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Operator learning has emerged as a powerful tool in scientific computing for approximating mappings between infinite-dimensional function spaces. A primary application of operator learning is the development of surrogate models for the…

Machine Learning · Statistics 2025-04-07 Unique Subedi , Ambuj Tewari

We investigate neural ordinary and stochastic differential equations (neural ODEs and SDEs) to model stochastic dynamics in fully and partially observed environments within a model-based reinforcement learning (RL) framework. Through a…

Machine Learning · Computer Science 2026-03-25 Chao Han , Stefanos Ioannou , Luca Manneschi , T. J. Hayward , Michael Mangan , Aditya Gilra , Eleni Vasilaki

We provide a solution to the heretofore open problem of stabilization of systems with arbitrarily long delays at the input and output of a nonlinear system using output feedback only. The solution is global, employs the predictor approach…

Optimization and Control · Mathematics 2013-08-15 Iasson Karafyllis , Miroslav Krstic

We complete the first step towards the resolution of several decades-old challenges in disturbance-robust adaptive control. For a scalar linear system with an unknown parameter for which no a priori bound is given, with a disturbance that…

Optimization and Control · Mathematics 2023-04-07 Iasson Karafyllis , Miroslav Krstic , Alexandros Aslanidis

When neural networks (NNs) are used as a type of nonlinear parametric representation to solve partial differential equations (PDEs), they often display frequency-dependent learning dynamics that can differ from those seen in direct function…

Numerical Analysis · Mathematics 2026-03-03 Roy Y. He , Ying Liang , Hongkai Zhao , Yimin Zhong

Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs). However, purely data-driven models often require extensive training data and can generalize poorly, especially in small-data…

Machine Learning · Computer Science 2026-02-16 Heechang Kim , Qianying Cao , Hyomin Shin , Seungchul Lee , George Em Karniadakis , Minseok Choi

We present bounded dynamic (but observer-free) output feedback laws that achieve global stabilization of equilibrium profiles of the partial differential equation (PDE) model of a simplified, age-structured chemostat model. The chemostat…

Optimization and Control · Mathematics 2016-09-30 Iasson Karafyllis , Miroslav Krstic

A computed approximation of the solution operator to a system of partial differential equations (PDEs) is needed in various areas of science and engineering. Neural operators have been shown to be quite effective at predicting these…

Machine Learning · Computer Science 2024-12-02 Zan Ahmad , Shiyi Chen , Minglang Yin , Avisha Kumar , Nicolas Charon , Natalia Trayanova , Mauro Maggioni

Neural operators provide a framework for learning solution operators of partial differential equations (PDEs), enabling efficient surrogate modeling for complex systems. While universal approximation results are now well understood,…

Machine Learning · Computer Science 2026-05-13 Takashi Furuya , Ryo Ozawa , Jenn-Nan Wang

Previous work has shown that Benjamin-Feir unstable traveling waves of the complex Ginzburg-Landau equation (CGLE) in two spatial dimensions cannot be stabilized using a particular time-delayed feedback control mechanism known as…

Pattern Formation and Solitons · Physics 2009-11-13 Claire M. Postlethwaite , Mary Silber

The well-known generalization problem hinders the application of artificial neural networks in continuous-time prediction tasks with varying latent dynamics. In sharp contrast, biological systems can neatly adapt to evolving environments…

Machine Learning · Computer Science 2025-03-10 Jindou Jia , Zihan Yang , Meng Wang , Kexin Guo , Jianfei Yang , Xiang Yu , Lei Guo

In stochastic multistable systems driven by the gradient of a potential, transitions between equilibria is possible because of noise. We study the ability of linear delay feedback control to mitigate these transitions, ensuring that the…

Optimization and Control · Mathematics 2020-02-06 Mohammad Farazmand

Asynchronous stochastic gradient descent (SGD) enables scalable distributed training but suffers from gradient staleness. Existing mitigation strategies, such as delay-adaptive learning rates and staleness-aware filtering, typically…

Machine Learning · Computer Science 2026-05-15 Tehila Dahan , Roie Reshef , Sharon Goldstein , Kfir Y. Levy

Neural operators have emerged as powerful tools for learning solution operators of partial differential equations. However, in time-dependent problems, standard training strategies such as teacher forcing introduce a mismatch between…

Machine Learning · Computer Science 2025-05-28 Zaijun Ye , Chen-Song Zhang , Wansheng Wang

This paper considers the backstepping state feedback control of coupled linear parabolic PDEs with spatially varying coefficients and bilateral actuation. By making use of the folding technique, a system representation with unilateral…

Optimization and Control · Mathematics 2021-04-13 Simon Kerschbaum , Joachim Deutscher

This work studies the problem of controlling the mean-field density of large-scale stochastic systems, which has applications in various fields such as swarm robotics. Recently, there is a growing amount of literature that employs…

Systems and Control · Electrical Eng. & Systems 2022-03-28 Tongjia Zheng , Qing Han , Hai Lin

In this paper, we design an output-feedback controller to stabilize n +m hetero-directional transport partial differential equations (PDEs) coupled on both domain boundaries to ordinary differential equations (ODEs). This class of systems…

Analysis of PDEs · Mathematics 2024-06-17 Jean Auriol , Federico Bribiesca Argomedo

We study the possibility to stabilize unstable steady states and unstable periodic orbits in chaotic fractional-order dynamical systems by the time-delayed feedback method. By performing a linear stability analysis, we establish the…

General Physics · Physics 2011-07-07 Aleksandar Gjurchinovski , Trifce Sandev , Viktor Urumov

We propose the Inverse Neural Operator (INO), a two-stage framework for recovering hidden ODE parameters from sparse, partial observations. In Stage 1, a Conditional Fourier Neural Operator (C-FNO) with cross-attention learns a…

Machine Learning · Computer Science 2026-03-13 Zhi-Song Liu , Wenqing Peng , Helmi Toropainen , Ammar Kheder , Andreas Rupp , Holger Froning , Xiaojie Lin , Michael Boy

Although neural operators are widely used in data-driven physical simulations, their training remains computationally expensive. Recent advances address this issue via downstream learning, where a model pretrained on simpler problems is…

Machine Learning · Computer Science 2025-11-17 Mikhail Masliaev , Dmitry Gusarov , Ilya Markov , Alexander Hvatov