Publications (63)
Sampling, feasibility, and priors in Bayesian estimation
Alexandre J. Chorin, Fei Lu, Robert N. Miller +2
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 pos…
NySALT: Nyström-type inference-based schemes adaptive to large time-stepping
Xingjie Li, Fei Lu, Molei Tao +1
Large time-stepping is important for efficient long-time simulations of deterministic and stochastic Hamiltonian dynamical systems. Conventional structure-preserving integrators, w…
Non-degeneracy of some Sobolev Pseudo-norms of fractional Brownian motion
Yaozhong Hu, Fei Lu, David Nualart
Applying an upper bound estimate for small ball probability for fractional Brownian motion (fBm), we prove the non-degeneracy of some Sobolev pseudo-norms of fBm.
Learning interacting particle systems from unlabeled data
Viska Wei, Fei Lu
Learning the potentials of interacting particle systems is a fundamental task across various scientific disciplines. A major challenge is that unlabeled data collected at discrete…
Joint state-parameter estimation of a nonlinear stochastic energy balance model from sparse noisy data
Fei Lu, Nils Weitzel, Adam H. Monahan
While nonlinear stochastic partial differential equations arise naturally in spatiotemporal modeling, inference for such systems often faces two major challenges: sparse noisy data…
Data-driven model reduction for stochastic Burgers equations
Fei Lu
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…
Small noise analysis for Tikhonov and RKHS regularizations
Quanjun Lang, Fei Lu
Regularization plays a pivotal role in ill-posed machine learning and inverse problems. However, the fundamental comparative analysis of various regularization norms remains open.…
Unsupervised learning of observation functions in state-space models by nonparametric moment methods
Qingci An, Yannis Kevrekidis, Fei Lu +1
We investigate the unsupervised learning of non-invertible observation functions in nonlinear state-space models. Assuming abundant data of the observation process along with the d…
Nonparametric learning of kernels in nonlocal operators
Fei Lu, Qingci An, Yue Yu
Nonlocal operators with integral kernels have become a popular tool for designing solution maps between function spaces, due to their efficiency in representing long-range dependen…
Cluster Prediction for Opinion Dynamics from Partial Observations
Zehong Zhang, Fei Lu
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 unobservab…
Minimax rates for learning kernels in operators
Sichong Zhang, Xiong Wang, Fei Lu
Learning kernels in operators from data lies at the intersection of inverse problems and statistical learning, providing a powerful framework for capturing non-local dependencies i…
Learning Lévy density via adaptive RKHS regression with bi-level optimization
Luxuan Yang, Fei Lu, Ting Gao +2
We propose a nonparametric method to learn the Lévy density from probability density data governed by a nonlocal Fokker-Planck equation. We recast the problem as identifying the k…
Automatic reproducing kernel and regularization for learning convolution kernels
Haibo Li, Fei Lu
Learning convolution kernels in operators from data arises in numerous applications and represents an ill-posed inverse problem of broad interest. With scant prior information, ker…
A Novel Approach to Evaluating Battery Charger Controller Design with Nonlinear PID Controller in an Extendable CHIL Setup
Shervin Salehi Rad, Micheal Muhlbaier, Oleg Fishman +4
The design and development of power electronics converters pose a multitude of challenges. The evaluation of power electronics converters, particularly when operating at high power…
Data adaptive RKHS Tikhonov regularization for learning kernels in operators
Fei Lu, Quanjun Lang, Qingci An
We present DARTR: a Data Adaptive RKHS Tikhonov Regularization method for the linear inverse problem of nonparametric learning of function parameters in operators. A key ingredient…
Data-based stochastic model reduction for the Kuramoto--Sivashinsky equation
Fei Lu, Kevin Lin, Alexandre J. Chorin
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…
From Events to Trending: A Multi-Stage Hotspots Detection Method Based on Generative Query Indexing
Kaichun Wang, Yanguang Chen, Ting Zhang +7
