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Partial differential equations (PDEs) govern a wide range of physical systems, but solving them efficiently remains a major challenge. The idea of a scientific foundation model (SciFM) is emerging as a promising tool for learning…

Machine Learning · Computer Science 2025-03-26 Amin Totounferoush , Serge Kotchourko , Michael W. Mahoney , Steffen Staab

Robots deployed in unstructured, real-world environments operate under considerable uncertainty due to imperfect state estimates, model error, and disturbances. Given this real-world context, the goal of this paper is to develop controllers…

Systems and Control · Electrical Eng. & Systems 2023-02-27 Ryan K. Cosner , Preston Culbertson , Andrew J. Taylor , Aaron D. Ames

This paper presents a comprehensive approach for the safety-critical control of robotic manipulators operating in dynamic environments. Building upon the framework of Control Barrier Functions (CBFs), we extend the collision cone…

Robotics · Computer Science 2025-03-04 Lucas Almeida

Foundation models for partial differential equations (PDEs) have emerged as powerful surrogates pre-trained on diverse physical systems, but adapting them to new downstream tasks remains challenging due to limited task-specific data and…

Machine Learning · Computer Science 2026-03-17 Vlad Medvedev , Leon Armbruster , Christopher Straub , Georg Kruse , Andreas Rosskopf

Neural ordinary differential equations are an attractive option for modelling temporal dynamics. However, a fundamental issue is that the solution to an ordinary differential equation is determined by its initial condition, and there is no…

Machine Learning · Computer Science 2020-11-06 Patrick Kidger , James Morrill , James Foster , Terry Lyons

In this paper, the safety-critical control problem for uncertain systems under multiple control barrier function (CBF) constraints and input constraints is investigated. A novel framework is proposed to generate a safety filter that…

Systems and Control · Electrical Eng. & Systems 2025-03-21 Jinyang Dong , Shizhen Wu , Rui Liu , Xiao Liang , Biao Lu , Yongchun Fang

Modern autonomous systems, such as flying, legged, and wheeled robots, are generally characterized by high-dimensional nonlinear dynamics, which presents challenges for model-based safety-critical control design. Motivated by the success of…

Systems and Control · Electrical Eng. & Systems 2024-09-21 Max H. Cohen , Tamas G. Molnar , Aaron D. Ames

Accurate modeling of boundary conditions is crucial in computational physics. The ever increasing use of neural networks as surrogates for physics-related problems calls for an improved understanding of boundary condition treatment, and its…

Machine Learning · Computer Science 2021-07-06 Antonio Alguacil , Wagner Gonçalves Pinto , Michael Bauerheim , Marc C. Jacob , Stéphane Moreau

Safety critical control of robotic manipulation tasks involving deformable media such as fluids, cloth, and soft objects remains challenging because existing learning based approaches encode safety indirectly through reward shaping, which…

Robotics · Computer Science 2026-05-05 Jiaxing Li , Hanjiang Hu , Zhuoyuan Wang , Yorie Nakahira , Changliu Liu

The combination of machine learning and physical laws has shown immense potential for solving scientific problems driven by partial differential equations (PDEs) with the promise of fast inference, zero-shot generalisation, and the ability…

Machine Learning · Computer Science 2024-09-11 Nacime Bouziani , David A. Ham , Ado Farsi

Guaranteeing the safety of controllers is vital for real-world applications, but is markedly difficult when the states are not perfectly known and when the control inputs are bounded. Backup control barrier functions (bCBFs) use predictions…

Systems and Control · Electrical Eng. & Systems 2026-04-23 David E. J. van Wijk , Tamas G. Molnar , Samuel Coogan , Manoranjan Majji , Aaron D. Ames , Joel W. Burdick

Optimal control of the singular nonlinear parabolic PDE which is a distributional formulation of multidimensional and multiphase Stefan-type free boundary problem is analyzed. Approximating sequence of finite-dimensional optimal control…

Analysis of PDEs · Mathematics 2020-06-16 Ugur G. Abdulla , Evan Cosgrove

This letter presents a nonlinear disturbance observer-parameterized control barrier function (DOp-CBF) designed for a robust safety control system under external disturbances. This framework emphasizes that the safety bounds are relevant to…

Systems and Control · Electrical Eng. & Systems 2025-09-03 Ziqi Yang , Lihua Xie

Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs), yet they often fail to achieve accurate convergence in the H1 norm, especially in the presence of boundary…

Numerical Analysis · Mathematics 2026-01-22 Qixuan Zhou , Chuqi Chen , Tao Luo , Yang Xiang

This study addresses the challenge of ensuring safe spacecraft proximity operations, focusing on collision avoidance between a chaser spacecraft and a complex-geometry target spacecraft under disturbances. To ensure safety in such…

Systems and Control · Electrical Eng. & Systems 2025-07-21 Hang Zhou , Tao Meng , Kun Wang , Chengrui Shi , Renhao Mao , Weijia Wang , Jiakun Lei

Many computer vision and image processing problems can be posed as solving partial differential equations (PDEs). However, designing PDE system usually requires high mathematical skills and good insight into the problems. In this paper, we…

Computer Vision and Pattern Recognition · Computer Science 2011-09-07 Risheng Liu , Zhouchen Lin , Wei Zhang , Kewei Tang , Zhixun Su

This paper proposes a safety controller for control-affine nonlinear systems with unmodelled dynamics and disturbances to improve closed-loop robustness. Uncertainty estimation-based control barrier functions (CBFs) are utilized to ensure…

Systems and Control · Electrical Eng. & Systems 2024-02-15 Ersin Daş , Skylar X. Wei , Joel W. Burdick

Safety is one of the fundamental challenges in control theory. Recently, multi-step optimal control problems for discrete-time dynamical systems were formulated to enforce stability, while subject to input constraints as well as…

Optimization and Control · Mathematics 2023-07-14 Shuo Liu , Jun Zeng , Koushil Sreenath , Calin A. Belta

Control barrier functions (CBFs) provide a powerful tool for enforcing safety constraints in control systems, but their direct application to complex, high-dimensional dynamics is often challenging. In many settings, safety certificates are…

Systems and Control · Electrical Eng. & Systems 2026-03-17 Nikolaos Bousias , Charalampia Stamouli , Anastasios Tsiamis , George Pappas

Neural networks have emerged as powerful surrogates for solving partial differential equations (PDEs), offering significant computational speedups over traditional methods. However, these models suffer from a critical limitation: error…

Machine Learning · Computer Science 2025-12-29 Xinquan Huang , Paris Perdikaris