arXiv subjects

Fei Lu

Publications and source records attributed to Fei Lu.

At least 55 records · Page 3Linked to original sources

arXiv2021

On the coercivity condition in the learning of interacting particle systems

In the learning of systems of interacting particles or agents, coercivity condition ensures identifiability of the interaction functions, providing the foundation of learning by nonparametric regression. The coercivity condition is equivalent to the strictly positive definiteness of an integral kernel arising in the learning. We show that for a class of interaction functions such that the system is ergodic, the integral kernel is strictly positive definite, and hence the coercivity condition holds true.

stat.ML↗

arXiv2021

Domain Adaptive Monocular Depth Estimation With Semantic Information

The advent of deep learning has brought an impressive advance to monocular depth estimation, e.g., supervised monocular depth estimation has been thoroughly investigated. However, the large amount of the RGB-to-depth dataset may not be always available since collecting accurate depth ground truth according to the RGB image is a time-consuming and expensive task. Although the network can be trained on an alternative dataset to overcome the dataset scale problem, the trained model is hard to generalize to the target domain due to the domain discrepancy. Adversarial domain alignment has demonstrated its efficacy to mitigate the domain shift on simple image classification tasks in previous works. However, traditional approaches hardly handle the conditional alignment as they solely consider the feature map of the network. In this paper, we propose an adversarial training model that leverages semantic information to narrow the domain gap. Based on the experiments conducted on the datasets for the monocular depth estimation task including KITTI and Cityscapes, the proposed compact model achieves state-of-the-art performance comparable to complex latest models and shows favorable results on boundaries and objects at far distances.

cs.CV↗

arXiv2021

ISALT: Inference-based schemes adaptive to large time-stepping for locally Lipschitz ergodic systems

Efficient simulation of SDEs is essential in many applications, particularly for ergodic systems that demand efficient simulation of both short-time dynamics and large-time statistics. However, locally Lipschitz SDEs often require special treatments such as implicit schemes with small time-steps to accurately simulate the ergodic measure. We introduce a framework to construct inference-based schemes adaptive to large time-steps (ISALT) from data, achieving a reduction in time by several orders of magnitudes. The key is the statistical learning of an approximation to the infinite-dimensional discrete-time flow map. We explore the use of numerical schemes (such as the Euler-Maruyama, a hybrid RK4, and an implicit scheme) to derive informed basis functions, leading to a parameter inference problem. We introduce a scalable algorithm to estimate the parameters by least squares, and we prove the convergence of the estimators as data size increases. We test the ISALT on three non-globally Lipschitz SDEs: the 1D double-well potential, a 2D multi-scale gradient system, and the 3D stochastic Lorenz equation with degenerate noise. Numerical results show that ISALT can tolerate time-step magnitudes larger than plain numerical schemes. It reaches optimal accuracy in reproducing the invariant measure when the time-step is medium-large.

math.NA↗

arXiv2020

Cluster Prediction for Opinion Dynamics from Partial Observations

We present a Bayesian approach to predict the clustering of opinions for a system of interacting agents from partial observations. The Bayesian formulation overcomes the unobservability of the system and quantifies the uncertainty in the prediction. We characterize the clustering by the posterior of the clusters' sizes and centers, and we represent the posterior by samples. To overcome the challenge in sampling the high-dimensional posterior, we introduce an auxiliary implicit sampling (AIS) algorithm using two-step observations. Numerical results show that the AIS algorithm leads to accurate predictions of the sizes and centers for the leading clusters, in both cases of noiseless and noisy observations. In particular, the centers are predicted with high success rates, but the sizes exhibit a considerable uncertainty that is sensitive to observation noise and the observation ratio.

stat.CO↗

arXiv2020

Data-driven model reduction for stochastic Burgers equations

We present a class of efficient parametric closure models for 1D stochastic Burgers equations. Casting it as statistical learning of the flow map, we derive the parametric form by representing the unresolved high wavenumber Fourier modes as functionals of the resolved variables' trajectory. The reduced models are nonlinear autoregression (NAR) time series models, with coefficients estimated from data by least squares. The NAR models can accurately reproduce the energy spectrum, the invariant densities, and the autocorrelations. Taking advantage of the simplicity of the NAR models, we investigate maximal and optimal space-time reduction. Reduction in space dimension is unlimited, and NAR models with two Fourier modes can perform well. The NAR model's stability limits time reduction, with a maximal time step smaller than that of the K-mode Galerkin system. We report a potential criterion for optimal space-time reduction: the NAR models achieve minimal relative error in the energy spectrum at the time step where the K-mode Galerkin system's mean CFL number agrees with the full model's.

