building blocks in the DeepM&Mnet and form constraints for the multiphysics solution along with some sparse available measurements of any of the fields. We demonstrate the new methodology and document the accuracy of each individual DeepONet, and subsequently we present two different DeepM&Mnet architectures that infer accurately and efficiently 2D electroconvection fields for unseen electric potentials. The DeepM&Mnet framework is general and can be applied for building any complex multiphysics and multiscale models based on very few measurements using pre-trained DeepONets in a plug-and-play mode.

physics.comp-ph↗

arXiv2020

Quantifying the generalization error in deep learning in terms of data distribution and neural network smoothness

The accuracy of deep learning, i.e., deep neural networks, can be characterized by dividing the total error into three main types: approximation error, optimization error, and generalization error. Whereas there are some satisfactory answers to the problems of approximation and optimization, much less is known about the theory of generalization. Most existing theoretical works for generalization fail to explain the performance of neural networks in practice. To derive a meaningful bound, we study the generalization error of neural networks for classification problems in terms of data distribution and neural network smoothness. We introduce the cover complexity (CC) to measure the difficulty of learning a data set and the inverse of the modulus of continuity to quantify neural network smoothness. A quantitative bound for expected accuracy/error is derived by considering both the CC and neural network smoothness. Although most of the analysis is general and not specific to neural networks, we validate our theoretical assumptions and results numerically for neural networks by several data sets of images. The numerical results confirm that the expected error of trained networks scaled with the square root of the number of classes has a linear relationship with respect to the CC. We also observe a clear consistency between test loss and neural network smoothness during the training process. In addition, we demonstrate empirically that the neural network smoothness decreases when the network size increases whereas the smoothness is insensitive to training dataset size.

stat.ML↗

arXiv2020

DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators

While it is widely known that neural networks are universal approximators of continuous functions, a less known and perhaps more powerful result is that a neural network with a single hidden layer can approximate accurately any nonlinear continuous operator. This universal approximation theorem is suggestive of the potential application of neural networks in learning nonlinear operators from data. However, the theorem guarantees only a small approximation error for a sufficient large network, and does not consider the important optimization and generalization errors. To realize this theorem in practice, we propose deep operator networks (DeepONets) to learn operators accurately and efficiently from a relatively small dataset. A DeepONet consists of two sub-networks, one for encoding the input function at a fixed number of sensors $x_i, i=1,\dots,m$ (branch net), and another for encoding the locations for the output functions (trunk net). We perform systematic simulations for identifying two types of operators, i.e., dynamic systems and partial differential equations, and demonstrate that DeepONet significantly reduces the generalization error compared to the fully-connected networks. We also derive theoretically the dependence of the approximation error in terms of the number of sensors (where the input function is defined) as well as the input function type, and we verify the theorem with computational results. More importantly, we observe high-order error convergence in our computational tests, namely polynomial rates (from half order to fourth order) and even exponential convergence with respect to the training dataset size.

cs.LG↗

arXiv2020

Diffusion multi-rate LMS algorithm for acoustic sensor networks

In this paper, we present a diffusion multi-rate least-mean-square (LMS) algorithm, named DMLMS, which is an effective solution for distributed estimation when two or more observation sequences are available with different sampling rates. Then, we focus on a more practical application in the wireless acoustic sensor networks (ASN). The filtered-x LMS (FxLMS) algorithm is extended to the distributed multi-rate system and it introduces collaboration between nodes following a diffusion strategy. Simulation results show that the effectiveness of the proposed algorithms.

eess.SY↗

arXiv2020

Physics-informed neural networks for inverse problems in nano-optics and metamaterials

In this paper we employ the emerging paradigm of physics-informed neural networks (PINNs) for the solution of representative inverse scattering problems in photonic metamaterials and nano-optics technologies. In particular, we successfully apply mesh-free PINNs to the difficult task of retrieving the effective permittivity parameters of a number of finite-size scattering systems that involve many interacting nanostructures as well as multi-component nanoparticles. Our methodology is fully validated by numerical simulations based on the Finite Element Method (FEM). The development of physics-informed deep learning techniques for inverse scattering can enable the design of novel functional nanostructures and significantly broaden the design space of metamaterials by naturally accounting for radiation and finite-size effects beyond the limitations of traditional effective medium theories.

physics.comp-ph↗

arXiv2020

Spatial Attention for Far-field Speech Recognition with Deep Beamforming Neural Networks

In this paper, we introduce spatial attention for refining the information in multi-direction neural beamformer for far-field automatic speech recognition. Previous approaches of neural beamformers with multiple look directions, such as the factored complex linear projection, have shown promising results. However, the features extracted by such methods contain redundant information, as only the direction of the target speech is relevant. We propose using a spatial attention subnet to weigh the features from different directions, so that the subsequent acoustic model could focus on the most relevant features for the speech recognition. Our experimental results show that spatial attention achieves up to 9% relative word error rate improvement over methods without the attention.

