About

Na Li is the Winokur Family Professor of Electrical Engineering and Applied Mathematics at Harvard John A. Paulson School of Engineering and Applied Sciences. She serves as the Area Chair for Electrical Engineering and is involved in teaching within this primary area. Her research spans multiple disciplines including control theory and stochastic systems, economics and computation, artificial intelligence, and science and engineering for ClimateTech. She has been recognized for her contributions to control, learning, and optimization, receiving awards such as the Ruberti Young Researcher Prize from IEEE and being elected an IEEE Fellow. Her work focuses on developing advanced control and learning algorithms, with applications across scientific disciplines and interface with instruments and robotics.

Research topics

• Computer Science
• Mathematics
• Mathematical optimization
• Artificial Intelligence
• Engineering
• Distributed computing

Selected publications

• Numerical Assessment of Interference Caused by Commissioning New Wells in the Shale Gas Gathering System

  Energies · 2026-05-13

  articleOpen access1st authorCorresponding

  During the development of multiple wells of shale gas, coproduction under varying pressures induces interference. High-pressure wells impose backpressure on low-pressure wells, thereby restricting overall reservoir productivity. Accurate interference characterization is critical for efficient development. This study examines 42 gathering platforms within the Changning 201 Block. A three-tier surface gathering network hydraulic model (‘Platform-Gathering Station-Central Station’) was established. The model calculates key node pressures in the pipeline system following the integration of new wells. Unlike conventional interference studies that primarily focus on the reservoir scale and overlook the critical role of the surface gathering pipeline network as a propagation pathway for interference, this paper, for the first time, extends interference analysis from the “reservoir–wellbore” system to the full surface pressure system encompassing “wellhead-platform-gas gathering station-central station”. A transferable three-stage engineering decision-making workflow of “diagnosis-comparison-coordination” is proposed. This evaluates the extent to which the production of new wells at different development stages interferes with the pressure and productivity of existing gas wells, and enables a quantitative assessment of the influence of pressure-boosting technology on well deliverability and auxiliary measures. This research confirms that the model presents calculation errors of less than 3%. The commissioning of seven new wells with a combined capacity of 531,000 m3/d resulted in a total output increase of 626,900 m3/d at the central processing station; Platform CN-30 gas well deliverability decreased by 20.7%; the implementation of appropriate pressure-boosting technology was effective, enabling an average deliverability increase of 1.27 × 104 m3/d per well, releasing the potential deliverability of the well.

  PublisherDOI

• Neural Process-Based Reactive Controller for Autonomous Racing

  ArXiv.org · 2026-01-17

  articleOpen accessSenior author

  Attention-based neural architectures have become central to state-of-the-art methods in real-time nonlinear control. As these data-driven models continue to be integrated into increasingly safety-critical domains, ensuring statistically grounded and provably safe decision-making becomes essential. This paper introduces a novel reactive control framework for gap-based navigation using the Attentive Neural Process (AttNP) and a physics-informed extension, the PI-AttNP. Both models are evaluated in a simulated F1TENTH-style Ackermann steering racecar environment, chosen as a fast-paced proxy for safety-critical autonomous driving scenarios. The PI-AttNP augments the AttNP architecture with approximate model-based priors to inject physical inductive bias, enabling faster convergence and improved prediction accuracy suited for real-time control. To further ensure safety, we derive and implement a control barrier function (CBF)-based filtering mechanism that analytically enforces collision avoidance constraints. This CBF formulation is fully compatible with the learned AttNP controller and generalizes across a wide range of racing scenarios, providing a lightweight and certifiable safety layer. Our results demonstrate competitive closed-loop performance while ensuring real-time constraint satisfaction.

  PublisherOA PDF

• Neural Process-Based Reactive Controller for Autonomous Racing

  arXiv (Cornell University) · 2026-01-17

  preprintOpen accessSenior author

  Attention-based neural architectures have become central to state-of-the-art methods in real-time nonlinear control. As these data-driven models continue to be integrated into increasingly safety-critical domains, ensuring statistically grounded and provably safe decision-making becomes essential. This paper introduces a novel reactive control framework for gap-based navigation using the Attentive Neural Process (AttNP) and a physics-informed extension, the PI-AttNP. Both models are evaluated in a simulated F1TENTH-style Ackermann steering racecar environment, chosen as a fast-paced proxy for safety-critical autonomous driving scenarios. The PI-AttNP augments the AttNP architecture with approximate model-based priors to inject physical inductive bias, enabling faster convergence and improved prediction accuracy suited for real-time control. To further ensure safety, we derive and implement a control barrier function (CBF)-based filtering mechanism that analytically enforces collision avoidance constraints. This CBF formulation is fully compatible with the learned AttNP controller and generalizes across a wide range of racing scenarios, providing a lightweight and certifiable safety layer. Our results demonstrate competitive closed-loop performance while ensuring real-time constraint satisfaction.

