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Varying power-infeed from converter-based generation units introduces great uncertainty on system parameters such as inertia and damping. As a consequence, system operators face increasing challenges in performing dynamic security…

Systems and Control · Electrical Eng. & Systems 2021-04-16 Jochen Stiasny , George S. Misyris , Spyros Chatzivasileiadis

This paper introduces a novel system identification and tracking method for PieceWise Smooth (PWS) nonlinear stochastic hybrid systems. We are able to correctly identify and track challenging problems with diverse dynamics and low…

We study the fundamental problem of learning a marginally stable unknown nonlinear dynamical system. We describe an algorithm for this problem, based on the technique of spectral filtering, which learns a mapping from past observations to…

Machine Learning · Computer Science 2025-08-19 Evan Dogariu , Anand Brahmbhatt , Elad Hazan

The identification of a nonlinear dynamic model is an open topic in control theory, especially from sparse input-output measurements. A fundamental challenge of this problem is that very few to zero prior knowledge is available on both the…

Systems and Control · Electrical Eng. & Systems 2022-06-13 Steeven Janny , Quentin Possamai , Laurent Bako , Madiha Nadri , Christian Wolf

A physics-informed neural network (PINN) that combines deep learning with physics is studied to solve the nonlinear Schr\"odinger equation for learning nonlinear dynamics in fiber optics. We carry out a systematic investigation and…

Optics · Physics 2021-09-03 Xiaotian Jiang , Danshi Wang , Qirui Fan , Min Zhang , Chao Lu , Alan Pak Tao Lau

Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…

Machine Learning · Computer Science 2024-11-05 Samuel A. Moore , Brian P. Mann , Boyuan Chen

The discovery of partial differential equations (PDEs) is a challenging task that involves both theoretical and empirical methods. Machine learning approaches have been developed and used to solve this problem; however, it is important to…

Machine Learning · Statistics 2023-06-09 Kalpesh More , Tapas Tripura , Rajdip Nayek , Souvik Chakraborty

Data-driven discovery of governing equations has kindled significant interests in many science and engineering areas. Existing studies primarily focus on uncovering equations that govern nonlinear dynamics based on direct measurement of the…

Computer Vision and Pattern Recognition · Computer Science 2024-04-30 Zitong Zhang , Yang Liu , Hao Sun

Machine learning, with its remarkable ability for retrieving information and identifying patterns from data, has emerged as a powerful tool for discovering governing equations. It has been increasingly informed by physics, and more recently…

Statistical Mechanics · Physics 2023-12-12 Shenglin Huang , Zequn He , Nicolas Dirr , Johannes Zimmer , Celia Reina

Complex systems in physics, chemistry, and biology that evolve over time with inherent randomness are typically described by stochastic differential equations (SDEs). A fundamental challenge in science and engineering is to determine the…

Machine Learning · Computer Science 2024-10-23 Qunxi Zhu , Bolin Zhao , Jingdong Zhang , Peiyang Li , Wei Lin

Modeling nonlinear spatiotemporal dynamical systems has primarily relied on partial differential equations (PDEs). However, the explicit formulation of PDEs for many underexplored processes, such as climate systems, biochemical reaction and…

Machine Learning · Computer Science 2023-05-23 Chengping Rao , Hao Sun , Yang Liu

Differential equations are indispensable to engineering and hence to innovation. In recent years, physics-informed neural networks (PINN) have emerged as a novel method for solving differential equations. PINN method has the advantage of…

Computational Engineering, Finance, and Science · Computer Science 2022-01-07 Mayank Raj , Pramod Kumbhar , Ratna Kumar Annabattula

We present Lift & Learn, a physics-informed method for learning low-dimensional models for large-scale dynamical systems. The method exploits knowledge of a system's governing equations to identify a coordinate transformation in which the…

Numerical Analysis · Mathematics 2020-07-14 Elizabeth Qian , Boris Kramer , Benjamin Peherstorfer , Karen Willcox

Physics-informed machine learning (PIML) is an emerging framework that integrates physical knowledge into machine learning models. This physical prior often takes the form of a partial differential equation (PDE) system that the regression…

Machine Learning · Statistics 2025-07-15 Nathan Doumèche

The convergence of statistical learning and molecular physics is transforming our approach to modeling biomolecular systems. Physics-informed machine learning (PIML) offers a systematic framework that integrates data-driven inference with…

Biomolecules · Quantitative Biology 2025-11-11 Aaryesh Deshpande

Discovering the governing laws underpinning physical and chemical phenomena is a key step towards understanding and ultimately controlling systems in science and engineering. We introduce Discovery of Dynamical Systems via Moving Horizon…

Dynamical Systems · Mathematics 2022-08-31 Fernando Lejarza , Michael Baldea

In recent years, identification of nonlinear dynamical systems from data has become increasingly popular. Sparse regression approaches, such as Sparse Identification of Nonlinear Dynamics (SINDy), fostered the development of novel governing…

Machine Learning · Statistics 2022-03-21 Alexandre Cortiella , Kwang-Chun Park , Alireza Doostan

Biologically-informed neural networks (BINNs), an extension of physics-informed neural networks [1], are introduced and used to discover the underlying dynamics of biological systems from sparse experimental data. In the present work, BINNs…

Quantitative Methods · Quantitative Biology 2021-01-27 John H. Lagergren , John T. Nardini , Ruth E. Baker , Matthew J. Simpson , Kevin B. Flores

We learn parameterized nonlinear elasticity on curved surfaces using a physics-informed neural network that enforces governing equations and boundary conditions directly through the loss function, enabling a single trained model to…

Biological Physics · Physics 2026-04-15 Yankang Liu , Ke Zhang , Maziar Raissi , Roya Zandi

Learning the full family of solutions to parameterized partial differential equations (PDEs) is a central challenge to our ability to model the behavior of heterogeneous systems, with a variety of fundamental and application-oriented…

Computational Physics · Physics 2026-01-26 Milad Panahi , Giovanni Michele Porta , Monica Riva , Alberto Guadagnini