eess.AS↗

arXiv2020

DeepXDE: A deep learning library for solving differential equations

Deep learning has achieved remarkable success in diverse applications; however, its use in solving partial differential equations (PDEs) has emerged only recently. Here, we present an overview of physics-informed neural networks (PINNs), which embed a PDE into the loss of the neural network using automatic differentiation. The PINN algorithm is simple, and it can be applied to different types of PDEs, including integro-differential equations, fractional PDEs, and stochastic PDEs. Moreover, from the implementation point of view, PINNs solve inverse problems as easily as forward problems. We propose a new residual-based adaptive refinement (RAR) method to improve the training efficiency of PINNs. For pedagogical reasons, we compare the PINN algorithm to a standard finite element method. We also present a Python library for PINNs, DeepXDE, which is designed to serve both as an education tool to be used in the classroom as well as a research tool for solving problems in computational science and engineering. Specifically, DeepXDE can solve forward problems given initial and boundary conditions, as well as inverse problems given some extra measurements. DeepXDE supports complex-geometry domains based on the technique of constructive solid geometry, and enables the user code to be compact, resembling closely the mathematical formulation. We introduce the usage of DeepXDE and its customizability, and we also demonstrate the capability of PINNs and the user-friendliness of DeepXDE for five different examples. More broadly, DeepXDE contributes to the more rapid development of the emerging Scientific Machine Learning field.

cs.LG↗

arXiv2019

Robots as Actors in a Film: No War, A Robot Story

Will the Third World War be fought by robots? This short film is a light-hearted comedy that aims to trigger an interesting discussion and reflexion on the terrifying killer-robot stories that increasingly fill us with dread when we read the news headlines. The fictional scenario takes inspiration from current scientific research and describes a future where robots are asked by humans to join the war. Robots are divided, sparking protests in robot society... will robots join the conflict or will they refuse to be employed in human warfare? Food for thought for engineers, roboticists and anyone imagining what the upcoming robot revolution could look like. We let robots pop on camera to tell a story, taking on the role of actors playing in the film, instructed through code on how to "act" for each scene.

cs.RO↗

arXiv2019

Progressive amorphization of GeSbTe phase-change material under electron beam irradiation

Fast and reversible phase transitions in chalcogenide phase-change materials (PCMs), in particular, Ge-Sb-Te compounds, are not only of fundamental interests, but also make PCMs based random access memory (PRAM) a leading candidate for non-volatile memory and neuromorphic computing devices. To RESET the memory cell, crystalline Ge-Sb-Te has to undergo phase transitions firstly to a liquid state and then to an amorphous state, corresponding to an abrupt change in electrical resistance. In this work, we demonstrate a progressive amorphization process in GeSb2Te4 thin films under electron beam irradiation on transmission electron microscope (TEM). Melting is shown to be completely absent by the in situ TEM experiments. The progressive amorphization process resembles closely the cumulative crystallization process that accompanies a continuous change in electrical resistance. Our work suggests that if displacement forces can be implemented properly, it should be possible to emulate symmetric neuronal dynamics by using PCMs.

cond-mat.mtrl-sci↗

arXiv2019

Statistical Analysis of Modern Reliability Data

Traditional reliability analysis has been using time to event data, degradation data, and recurrent event data, while the associated covariates tend to be simple and constant over time. Over the past years, we have witnessed the rapid development of sensor and wireless technology, which enables us to track how the product has been used and under which environmental conditions it has been used. Nowadays, we are able to collect richer information on covariates which provides opportunities for better reliability predictions. In this chapter, we first review recent development on statistical methods for reliability analysis. We then focus on introducing several specific methods that were developed for different types of reliability data with covariate information. Illustrations of those methods are also provided using examples from industry. Test planning is also an important part of reliability analysis. In addition to data analysis, we also provide a briefly review on recent developments of test planning and then focus on illustrating the sequential Bayesian design with an example of fatigue testing for polymer composites. The paper is concluded with some discussions and remarks.

stat.AP↗

arXiv2019

Mean-Square Performance Analysis of Noise-Robust Normalized Subband Adaptive Filter Algorithm

This paper studies the statistical models of the noise-robust normalized subband adaptive filter (NR-NSAF) algorithm in the mean and mean square deviation senses involving transient-state and steady-state behavior by resorting to the method of the vectorization operation and the Kronecker product. The analysis method does not require the Gaussian input signal. Moreover, the proposed analysis removes the paraunitary assumption imposed on the analysis filter banks as in the existing analyses of subband adaptive algorithms. Simulation results in various conditions demonstrate the effectiveness of our theoretical analysis. For a special form of the algorithm, the proposed steady-state expression is also better accurate than the previous analysis.

