About

Jianfeng Lu is an applied mathematician with a focus on mathematical analysis and algorithm development for problems originating from computational physics, theoretical chemistry, materials science, machine learning, and related fields. His current research includes high dimensional partial differential equations (PDEs), generative models and sampling methods, control and reinforcement learning, electronic structure and many-body problems, quantum molecular dynamics, and multiscale modeling and analysis. He holds the position of James B. Duke Distinguished Professor of Mathematics at Duke University and has been actively involved in teaching and research since at least 2020. His academic appointments also include professorships in chemistry and physics at Trinity College of Arts & Sciences. His work is recognized through various grants, including those from the National Science Foundation, and he has contributed to advancing computational methods and theoretical understanding in his areas of expertise.

Research topics

• Electrical engineering
• Engineering
• Optoelectronics
• Composite material
• Materials science
• Nanotechnology
• Chemical engineering
• Business
• Engineering physics

Selected publications

• Gastric retraction time as a metric for comparing suspension techniques in laparoscopic pancreatic resection:a retrospective cohort study

  Research Square · 2026-01-12

  preprintOpen access
  PublisherOA PDFDOI

• A Randomized Method for Simulating Lindblad Equations and Thermal State Preparation

  Quantum · 2025-11-20

  preprintOpen access

  We study a qDRIFT-type randomized method to simulate Lindblad dynamics by decomposing its generator into an ensemble of Lindbladians, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">L</mml:mi> </mml:mrow> <mml:mo>=</mml:mo> <mml:munder> <mml:mo>&amp;#x2211;</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>a</mml:mi> <mml:mo>&amp;#x2208;</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">A</mml:mi> </mml:mrow> </mml:mrow> </mml:munder> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">L</mml:mi> </mml:mrow> <mml:mi>a</mml:mi> </mml:msub> </mml:math> , where each <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">L</mml:mi> </mml:mrow> <mml:mi>a</mml:mi> </mml:msub> </mml:math> comprises a simple Hamiltonian and a single jump operator. Assuming an efficient quantum simulation is available for the Lindblad evolution <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>e</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>t</mml:mi> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">L</mml:mi> </mml:mrow> <mml:mi>a</mml:mi> </mml:msub> </mml:mrow> </mml:msup> </mml:math> , we implement <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>e</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>t</mml:mi> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">L</mml:mi> </mml:mrow> <mml:mi>a</mml:mi> </mml:msub> </mml:mrow> </mml:msup> </mml:math> for a randomly sampled <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">L</mml:mi> </mml:mrow> <mml:mi>a</mml:mi> </mml:msub> </mml:math> at each time step according to a probability distribution <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>&amp;#x03BC;</mml:mi> </mml:math> over the ensemble <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo fence="false" stretchy="false">{</mml:mo> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">L</mml:mi> </mml:mrow> <mml:mi>a</mml:mi> </mml:msub> <mml:msub> <mml:mo fence="false" stretchy="false">}</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>a</mml:mi> <mml:mo>&amp;#x2208;</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">A</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> </mml:math> . This randomized strategy reduces the quantum cost of simulating Lindblad dynamics, particularly in quantum many-body systems with a large or even infinite number of jump operators.Our contributions are two-fold. First, we provide a detailed convergence analysis of the proposed randomized method, covering both average and typical algorithmic realizations. This analysis extends the known results for the random product formula from closed systems to open systems, ensuring rigorous performance guarantees. Second, based on the random product approximation, we derive a new quantum Gibbs sampler algorithm that utilizes jump operators sampled from a Clifford-random circuit. This generator (i) can be efficiently implemented using our randomized algorithm, and (ii) exhibits a spectral gap lower bound that depends on the spectrum of the Hamiltonian. Our results present a new instance of a class of Hamiltonians for which the thermal states can be efficiently prepared using a quantum Gibbs sampling algorithm.

  PublisherOA PDFDOI

• Convergence of Stochastic Gradient Descent under a Local Łojasiewicz Condition for Deep Neural Networks

  Journal of Machine Learning · 2025-03-11 · 1 citations

  articleOpen accessSenior author

  We study the convergence of stochastic gradient descent (SGD) for non-convex objective functions. We establish the local convergence with positive probability under the local Łojasiewicz condition introduced by Chatterjee [arXiv:2203.16462, 2022] and an additional local structural assumption of the loss function landscape. A key component of our proof is to ensure that the whole trajectories of SGD stay inside the local region with a positive probability. We also provide examples of neural networks with finite widths such that our assumptions hold.

  PublisherOA PDFDOI

• Mean square error analysis of stochastic gradient and variance-reduced sampling algorithms

  ArXiv.org · 2025-11-06

  preprintOpen access1st authorCorresponding

  This paper considers mean square error (MSE) analysis for stochastic gradient sampling algorithms applied to underdamped Langevin dynamics under a global convexity assumption. A novel discrete Poisson equation framework is developed to bound the time-averaged sampling error. For the Stochastic Gradient UBU (SG-UBU) sampler, we derive an explicit MSE bound and establish that the numerical bias exhibits first-order convergence with respect to the step size $h$, with the leading error coefficient proportional to the variance of the stochastic gradient. The analysis is further extended to variance-reduced algorithms for finite-sum potentials, specifically the SVRG-UBU and SAGA-UBU methods. For these algorithms, we identify a phase transition phenomenon whereby the convergence rate of the numerical bias shifts from first to second order as the step size decreases below a critical threshold. Theoretical findings are validated by numerical experiments. In addition, the analysis provides a practical empirical criterion for selecting between the mini-batch SG-UBU and SVRG-UBU samplers to achieve optimal computational efficiency.