math.NA↗

arXiv2020

Learning interaction kernels in mean-field equations of 1st-order systems of interacting particles

We introduce a nonparametric algorithm to learn interaction kernels of mean-field equations for 1st-order systems of interacting particles. The data consist of discrete space-time observations of the solution. By least squares with regularization, the algorithm learns the kernel on data-adaptive hypothesis spaces efficiently. A key ingredient is a probabilistic error functional derived from the likelihood of the mean-field equation's diffusion process. The estimator converges, in a reproducing kernel Hilbert space and an L2 space under an identifiability condition, at a rate optimal in the sense that it equals the numerical integrator's order. We demonstrate our algorithm on three typical examples: the opinion dynamics with a piecewise linear kernel, the granular media model with a quadratic kernel, and the aggregation-diffusion with a repulsive-attractive kernel.

stat.ML↗

arXiv2020

Data-driven model reduction, Wiener projections, and the Koopman-Mori-Zwanzig formalism

Model reduction methods aim to describe complex dynamic phenomena using only relevant dynamical variables, decreasing computational cost, and potentially highlighting key dynamical mechanisms. In the absence of special dynamical features such as scale separation or symmetries, the time evolution of these variables typically exhibits memory effects. Recent work has found a variety of data-driven model reduction methods to be effective for representing such non-Markovian dynamics, but their scope and dynamical underpinning remain incompletely understood. Here, we study data-driven model reduction from a dynamical systems perspective. For both chaotic and randomly-forced systems, we show the problem can be naturally formulated within the framework of Koopman operators and the Mori-Zwanzig projection operator formalism. We give a heuristic derivation of a NARMAX (Nonlinear Auto-Regressive Moving Average with eXogenous input) model from an underlying dynamical model. The derivation is based on a simple construction we call Wiener projection, which links Mori-Zwanzig theory to both NARMAX and to classical Wiener filtering. We apply these ideas to the Kuramoto-Sivashinsky model of spatiotemporal chaos and a viscous Burgers equation with stochastic forcing.

math.NA↗

arXiv2020

On the identifiability of interaction functions in systems of interacting particles

We address a fundamental issue in the nonparametric inference for systems of interacting particles: the identifiability of the interaction functions. We prove that the interaction functions are identifiable for a class of first-order stochastic systems, including linear systems with general initial laws and nonlinear systems with stationary distributions. We show that a coercivity condition is sufficient for identifiability and becomes necessary when the number of particles approaches infinity. The coercivity is equivalent to the strict positivity of related integral operators, which we prove by showing that their integral kernels are strictly positive definite by using Müntz type theorems.

math.ST↗

arXiv2020

Learning interaction kernels in stochastic systems of interacting particles from multiple trajectories

We consider stochastic systems of interacting particles or agents, with dynamics determined by an interaction kernel which only depends on pairwise distances. We study the problem of inferring this interaction kernel from observations of the positions of the particles, in either continuous or discrete time, along multiple independent trajectories. We introduce a nonparametric inference approach to this inverse problem, based on a regularized maximum likelihood estimator constrained to suitable hypothesis spaces adaptive to data. We show that a coercivity condition enables us to control the condition number of this problem and prove the consistency of our estimator, and that in fact it converges at a near-optimal learning rate, equal to the min-max rate of $1$-dimensional non-parametric regression. In particular, this rate is independent of the dimension of the state space, which is typically very high. We also analyze the discretization errors in the case of discrete-time observations, showing that it is of order $1/2$ in terms of the time gaps between observations. This term, when large, dominates the sampling error and the approximation error, preventing convergence of the estimator. Finally, we exhibit an efficient parallel algorithm to construct the estimator from data, and we demonstrate the effectiveness of our algorithm with numerical tests on prototype systems including stochastic opinion dynamics and a Lennard-Jones model.

math.ST↗

arXiv2020

Learning interaction kernels in heterogeneous systems of agents from multiple trajectories

