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Solving parametric partial differential equations (PDEs) and associated PDE-based, inverse problems is a central task in engineering and physics, yet existing neural operator methods struggle with high-dimensional, discontinuous inputs and…

Machine Learning · Computer Science 2025-07-03 Yaohua Zang , Phaedon-Stelios Koutsourelakis

Machine learning techniques have outperformed numerous rule-based methods for decision-making in autonomous vehicles. Despite recent efforts, lane changing remains a major challenge, due to the complex driving scenarios and changeable…

Robotics · Computer Science 2024-02-20 Kunpeng Xu , Lifei Chen , Shengrui Wang

The macroscopic traffic flow model is widely used for traffic control and management. To incorporate drivers' anticipative behaviors and to remove impractical speed discontinuity inherent in the classic Lighthill-Whitham-Richards (LWR)…

Machine Learning · Computer Science 2023-12-06 Chenguang Zhao , Huan Yu

Real-time traffic flow prediction can not only provide travelers with reliable traffic information so that it can save people's time, but also assist the traffic management agency to manage traffic system. It can greatly improve the…

Machine Learning · Statistics 2018-08-17 Zeren Tan , Ruimin Li

Neural Ordinary Differential Equations (NODEs) have proven to be a powerful modeling tool for approximating (interpolation) and forecasting (extrapolation) irregularly sampled time series data. However, their performance degrades…

Machine Learning · Computer Science 2020-04-29 Hammad A. Ayyubi , Yi Yao , Ajay Divakaran

Predicting traffic conditions has been recently explored as a way to relieve traffic congestion. Several pioneering approaches have been proposed based on traffic observations of the target location as well as its adjacent regions, but they…

Artificial Intelligence · Computer Science 2023-08-22 Xingyi Cheng , Ruiqing Zhang , Jie Zhou , Wei Xu

This paper deals with the tracking control problem for a very simple class of unknown nonlinear systems. In this paper, we presents a design strategy for tracking control of time-varying state constrained nonlinear systems in an adaptive…

Systems and Control · Electrical Eng. & Systems 2022-10-12 Pankaj Kumar Mishra , Nishchal K Verma

Neural Operators (NOs) provide a powerful framework for computations involving physical laws that can be modelled by (integro-) partial differential equations (PDEs), directly learning maps between infinite-dimensional function spaces that…

Machine Learning · Computer Science 2025-09-18 Gianluca Fabiani , Hannes Vandecasteele , Somdatta Goswami , Constantinos Siettos , Ioannis G. Kevrekidis

The modeling and control of single-phase flow systems governed by Partial Differential Equations (PDEs) present challenges, especially under transient conditions. In this work, we extend the Physics-Informed Neural Nets for Control (PINC)…

Machine Learning · Computer Science 2025-06-09 Luis Kin Miyatake , Eduardo Camponogara , Eric Aislan Antonelo , Alexey Pavlov

We present a convolutional framework which significantly reduces the complexity and thus, the computational effort for distributed reinforcement learning control of dynamical systems governed by partial differential equations (PDEs).…

Machine Learning · Computer Science 2023-12-27 Sebastian Peitz , Jan Stenner , Vikas Chidananda , Oliver Wallscheid , Steven L. Brunton , Kunihiko Taira

The neural Ordinary Differential Equation (ODE) model has shown success in learning complex continuous-time processes from observations on discrete time stamps. In this work, we consider the modeling and forecasting of time series data that…

Machine Learning · Statistics 2023-06-05 Yixuan Tan , Liyan Xie , Xiuyuan Cheng

Classical numerical methods solve partial differential equations (PDEs) efficiently on regular meshes, but many of them become unstable on irregular domains. In practice, multiphysics interactions such as diffusion, damage, and healing…

Machine Learning · Computer Science 2025-12-16 Yuelian Li , Andrew Rushing Hands

This study introduces a novel control framework for adaptive cruise control (ACC) in automated driving, leveraging Long Short-Term Memory (LSTM) networks and physics-informed constraints. As automated vehicles (AVs) adopt advanced features…

Robotics · Computer Science 2025-10-28 Yuhui Liu , Samannita Halder , Shian Wang , Tianyi Li

Predicting outcomes and planning interactions with the physical world are long-standing goals for machine learning. A variety of such tasks involves continuous physical systems, which can be described by partial differential equations…

Machine Learning · Computer Science 2020-01-22 Philipp Holl , Vladlen Koltun , Nils Thuerey

This work presents a new sufficient condition for synthesizing nonlinear controllers that yield bounded closed-loop tracking error transients despite the presence of unmatched uncertainties that are concurrently being learned online. The…

Systems and Control · Electrical Eng. & Systems 2023-10-23 Samuel G. Gessow , Brett T. Lopez

Adaptive control is subject to stability and performance issues when a learned model is used to enhance its performance. This paper thus presents a deep learning-based adaptive control framework for nonlinear systems with…

Machine Learning · Computer Science 2021-10-05 Hiroyasu Tsukamoto , Soon-Jo Chung , Jean-Jacques Slotine

Route alignment design in surveying and transportation engineering frequently involves fixed waypoint constraints, where a path must precisely traverse specific coordinates. While existing literature primarily relies on geometric…

Methodology · Statistics 2026-01-06 Shiyin Du , Yiting Chen , Wenzhi Yang , Qiong Li , Xiaoping Shi

Randomized neural network (RaNN) methods have been proposed for solving various partial differential equations (PDEs), demonstrating high accuracy and efficiency. However, initializing the fixed parameters remains challenging. Additionally,…

Numerical Analysis · Mathematics 2025-11-25 Haoning Dang , Fei Wang , Song Jiang

Deep learning has been proposed as an efficient alternative for the numerical approximation of PDE solutions, offering fast, iterative simulation of PDEs through the approximation of solution operators. However, deep learning solutions have…

Machine Learning · Computer Science 2026-02-02 Sean Current , Chandan Kumar , Datta Gaitonde , Srinivasan Parthasarathy

Autonomous driving depends on perception systems to understand the environment and to inform downstream decision-making. While advanced perception systems utilizing black-box Deep Neural Networks (DNNs) demonstrate human-like comprehension,…

Artificial Intelligence · Computer Science 2024-03-26 Xiao Li , H. Eric Tseng , Anouck Girard , Ilya Kolmanovsky