LLM-based conversational systems have become a popular gateway for information access, yet most existing chatbots struggle to handle news-related trending queries effectively. To i…
The Unconstrained Ear Recognition Challenge 2019 - ArXiv Version With Appendix
Žiga EmerÅ¡iÄ, Aruna Kumar S. V., B. S. Harish +28
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…
Investigation of the near-threshold cluster resonance in
Hong-Liang Zang, Yan-Lin Ye, Zhi-Huan Li +26
An experiment for , inelastic excitation and decay was performed in inverse kinematics at a beam energy of 25.3…
Self-test loss functions for learning weak-form operators and gradient flows
Yuan Gao, Quanjun Lang, Fei Lu
The construction of loss functions presents a major challenge in data-driven modeling involving weak-form operators in PDEs and gradient flows, particularly due to the need to sele…
Bias-Independent Subthreshold Swing in Nanoscale Cold-Source Field-Effect Transistors by Drain Density-of-States Engineering
Kunyi Liu, Fei Lu, Yuan Li
We report a strategy to design nanoscale cold-source field-effect transistors (CS-FETs) with bias-independent sub-60 mV/dec subthreshold swing (SS). By first-principles calculation…
Stochastic Data-Driven Variational Multiscale Reduced Order Models
Fei Lu, Changhong Mou, Honghu Liu +1
Trajectory-wise data-driven reduced order models (ROMs) tend to be sensitive to training data, and thus lack robustness. We propose to construct a robust stochastic ROM closure (S-…
Nonlocal Attention Operator: Materializing Hidden Knowledge Towards Interpretable Physics Discovery
Yue Yu, Ning Liu, Fei Lu +3
Despite the recent popularity of attention-based neural architectures in core AI fields like natural language processing (NLP) and computer vision (CV), their potential in modeling…
Optimal minimax rate of learning nonlocal interaction kernels
Xiong Wang, Inbar Seroussi, Fei Lu
Nonparametric estimation of nonlocal interaction kernels is crucial in various applications involving interacting particle systems. The inference challenge, situated at the nexus o…
A Data-Adaptive Prior for Bayesian Learning of Kernels in Operators
Neil K. Chada, Quanjun Lang, Fei Lu +1
Kernels are efficient in representing nonlocal dependence and they are widely used to design operators between function spaces. Thus, learning kernels in operators from data is an…
Data-driven model reduction, Wiener projections, and the Koopman-Mori-Zwanzig formalism
Kevin K. Lin, Fei Lu
Model reduction methods aim to describe complex dynamic phenomena using only relevant dynamical variables, decreasing computational cost, and potentially highlighting key dynamical…
Hölder Continuity of the Solution for a Class of Nonlinear SPDE Arising from One Dimensional Superprocesses
Yaozhong Hu, Fei Lu, David Nualart
The Hölder continuity of the solution to a nonlinear stochastic partial differential equation arising from one dimensional super process is obtained. It is proved that the Hölder…
The Influence of in-medium NN cross-sections, symmetry potential and impact parameter on the isospin observables
Yingxun Zhang, D. D. S. Coupland, P. Danielewicz +5
We explore the influence of in-medium nucleon-nucleon cross section, symmetry potential and impact parameter on isospin sensitive observables in intermediate-energy heavy-ion colli…
Gallium Nitride (GaN) based High-Power Multilevel H-Bridge Inverter for Wireless Power Transfer of Electric Vehicles
Javad Chevinly, Shervin Salehi Rad, Elias Nadi +5
This paper presents a design and implementation of a high-power Gallium Nitride (GaN)-based multilevel Hbridge inverter to excite wireless charging coils for the wireless power tra…
The -type P-wave bottom baryon states via the QCD sum rules
Qi Xin, Zhi-Gang Wang, Fei Lu
Our study focuses on the -type P-wave bottom baryon states with the spin-parity , . We introduce an explicit P-wave between the two light quar…
Nonparametric inference of interaction laws in systems of agents from trajectory data
Fei Lu, Mauro Maggioni, Sui Tang +1
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…
Learning interaction kernels in mean-field equations of 1st-order systems of interacting particles
Quanjun Lang, Fei Lu
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…