  PublisherDOI

• Medical irregular multivariate time series forecasting based on multi-scale temporal-frequency domain patch fusion and dynamic graph

  Frontiers in Physiology · 2026-04-15

  articleOpen access

  Introduction: Accurate forecasting of medical irregular multivariate time series is an important prerequisite for downstream monitoring and decision-support research. However, this task remains challenging because physiological data are typically characterized by irregular sampling, missing values, and complex temporal and inter-variable dependencies. Methods: To address these challenges, we propose a novel method termed Multi-scale Temporal-Frequency domain fusion Patching and Dynamic Graph modeling (MTFP-DG). The method first transforms irregular time series into multi-scale patches with unified temporal resolution, enabling temporal alignment without interpolation and thereby handling irregularity and asynchrony. It then employs a dual-domain encoding mechanism that fuses temporal features extracted by a Transformable Time-aware Convolution Network with frequency features extracted by an Irregular Fourier Analysis Network to obtain rich patch representations. Based on these representations and Fourier coefficients, dynamic graphs are further constructed to capture evolving inter-variable correlations. Results: Extensive experiments on five real-world medical datasets demonstrate that MTFP-DG outperforms state-of-the-art baselines on retrospective irregular multivariate time series forecasting benchmarks. Discussion: These findings indicate that integrating multi-scale patching with dynamic graph modeling is effective for capturing complex temporal dependencies and inter-series relationships in medical irregular multivariate time series. MTFP-DG may provide a robust methodological tool for proactive healthcare planning, although its clinical utility still requires further prospective validation.

  PublisherOA PDFDOI

• Energy Efficiency in 6G Native AI Networks: Task Schedule based on NOMA Transmission

  2025-10-19

  article

  Toward the sixth generation (6G) Internet of vehicles (IoV) networks, key challenges such as massive connectivity, high mobility and superior energy efficiency have driven the development of advanced wireless technologies. Native artificial intelligence (AI) is expected to support diverse vertical industries and offer numerous emerging AI services for 6G. However, how to efficiently process AI services and improve resource utilization while ensuring quality of service is still a challenging problem. In this paper, non-orthogonal multiple access (NOMA) is applied in the designed three-layer IoV network architecture. Then, an energy efficiency maximization problem is formulated by jointly optimizing NOMA transmission power and AI task deployment decisions. Third, a two-level iterative algorithm is proposed using the Dinkelbac’s method. Simulation results verify that our proposed algorithm outperforms benchmarks in terms of energy efficiency.

  PublisherDOI

• Optimizing radiant floor heating control with night setbacks using model-free reinforcement learning and transfer learning

  Building and Environment · 2025-09-27

  articleSenior author
  PublisherDOI

• AVERAGING ESTIMATORS OF HETEROGENEOUS TREATMENT EFFECTS UNDER ADDITIVE MODELS

  Econometric Theory · 2025-10-22 · 1 citations

  article1st author

  We consider spline-based additive models for estimation of conditional treatment effects. To handle the uncertainty due to variable selection, we propose a method of model averaging with weights obtained by minimizing a J -fold cross-validation criterion, in which a nearest neighbor matching is used to approximate the unobserved potential outcomes. We show that the proposed method is asymptotically optimal in the sense of achieving the lowest possible squared loss in some settings and assigning all weight to the correctly specified models if such models exist in the candidate set. Moreover, consistency properties of the optimal weights and model averaging estimators are established. A simulation study and an empirical example demonstrate the superiority of the proposed estimator over other methods.

  PublisherDOI

• Predictive framework for cervical cancer brachytherapy fractionation mode integrating generative model and dynamic feature aggregation GNNs