  PublisherOA PDFDOI

• Effect of carbonate impurity on thermophysical properties and structure of chloride molten salt

  Solar Energy Materials and Solar Cells · 2025-09-08 · 1 citations

  articleCorresponding
  PublisherDOI

• Asymptotic Analysis for Bloch Electrons with Weyl Nodes

  Multiscale Modeling and Simulation · 2025-06-18

  article1st authorCorresponding
  PublisherDOI

• Mixing Time of Open Quantum Systems via Hypocoercivity

  Physical Review Letters · 2025-04-11 · 5 citations

  articleOpen access

  Understanding the mixing of open quantum systems is a fundamental problem in physics and quantum information science. Existing approaches for estimating the mixing time often rely on the spectral gap estimation of the Lindbladian generator, which can be challenging to obtain in practice. We propose a novel theoretical framework to estimate the mixing time of open quantum systems that treats the Hamiltonian and dissipative part separately, thus circumventing the need for a priori estimation of the spectral gap of the full Lindbladian generator. This framework yields mixing time estimates for a class of quantum systems that are otherwise hard to analyze, even though it does not apply to arbitrary Lindbladians. The technique is based on the construction of an energy functional inspired by the hypocoercivity of (classical) kinetic theory.

  PublisherOA PDFDOI

• A Policy Gradient Framework for Stochastic Optimal Control Problems with Global Convergence Guarantee

  SIAM Journal on Control and Optimization · 2025-07-28 · 1 citations

  articleSenior author
  PublisherDOI

• Bi-Lipschitz Ansatz for Anti-Symmetric Functions

  ArXiv.org · 2025-03-06

  preprintOpen access

  Motivated by applications for simulating quantum many body functions, we propose a new universal ansatz for approximating anti-symmetric functions. The main advantage of this ansatz over previous alternatives is that it is bi-Lipschitz with respect to a naturally defined metric. As a result, we are able to obtain quantitative approximation results for approximation of Lipschitz continuous antisymmetric functions. Moreover, we provide preliminary experimental evidence to the improved performance of this ansatz for learning antisymmetric functions.

  PublisherOA PDFDOI

• Text as Any-Modality for Zero-Shot Classification by Consistent Prompt Tuning

  ArXiv.org · 2025-08-08

  preprintOpen accessSenior author

  The integration of prompt tuning with multimodal learning has shown significant generalization abilities for various downstream tasks. Despite advancements, existing methods heavily depend on massive modality-specific labeled data (e.g., video, audio, and image), or are customized for a single modality. In this study, we present Text as Any-Modality by Consistent Prompt Tuning (TaAM-CPT), a scalable approach for constructing a general representation model toward unlimited modalities using solely text data. TaAM-CPT comprises modality prompt pools, text construction, and modality-aligned text encoders from pre-trained models, which allows for extending new modalities by simply adding prompt pools and modality-aligned text encoders. To harmonize the learning across different modalities, TaAM-CPT designs intra- and inter-modal learning objectives, which can capture category details within modalities while maintaining semantic consistency across different modalities. Benefiting from its scalable architecture and pre-trained models, TaAM-CPT can be seamlessly extended to accommodate unlimited modalities. Remarkably, without any modality-specific labeled data, TaAM-CPT achieves leading results on diverse datasets spanning various modalities, including video classification, image classification, and audio classification. The code is available at https://github.com/Jinx630/TaAM-CPT.

  PublisherOA PDFDOI

Recent grants

• Mathematical Problems for Electronic Structure Models

  NSF · $168k · 2013–2016

• CAREER: Research and training in advanced computational methods for quantum and statistical mechanics

  NSF · $420k · 2015–2020

• Innovative Numerical Methods for High-Dimensional Applications

  NSF · $293k · 2020–2024

• EAGER: QAC-QSA: Resource Reduction in Quantum Computational Chemistry Mapping by Optimizing Orbital Basis Sets

  NSF · $300k · 2020–2023

• Innovation of Numerical Methods for High-Dimensional Partial Differential Equations

  NSF · $400k · 2023–2027

Frequent coauthors

• E Weinan

  44 shared

• Lin Lin

  Lawrence Berkeley National Laboratory

  36 shared

• Jing Ding

  Sun Yat-sen University

  35 shared

• Lexing Ying

  34 shared

• Qin Li

  Weifang Chinese Medicine Hospital

  29 shared

• Yulong Lu

  25 shared

• Yingzhou Li

  Fudan University

  24 shared

• Stefan Steinerberger

  University of Washington

  22 shared

Labs

• Jianfeng Lu's GroupPI

  Not provided

Education

• PhD

  Princeton University

  2009

Awards & honors

• James B. Duke Distinguished Professor of Mathematics (2024 -…