eess.SP↗

arXiv2019

The Next Generation of IceCube Realtime Neutrino Alerts

In 2016, IceCube initiated a system of public real-time alerts that are typically issued within one minute, following the detection of a neutrino candidate event that is likely to be of astrophysical origin. The goal of these alerts is to enable multi-messenger observations that may identify the neutrino source. Through January 31, 2019, a total of 20 public alerts have been issued, with many of them receiving follow-up observations across multiple wavelength bands. One alert in particular, IceCube-170922A, was found to be associated with a flaring gamma-ray blazar, TXS 0506+056. This was the first >3 sigma association of a high-energy neutrino with an electromagnetic counterpart. In 2019, the IceCube collaboration is introducing a new set of neutrino candidate selections that expand the alert program. These new selections provide two alert channels. A "Gold" channel will issue alerts for neutrino candidates at least 50% likely to be of astrophysical origin and is expected to deliver $\sim$10 alerts per year. Additionally a more frequent "Bronze" channel will provide $\sim$20 alerts per year for neutrino candidates that are between 30% and 50% likely to be of astrophysical origin. We present the neutrino event selections used to generate these alerts, the expected alert rates, and a description of the alert message.

astro-ph.HE↗

arXiv2019

Gated Multiple Feedback Network for Image Super-Resolution

The rapid development of deep learning (DL) has driven single image super-resolution (SR) into a new era. However, in most existing DL based image SR networks, the information flows are solely feedforward, and the high-level features cannot be fully explored. In this paper, we propose the gated multiple feedback network (GMFN) for accurate image SR, in which the representation of low-level features are efficiently enriched by rerouting multiple high-level features. We cascade multiple residual dense blocks (RDBs) and recurrently unfolds them across time. The multiple feedback connections between two adjacent time steps in the proposed GMFN exploits multiple high-level features captured under large receptive fields to refine the low-level features lacking enough contextual information. The elaborately designed gated feedback module (GFM) efficiently selects and further enhances useful information from multiple rerouted high-level features, and then refine the low-level features with the enhanced high-level information. Extensive experiments demonstrate the superiority of our proposed GMFN against state-of-the-art SR methods in terms of both quantitative metrics and visual quality. Code is available at https://github.com/liqilei/GMFN.

cs.CV↗

arXiv2019

How to Host a Data Competition: Statistical Advice for Design and Analysis of a Data Competition

Data competitions rely on real-time leaderboards to rank competitor entries and stimulate algorithm improvement. While such competitions have become quite popular and prevalent, particularly in supervised learning formats, their implementations by the host are highly variable. Without careful planning, a supervised learning competition is vulnerable to overfitting, where the winning solutions are so closely tuned to the particular set of provided data that they cannot generalize to the underlying problem of interest to the host. This paper outlines some important considerations for strategically designing relevant and informative data sets to maximize the learning outcome from hosting a competition based on our experience. It also describes a post-competition analysis that enables robust and efficient assessment of the strengths and weaknesses of solutions from different competitors, as well as greater understanding of the regions of the input space that are well-solved. The post-competition analysis, which complements the leaderboard, uses exploratory data analysis and generalized linear models (GLMs). The GLMs not only expand the range of results we can explore, they also provide more detailed analysis of individual sub-questions including similarities and differences between algorithms across different types of scenarios, universally easy or hard regions of the input space, and different learning objectives. When coupled with a strategically planned data generation approach, the methods provide richer and more informative summaries to enhance the interpretation of results beyond just the rankings on the leaderboard. The methods are illustrated with a recently completed competition to evaluate algorithms capable of detecting, identifying, and locating radioactive materials in an urban environment.

stat.AP↗

arXiv2018

Collapse of Deep and Narrow Neural Nets

Recent theoretical work has demonstrated that deep neural networks have superior performance over shallow networks, but their training is more difficult, e.g., they suffer from the vanishing gradient problem. This problem can be typically resolved by the rectified linear unit (ReLU) activation. However, here we show that even for such activation, deep and narrow neural networks (NNs) will converge to erroneous mean or median states of the target function depending on the loss with high probability. Deep and narrow NNs are encountered in solving partial differential equations with high-order derivatives. We demonstrate this collapse of such NNs both numerically and theoretically, and provide estimates of the probability of collapse. We also construct a diagram of a safe region for designing NNs that avoid the collapse to erroneous states. Finally, we examine different ways of initialization and normalization that may avoid the collapse problem. Asymmetric initializations may reduce the probability of collapse but do not totally eliminate it.

stat.ML↗