  BMC Medical Informatics and Decision Making · 2025-12-01 · 1 citations

  articleOpen access

  Cervical cancer is among the top four most prevalent cancers in women globally. Its treatment strategy necessitates a combination of external beam radiation therapy (EBRT) and brachytherapy, demanding precise treatment decisions from doctors. However, current clinical guidelines often provide only principled implementation standards, leaving significant freedom in clinical treatment operations. This study aims to develop a predictive framework to assist in determining cervical cancer brachytherapy fractionation modes. In response to the intricate dynamics between patient characteristics and inter-patient relationships, we introduce a novel approach: the dynamic feature aggregation graph neural network (DyFAGNN). This model incorporates a phase-aware module to capture nuanced connections between patient characteristics and leverages graph neural network technology to illustrate interactions among patients. We collected data from 1271 real clinical patients and employed a GPT-2 based generative model to simulate clinically realistic treatment data to overcome data scarcity. Employing the generated datasets, we conducted comparative analyses across eight models. The results demonstrated that the DyFAGNN model, when trained on synthetic data balanced with the ADASYN technique, achieved the highest performance, with an accuracy of 82.55%, macro-precision of 82.91%, macro-recall of 82.59%, and macro-F1 score of 82.68%. The proposed framework, integrating a generative model with DyFAGNN, provides a robust and accurate method for predicting cervical cancer brachytherapy fractionation modes. This approach can serve as a valuable tool to support clinical decision-making and personalize treatment strategies. The study was conducted following the Declaration of Helsinki and was approved by the Ethics Committee of The First Hospital of China Medical University. As it was a retrospective study with anonymized data, informed consent was waived.

  PublisherDOI

• Optimism as Risk-Seeking in Multi-Agent Reinforcement Learning

  IEEE Control Systems Letters · 2025-12-17

  article

  Risk sensitivity has become a central theme in reinforcement learning (RL), where convex risk measures and robust formulations provide principled ways to model preferences beyond expected return. Recent extensions to multi-agent RL (MARL) have largely emphasized the risk-averse setting, prioritizing robustness to uncertainty. In cooperative MARL, however, such conservatism often leads to suboptimal equilibria, and a parallel line of work has shown that optimism can promote cooperation. Existing optimistic methods, though effective in practice, are typically heuristic and lack theoretical grounding. Building on the dual representation for convex risk measures, we propose a principled framework that interprets risk-seeking objectives as optimism. We introduce optimistic value functions, which formalize optimism as divergence-penalized risk-seeking evaluations. Building on this foundation, we derive a policy-gradient theorem for optimistic value functions, including explicit formulas for the entropic risk/KL-penalty setting, and develop decentralized optimistic actor-critic algorithms that implement these updates. Empirical results on cooperative benchmarks demonstrate that risk-seeking optimism consistently improves coordination over both risk-neutral baselines and heuristic optimistic methods. Our framework thus unifies risk-sensitive learning and optimism, offering a theoretically grounded and practically effective approach to cooperation in MARL.

  PublisherDOI

• Research on spatial layered representation technology of railway GIS based on vector tiles

  2025-12-05

  article1st authorCorresponding

  The spatial data of railway GIS is mostly grid tiles on the web end of geographic information systems, and vector tile technology has not been well applied in the railway GIS industry. This article focuses on the current issues of low utilization, weak interactivity, and lack of universality in layer levels and expression effects of railway GIS spatial vector data on the web end of the railway system. A new data visualization application model based on vector tile technology and railway GIS spatial layered expression technology is studied, and the application scenarios and effectiveness of railway GIS spatial layered expression technology are explored. The results show that the construction of railway GIS spatial maps under the new model greatly improves development efficiency, utilization of vector data, and standardization level of feature expression. The research results provide a reference basis for a more effective spatial hierarchical expression mode of railway GIS and provide new ideas for the efficient application of railway GIS maps.

  PublisherDOI

Recent grants

• CAREER: Optimization, Control, and Incentive Design for Power Networks with High Levels of Distributed Energy Resources

  NSF · $500k · 2016–2022

• Collaborative Research: MLWiNS: Distributed Learning over Multi-Access Channels: From Bandlimited Coordinate Descent to Gradient Sketching

  NSF · $200k · 2020–2024

• EAGER: Real-Time: Learning, Selection, and Control in Residential Demand Response for Grid Reliability

  NSF · $284k · 2018–2021

• Collaborative Research: Towards Communication-Cognizant Voltage Regulation and Energy Management for Power Distribution Systems

  NSF · $221k · 2016–2019

Frequent coauthors

• Guannan Qu

  39 shared

• M. Vidyasagar

  Indian Institute of Technology Hyderabad

  36 shared

• Ankur A. Kulkarni

  Indian Institute of Technology Bombay

  36 shared

• Atreyee Kundu

  36 shared

• V. Chellaboina

  GITAM University

  36 shared

• Sindri Magnússon

  Stockholm University

  27 shared

• Runyu Zhang

  Beijing University of Technology

  23 shared

• Steven H. Low

  22 shared

Labs

• Na Li LabPI

Education

• PhD, Control and Dynamical Systems

  California Institute of Technology

  2013

Awards & honors

• IEEE Fellow (2025)
• Ruberti Young Researcher Prize awarded by IEEE Applied Mathe…