Learning interaction kernels in heterogeneous systems of agents from multiple trajectories
Fei Lu, Mauro Maggioni, Sui Tang
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 l…
Shock trace prediction by reduced models for a viscous stochastic Burgers equation
Nan Chen, Honghu Liu, Fei Lu
Viscous shocks are a particular type of extreme events in nonlinear multiscale systems, and their representation requires small scales. Model reduction can thus play an important r…
Convergence of densities of some functionals of Gaussian processes
Yaozhong Hu, Fei Lu, David Nualart
The aim of this paper is to establish the uniform convergence of the densities of a sequence of random variables, which are functionals of an underlying Gaussian process, to a norm…
Analysis of the D-wave -type charmed baryon states with the QCD sum rules
Zhi-Gang Wang, Fei Lu, Yang Liu
We construct the -type currents to investigate the D-wave charmed baryon states with the QCD sum rules systematically. The predicted masses (…
Domain Adaptive Monocular Depth Estimation With Semantic Information
Fei Lu, Hyeonwoo Yu, Jean Oh
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,…
A Low Temperature Functioning CoFeB/MgO Based Perpendicular Magnetic Tunnel Junction for Cryogenic Nonvolatile Random Access Memory
Lili Lang, Yujie Jiang, Fei Lu +4
We investigated the low temperature performance of CoFeB/MgO based perpendicular magnetic tunnel junctions (pMTJs) by characterizing their quasi-static switching voltage, high spee…
Scalable iterative data-adaptive RKHS regularization
Haibo Li, Jinchao Feng, Fei Lu
We present iDARR, a scalable iterative Data-Adaptive RKHS Regularization method, for solving ill-posed linear inverse problems. The method searches for solutions in subspaces where…
ISALT: Inference-based schemes adaptive to large time-stepping for locally Lipschitz ergodic systems
Xingjie Li, Fei Lu, Felix X. -F. Ye
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 statist…
Energy-Aware Routing Algorithm for Mobile Ground-to-Air Charging
Bill Cai, Fei Lu, Lifeng Zhou
We investigate the problem of energy-constrained planning for a cooperative system of an Unmanned Ground Vehicles (UGV) and an Unmanned Aerial Vehicle (UAV). In scenarios where the…
Transformer learns the cross-task prior and regularization for in-context learning
Fei Lu, Yue Yu
Transformers have shown a remarkable ability for in-context learning (ICL), making predictions based on contextual examples. However, while theoretical analyses have explored this…
Robust First and Second-Order Differentiation for Regularized Optimal Transport
Xingjie Li, Fei Lu, Molei Tao +1
Applications such as unbalanced and fully shuffled regression can be approached by optimizing regularized optimal transport (OT) distances, such as the entropic OT and Sinkhorn dis…
ABot-World-0: Infinite Interactive World Rollout on a Single Desktop GPU
Fan Jiang, Zhaoxu Sun, Mengchao Wang +38
We present ABot-World-0, an action-conditioned video world model for real-time, long-horizon closed-loop interaction, supported by a multi-source data infrastructure spanning AAA g…
Differential cross-section measurements for neutron-induced production reactions on carbon across neutron energy range of 6.2 to 76 MeV
Longxiang Liu, Kang Sun, Han Yi +24
Angle-differential cross sections for neutron-induced production in carbon were determined at thirty discrete neutron energy levels ranging from 6.2 to 76 MeV at the Back-n wh…
Identifiability of interaction kernels in mean-field equations of interacting particles
Quanjun Lang, Fei Lu
This study examines the identifiability of interaction kernels in mean-field equations of interacting particles or agents, an area of growing interest across various scientific and…
Benchmarking optimality of time series classification methods in distinguishing diffusions
Zehong Zhang, Fei Lu, Esther Xu Fei +3
Statistical optimality benchmarking is crucial for analyzing and designing time series classification (TSC) algorithms. This study proposes to benchmark the optimality of TSC algor…
On the coercivity condition in the learning of interacting particle systems
Zhongyang Li, Fei Lu
In the learning of systems of interacting particles or agents, coercivity condition ensures identifiability of the interaction functions, providing the foundation of learning by no…
