Related papers: Towards Model Reduction for Power System Transient…
Partial Differential Equations (PDEs) are the bedrock for modern computational sciences and engineering, and inherently computationally expensive. While PDE foundation models have shown much promise for simulating such complex…
Modeling complex spatiotemporal dynamical systems, such as the reaction-diffusion processes, have largely relied on partial differential equations (PDEs). However, due to insufficient prior knowledge on some under-explored dynamical…
Partial differential equations (PDEs) play a central role in describing many physical phenomena. Various scientific and engineering applications demand a versatile and differentiable PDE solver that can quickly generate solutions with…
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).…
This research focuses on the evolving dynamics of the power grid, where traditional synchronous generators are being replaced by non-synchronous power electronic converter (PEC)-interfaced renewable energy sources. The non-linear dynamics…
This paper presents a novel and scalable screw-theoretic multibody synthesis framework for PDE-based dynamic modeling of serial robotic manipulators with an arbitrary number of flexible links in three-dimensional space. The proposed…
In this article we propose and investigate a hierarchy of mathematical models based on partial differential equations (PDE) and ordinary differential equations (ODE) for the simulation of the biophysical phenomena occurring in the…
This paper is a preliminary work to address the problem of dynamical systems with parameters varying in time. An idea to predict their behaviour is proposed. These systems are called \emph{transient systems}, and are distinguished from…
An equation based reduced order model applicable to generalized heat equation and thermal simulations of power electronics systems developed in commercial CFD tools, is presented in this work. The model considers the physics of heat…
Partial differential equations (PDEs) are commonly derived based on empirical observations. However, recent advances of technology enable us to collect and store massive amount of data, which offers new opportunities for data-driven…
The dynamics of power grids are governed by a large number of nonlinear differential and algebraic equations (DAEs). To safely operate the system, operators need to check that the states described by these DAEs stay within prescribed limits…
This work formulates a new approach to reduced modeling of parameterized, time-dependent partial differential equations (PDEs). The method employs Operator Inference, a scientific machine learning framework combining data-driven learning…
This work addresses the problem of transient stabilization of a power grid, following a destabilizing disturbance. The model considered is the cascade interconnection of seven New England test models with the disturbance (e.g., a powerline…
Traditional grid analytics are model-based, relying strongly on accurate models of power systems, especially the dynamic models of generators, controllers, loads and other dynamic components. However, acquiring thorough power system models…
We present a new data-driven reduced-order modeling approach to efficiently solve parametrized partial differential equations (PDEs) for many-query problems. This work is inspired by the concept of implicit neural representation (INR),…
We propose a two-stage method called \textit{Spline Assisted Partial Differential Equation based Model Identification (SAPDEMI)} to identify partial differential equation (PDE)-based models from noisy data. In the first stage, we employ the…
Foundation models, such as large language models, have demonstrated success in addressing various language and image processing tasks. In this work, we introduce a multi-modal foundation model for scientific problems, named PROSE-PDE. Our…
The letter proposes an adaptive model reduction approach based on tensor decomposition to speed up time-domain power system simulation. Taylor series expansion of a power system dynamic model is calculated around multiple equilibria…
Contemporary theories and models for electric power system stability are predicated on a widely held assumption that the mechanical inertia of the rotating mass of synchronous generators provides the sole contribution to stable and…
We present a computational technique for modeling the evolution of dynamical systems in a reduced basis, with a focus on the challenging problem of modeling partially-observed partial differential equations (PDEs) on high-dimensional…