arXiv subjects

Xiyu Deng

Publications and source records attributed to Xiyu Deng.

6 recordsLinked to original sources

arXiv2026

OpInf-LLM: Parametric PDE Solving with LLMs via Operator Inference

Solving diverse partial differential equations (PDEs) is fundamental in science and engineering. Large language models (LLMs) have demonstrated strong capabilities in code generation, symbolic reasoning, and tool use, but reliably solving PDEs across heterogeneous settings remains challenging. Prior work on LLM-based code generation and transformer-based foundation models for PDE learning has shown promising advances. However, a persistent trade-off between execution success rate and numerical accuracy arises, particularly when generalization to unseen parameters and boundary conditions is required. In this work, we propose OpInf-LLM, an LLM parametric PDE solving framework via operator inference. The proposed framework leverages small amounts of solution data to enable accurate prediction of diverse PDE instances, including unseen parameters and configurations, and provides seamless integration with LLMs for natural language task specification and physics-based reasoning of proper feature parameterization. Its low computational demands and unified solution pipeline further enable a high execution success rate across heterogeneous settings, opening new possibilities for generalizable reduced-order modeling in LLM-based PDE solving.

cs.LG↗

arXiv2026

UAVGENT: A Language-Guided Distributed Control Framework

We study language-in-the-loop control for multi-drone systems that execute evolving, high-level missions while retaining formal robustness guarantees at the physical layer. We propose a three-layer architecture in which (i) a human operator issues natural-language instructions, (ii) an LLM-based supervisor periodically interprets, verifies, and corrects the commanded task in the context of the latest state and target estimates, and (iii) a distributed inner-loop controller tracks the resulting reference using only local relative information. We derive a theoretical guarantee that characterizes tracking performance under bounded disturbances and piecewise-smooth references with discrete jumps induced by LLM updates. Overall, our results illustrate how centralized language-based task reasoning can be combined with distributed feedback control to achieve complex behaviors with provable robustness and stability.

cs.RO↗

arXiv2025

Online Adaptive Probabilistic Safety Certificate with Language Guidance

Achieving long-term safety in uncertain/extreme environments while accounting for human preferences remains a fundamental challenge for autonomous systems. Existing methods often trade off long-term guarantees for fast real-time control and cannot adapt to variability in human preferences or risk tolerance. To address these limitations, we propose a language-guided adaptive probabilistic safety certificate (PSC) framework that guarantees long-term safety for stochastic systems under environmental uncertainty while accommodating diverse human preferences. The proposed framework integrates natural-language inputs from users and Bayesian estimators of the environment into adaptive safety certificates that explicitly account for user preferences, system dynamics, and quantified uncertainties. Our key technical innovation leverages probabilistic invariance--a generalization of forward invariance to a probability space--to obtain myopic safety conditions with long-term safety guarantees. We validate the framework through numerical simulations of autonomous lane-keeping with human-in-the-loop guidance under uncertain and extreme road conditions, demonstrating enhanced safety-performance trade-offs, adaptability to changing environments, and personalization to different user preferences. Code is available at https://github.com/hoshino06/adaptive_lane_keeping.

eess.SY↗

arXiv2024

Physics-Informed Representation and Learning: Control and Risk Quantification

Optimal and safety-critical control are fundamental problems for stochastic systems, and are widely considered in real-world scenarios such as robotic manipulation and autonomous driving. In this paper, we consider the problem of efficiently finding optimal and safe control for high-dimensional systems. Specifically, we propose to use dimensionality reduction techniques from a comparison theorem for stochastic differential equations together with a generalizable physics-informed neural network to estimate the optimal value function and the safety probability of the system. The proposed framework results in substantial sample efficiency improvement compared to existing methods. We further develop an autoencoder-like neural network to automatically identify the low-dimensional features of the system to enhance the ease of design for system integration. We also provide experiments and quantitative analysis to validate the efficacy of the proposed method. Source code is available at https://github.com/jacobwang925/path-integral-PINN.

eess.SY↗

arXiv2024

Context-aware LLM-based Safe Control Against Latent Risks

Autonomous control systems face significant challenges in performing complex tasks in the presence of latent risks. To address this, we propose an integrated framework that combines Large Language Models (LLMs), numerical optimization, and optimization-based control to facilitate efficient subtask learning while ensuring safety against latent risks. The framework decomposes complex tasks into a sequence of context-aware subtasks that account for latent risks. These subtasks and their parameters are then refined through a multi-time-scale process: high-layer multi-turn in-context learning, mid-layer LLM Chain-of-Thought reasoning and numerical optimization, and low-layer model predictive control. The framework iteratively improves decisions by leveraging qualitative feedback and optimized trajectory data from lower-layer optimization processes and a physics simulator. We validate the proposed framework through simulated case studies involving robot arm and autonomous vehicle scenarios. The experiments demonstrate that the proposed framework can mediate actions based on the context and latent risks and learn complex behaviors efficiently.

eess.SY↗

arXiv2022

A Learning and Control Perspective for Microfinance

Microfinance, despite its significant potential for poverty reduction, is facing sustainability hardships due to high default rates. Although many methods in regular finance can estimate credit scores and default probabilities, these methods are not directly applicable to microfinance due to the following unique characteristics: a) under-explored (developing) areas such as rural Africa do not have sufficient prior loan data for microfinance institutions (MFIs) to establish a credit scoring system; b) microfinance applicants may have difficulty providing sufficient information for MFIs to accurately predict default probabilities; and c) many MFIs use group liability (instead of collateral) to secure repayment. Here, we present a novel control-theoretic model of microfinance that accounts for these characteristics. We construct an algorithm to learn microfinance decision policies that achieve financial inclusion, fairness, social welfare, and sustainability. We characterize the convergence conditions to Pareto-optimum and the convergence speeds. We demonstrate, in numerous real and synthetic datasets, that the proposed method accounts for the complexities induced by group liability to produce robust decisions before sufficient loans are given to establish credit scoring systems and for applicants whose default probability cannot be accurately estimated due to missing information. To the best of our knowledge, this paper is the first to connect microfinance and control theory. We envision that the connection will enable safe learning and control techniques to help modernize microfinance and alleviate poverty.

q-fin.GN↗