Limitations of polynomial chaos expansions in the Bayesian solution of inverse problems
Fei Lu, Matthias Morzfeld, Xuemin Tu +1
Polynomial chaos expansions are used to reduce the computational cost in the Bayesian solutions of inverse problems by creating a surrogate posterior that can be evaluated inexpens…
Probabilistic cellular automata with local transition matrices: synchronization, ergodicity, and inference
Erhan Bayraktar, Fei Lu, Mauro Maggioni +2
We introduce a new class of probabilistic cellular automata that are capable of exhibiting rich dynamics such as synchronization and ergodicity and can be easily inferred from data…
Minimax Rates for Learning Pairwise Interactions in Attention-Style Models
Shai Zucker, Xiong Wang, Fei Lu +1
We study the convergence rate of learning pairwise interactions in single-layer attention-style models, where tokens interact through a weight matrix and a nonlinear activation fun…
MathOdyssey: Benchmarking Mathematical Problem-Solving Skills in Large Language Models Using Odyssey Math Data
Meng Fang, Xiangpeng Wan, Fei Lu +2
Large language models (LLMs) have significantly advanced natural language understanding and demonstrated strong problem-solving abilities. Despite these successes, most LLMs still…
The Formation and Characteristics of Acrylonitrile/Urea Inclusion Compound
Jun-Ting Zou, Yu-Song Wang, Wen-Min Pang +2
The formation process and composition of the acrylonitrile/urea inclusion compounds (AN/UIC) with different aging times and AN/urea molar feed ratios are studied by differential sc…
When Rough Data Helps: A Phase Transition in Convergence Rates for Kernel Recovery in Integral Operators
Jihong Wang, Fei Lu, Yue Yu
Learning kernels in operators from data is a fundamental task that arises in nonlocal continuum mechanics, operator learning, and interacting particle systems. A central question i…
Interacting Particle Systems on Networks: joint inference of the network and the interaction kernel
Quanjun Lang, Xiong Wang, Fei Lu +1
Modeling multi-agent systems on networks is a fundamental challenge in a wide variety of disciplines. Given data consisting of multiple trajectories, we jointly infer the (weighted…
Synthesis and spectroscopic characterization of completely isotactic polyacrylonitrile
Jun-Ting Zou, Yu-Song Wang, Wen-Min Pang +2
Completely isotactic polyacrylonitrile (i-PAN) has been synthesized successfully by an improved urea inclusion polymerization. The tacticity of prepared samples were confirmed by 1…
Feynman--Kac formula for the heat equation driven by fractional noise with Hurst parameter
Yaozhong Hu, Fei Lu, David Nualart
In this paper, a Feynman-Kac formula is established for stochastic partial differential equation driven by Gaussian noise which is, with respect to time, a fractional Brownian moti…
Learning Multi-type heterogeneous interacting particle systems
Quanjun Lang, Xiong Wang, Fei Lu +1
We propose a framework for the joint inference of network topology, multi-type interaction kernels, and latent type assignments in heterogeneous interacting particle systems from m…
An adaptive RKHS regularization for Fredholm integral equations
Fei Lu, Miao-Jung Yvonne Ou
Regularization is a long-standing challenge for ill-posed linear inverse problems, and a prototype is the Fredholm integral equation of the first kind with additive Gaussian measur…
On the identifiability of interaction functions in systems of interacting particles
Zhongyang Li, Fei Lu, Mauro Maggioni +2
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…
Learning interaction kernels in stochastic systems of interacting particles from multiple trajectories
Fei Lu, Mauro Maggioni, Sui Tang
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…
A discrete approach to stochastic parametrization and dimensional reduction in nonlinear dynamics
Alexandre J. Chorin, Fei Lu
Many physical systems are described by nonlinear differential equations that are too complicated to solve in full. A natural way to proceed is to divide the variables into those th…
Comparison of continuous and discrete-time data-based modeling for hypoelliptic systems
Fei Lu, Kevin K. Lin, Alexandre J. Chorin
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…