10 papers
Optimal nodal control and the exponential turnpike property for the flow in gas networks
Martin Gugat, Michael Herty, Michael Schuster +1
We study an optimal boundary control problem for a quasilinear hyperbolic system describing isothermal gas flow in pipelines. The control acts at network nodes and models the actio…
Computation of entanglement for quantum states by a Consensus-Based Optimization method
Michael Herty, Yijia Tang, Yizhou Zhou
The computation of quantum entanglement can be formulated as a high-dimensional nonconvex optimization problem with orthogonality constraints. In this work, we propose structure-pr…
Interface layers and coupling conditions for discrete kinetic models on networks: a spectral approac
Raul Borsche, Tobias Damm, Axel Klar +1
We consider kinetic and related macroscopic equations on networks. A class of linear kinetic BGK models is considered, where the limit equation for small Knudsen numbers is given b…
Turnpike property for hierarchical optimal control problems: from particle systems to hydrodynamic equations
Michael Herty, Yizhou Zhou
This work is concerned with a hierarchical framework of optimal control problems connecting interacting particle systems, the mean field limit equations, and associated hydrodynami…
On the Generalization of SFT: A Reinforcement Learning Perspective with Reward Rectification
Yongliang Wu, Yizhou Zhou, Zhou Ziheng +7
In this work, we present a simple yet theoretically motivated improvement to Supervised Fine-Tuning (SFT) for the Large Language Model (LLM), addressing its limited generalization…
Asymptotic-preserving schemes for the initial-boundary value problem of hyperbolic relaxation systems
Yizhou Zhou
In this work, we present a numerical method for the initial-boundary value problem (IBVP) of first-order hyperbolic systems with source terms. The scheme directly solves the relaxa…
Slide2Text: Leveraging LLMs for Personalized Textbook Generation from PowerPoint Presentations
Yizhou Zhou
The rapid advancements in Large Language Models (LLMs) have revolutionized educational technology, enabling innovative approaches to automated and personalized content creation. Th…
Solving Random Hyperbolic Conservation Laws Using Linear Programming
Shaoshuai Chu, Michael Herty, Maria Lukacova-Medvidova +1
A novel structure-preserving numerical method to solve random hyperbolic systems of conservation laws is presented. The method uses a concept of generalized, measure-valued solutio…
A numerical method for solving the generalized tangent vector of hyperbolic systems
Michael Herty, Yizhou Zhou
This work is concerned with the computation of the first-order variation for one-dimensional hyperbolic partial differential equations. In the case of shock waves the main challeng…
Exponential turnpike property for particle systems and mean-field limit
Michael Herty, Yizhou Zhou
This work is concerned with the exponential turnpike property for optimal control problems of particle systems and their mean-field limit. Under the assumption of the strict dissip…