Systems of interacting particles or agents have wide applications in many disciplines such as Physics, Chemistry, Biology and Economics. These systems are governed by interaction laws, which are often unknown: estimating them from observation data is a fundamental task that can provide meaningful insights and accurate predictions of the behaviour of the agents. In this paper, we consider the inverse problem of learning interaction laws given data from multiple trajectories, in a nonparametric fashion, when the interaction kernels depend on pairwise distances. We establish a condition for learnability of interaction kernels, and construct estimators that are guaranteed to converge in a suitable $L^2$ space, at the optimal min-max rate for 1-dimensional nonparametric regression. We propose an efficient learning algorithm based on least squares, which can be implemented in parallel for multiple trajectories and is therefore well-suited for the high dimensional, big data regime. Numerical simulations on a variety examples, including opinion dynamics, predator-swarm dynamics and heterogeneous particle dynamics, suggest that the learnability condition is satisfied in models used in practice, and the rate of convergence of our estimator is consistent with the theory. These simulations also suggest that our estimators are robust to noise in the observations, and produce accurate predictions of dynamics in relative large time intervals, even when they are learned from data collected in short time intervals.

stat.ML↗

arXiv2019

A Low Temperature Functioning CoFeB/MgO Based Perpendicular Magnetic Tunnel Junction for Cryogenic Nonvolatile Random Access Memory

We investigated the low temperature performance of CoFeB/MgO based perpendicular magnetic tunnel junctions (pMTJs) by characterizing their quasi-static switching voltage, high speed pulse write error rate and endurance down to 9 K. pMTJ devices exhibited high magnetoresistance (>120%) and reliable (error rate<10-4) bi-directional switching with 2 to 200 ns voltage pulses. The endurance of the devices at 9 K surpassed that at 300 K by three orders of magnitude under the same write conditions, functioning for more than 10^12 cycles with 10 ns write pulses. The critical switching voltage at 9 K was observed to increase by 33% to 93%, depending on pulse duration, compared to that at 350 K. Ferromagnetic resonance and magnetization measurements on blanket pMTJ film stacks suggest that the increased switching voltage is associated with an increase in effective magnetic anisotropy and magnetization of free layer with decreasing temperature. Our work demonstrates that CoFeB/MgO based pMTJs have great potential to enable cryogenic MRAM and that their low temperature magnetization and effective magnetic anisotropy can be further optimized to lower operating power and improve endurance.

cond-mat.mes-hall↗

arXiv2019

Joint state-parameter estimation of a nonlinear stochastic energy balance model from sparse noisy data

While nonlinear stochastic partial differential equations arise naturally in spatiotemporal modeling, inference for such systems often faces two major challenges: sparse noisy data and ill-posedness of the inverse problem of parameter estimation. To overcome the challenges, we introduce a strongly regularized posterior by normalizing the likelihood and by imposing physical constraints through priors of the parameters and states. We investigate joint parameter-state estimation by the regularized posterior in a physically motivated nonlinear stochastic energy balance model (SEBM) for paleoclimate reconstruction. The high-dimensional posterior is sampled by a particle Gibbs sampler that combines MCMC with an optimal particle filter exploiting the structure of the SEBM. In tests using either Gaussian or uniform priors based on the physical range of parameters, the regularized posteriors overcome the ill-posedness and lead to samples within physical ranges, quantifying the uncertainty in estimation. Due to the ill-posedness and the regularization, the posterior of parameters presents a relatively large uncertainty, and consequently, the maximum of the posterior, which is the minimizer in a variational approach, can have a large variation. In contrast, the posterior of states generally concentrates near the truth, substantially filtering out observation noise and reducing uncertainty in the unconstrained SEBM.

math.NA↗

arXiv2019

Nonparametric inference of interaction laws in systems of agents from trajectory data

Inferring the laws of interaction between particles and agents in complex dynamical systems from observational data is a fundamental challenge in a wide variety of disciplines. We propose a non-parametric statistical learning approach to estimate the governing laws of distance-based interactions, with no reference or assumption about their analytical form, from data consisting trajectories of interacting agents. We demonstrate the effectiveness of our learning approach both by providing theoretical guarantees, and by testing the approach on a variety of prototypical systems in various disciplines. These systems include homogeneous and heterogeneous agents systems, ranging from particle systems in fundamental physics to agent-based systems modeling opinion dynamics under the social influence, prey-predator dynamics, flocking and swarming, and phototaxis in cell dynamics.

cs.LG↗

arXiv2019

The Unconstrained Ear Recognition Challenge 2019 - ArXiv Version With Appendix

This paper presents a summary of the 2019 Unconstrained Ear Recognition Challenge (UERC), the second in a series of group benchmarking efforts centered around the problem of person recognition from ear images captured in uncontrolled settings. The goal of the challenge is to assess the performance of existing ear recognition techniques on a challenging large-scale ear dataset and to analyze performance of the technology from various viewpoints, such as generalization abilities to unseen data characteristics, sensitivity to rotations, occlusions and image resolution and performance bias on sub-groups of subjects, selected based on demographic criteria, i.e. gender and ethnicity. Research groups from 12 institutions entered the competition and submitted a total of 13 recognition approaches ranging from descriptor-based methods to deep-learning models. The majority of submissions focused on ensemble based methods combining either representations from multiple deep models or hand-crafted with learned image descriptors. Our analysis shows that methods incorporating deep learning models clearly outperform techniques relying solely on hand-crafted descriptors, even though both groups of techniques exhibit similar behaviour when it comes to robustness to various covariates, such presence of occlusions, changes in (head) pose, or variability in image resolution. The results of the challenge also show that there has been considerable progress since the first UERC in 2017, but that there is still ample room for further research in this area.

cs.CV↗

arXiv2018

Investigation of the near-threshold cluster resonance in $^{14}\rm{C}$

An experiment for $p(^{14}\rm{C}$,$^{14}\rm{C}^{*}\rightarrow^{10}\rm{Be}+α)\mathit{p}$ inelastic excitation and decay was performed in inverse kinematics at a beam energy of 25.3 MeV/u. A series of $^{14}\rm{C}$ excited states, including a new one at 18.3(1) MeV, were observed which decay to various states of the final nucleus of $^{10}\rm{Be}$. A specially designed telescope-system, installed around the zero degree, played an essential role in detecting the resonant states near the $α$-separation threshold. A state at 14.1(1) MeV is clearly identified, being consistent with the predicted band-head of the molecular rotational band characterized by the $π$-bond linear-chain-configuration. Further clarification of the properties of this exotic state is suggested by using appropriate reaction tools.

nucl-ex↗

arXiv2016

Comparison of continuous and discrete-time data-based modeling for hypoelliptic systems

We compare two approaches to the predictive modeling of dynamical systems from partial observations at discrete times. The first is continuous in time, where one uses data to infer a model in the form of stochastic differential equations, which are then discretized for numerical solution. The second is discrete in time, where one directly infers a discrete-time model in the form of a nonlinear autoregression moving average model. The comparison is performed in a special case where the observations are known to have been obtained from a hypoelliptic stochastic differential equation. We show that the discrete-time approach has better predictive skills, especially when the data are relatively sparse in time. We discuss open questions as well as the broader significance of the results.

math.NA↗

arXiv2016

Data-based stochastic model reduction for the Kuramoto--Sivashinsky equation

The problem of constructing data-based, predictive, reduced models for the Kuramoto-Sivashinsky equation is considered, under circumstances where one has observation data only for a small subset of the dynamical variables. Accurate prediction is achieved by developing a discrete-time stochastic reduced system, based on a NARMAX (Nonlinear Autoregressive Moving Average with eXogenous input) representation. The practical issue, with the NARMAX representation as with any other, is to identify an efficient structure, i.e., one with a small number of terms and coefficients. This is accomplished here by estimating coefficients for an approximate inertial form. The broader significance of the results is discussed.

math.NA↗

arXiv2015

Sampling, feasibility, and priors in Bayesian estimation

Importance sampling algorithms are discussed in detail, with an emphasis on implicit sampling, and applied to data assimilation via particle filters. Implicit sampling makes it possible to use the data to find high-probability samples at relatively low cost, making the assimilation more efficient. A new analysis of the feasibility of data assimilation is presented, showing in detail why feasibility depends on the Frobenius norm of the covariance matrix of the noise and not on the number of variables. A discussion of the convergence of particular particle filters follows. A major open problem in numerical data assimilation is the determination of appropriate priors, a progress report on recent work on this problem is given. The analysis highlights the need for a careful attention both to the data and to the physics in data assimilation problems.

stat.CO↗