Related papers: Towards Model Reduction for Power System Transient…
In this paper, Multirate Partial Differential Equations (MPDEs) are used for the efficient simulation of problems with 2-level pulsed excitations as they often occur in power electronics, e.g., DC-DC switch-mode converters. The differential…
We present a lightweighted neural PDE representation to discover the hidden structure and predict the solution of different nonlinear PDEs. Our key idea is to leverage the prior of ``translational similarity'' of numerical PDE differential…
Spatiotemporal partial differential equations (PDEs) underpin a wide range of scientific and engineering applications. Neural PDE solvers offer a promising alternative to classical numerical methods. However, existing approaches typically…
A class of physics-informed spatio-temporal models has recently been proposed for modeling spatio-temporal processes governed by advection-diffusion equations. The central idea is to approximate the process by a truncated Fourier series and…
We propose a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of parametric partial differential equations (PDEs) conditioned on partial observations, which includes,…
This work presents a model reduction approach for problems with coherent structures that propagate over time such as convection-dominated flows and wave-type phenomena. Traditional model reduction methods have difficulties with these…
Physics-based models often involve large systems of parametrized partial differential equations, where design parameters control various properties. However, high-fidelity simulations of such systems on large domains or with high grid…
Power systems are globally experiencing an unprecedented growth in size and complexity due to the advent of nonconventional generation and consumption technologies. To navigate computational complexity, power system dynamic models are often…
We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems. Starting from a model trained on low-fidelity or observational data, we apply a…
In this paper we introduce a new PDE model in frequency space for the inertial energy cascade that reproduces the classical scaling laws of Kolmogorov's theory of turbulence. Our point of view is based upon studying the energy flux through…
Developing fast surrogates for Partial Differential Equations (PDEs) will accelerate design and optimization in almost all scientific and engineering applications. Neural networks have been receiving ever-increasing attention and…
This paper investigates the stability and stabilization of semilinear single-track vehicle models with distributed tire friction dynamics, modeled as interconnections of ordinary differential equations (ODEs) and hyperbolic partial…
Physics-informed neural network architectures have emerged as a powerful tool for developing flexible PDE solvers which easily assimilate data, but face challenges related to the PDE discretization underpinning them. By instead adapting a…
Objective: This research pioneers a novel approach to obtain a closed-form analytic solution to the nonlinear second order differential swing equation that models power system dynamics. The distinctive element of this study is the…
The increasing integration of renewable energy sources has introduced complex dynamic behavior in power systems that challenge the adequacy of traditional continuous-time modeling approaches. These developments call for modeling frameworks…
This work proposes a systematic model reduction approach based on rank adaptive tensor recovery for partial differential equation (PDE) models with high-dimensional random parameters. Since the standard outputs of interest of these models…
We study synchronous phenomena of a coarse-grained power grid model, the swing equation, on small-world networks. We show that its steady state, which stands for the normal operation of the power systems, can be realized even if the phases…
The neural ordinary differential equation (ODE) framework has emerged as a powerful tool for developing accelerated surrogate models of complex physical systems governed by partial differential equations (PDEs). A popular approach for PDE…
A simplified transient energy-transport system for semiconductors subject to mixed Dirichlet-Neumann boundary conditions is analyzed. The model is formally derived from the non-isothermal hydrodynamic equations in a particular vanishing…
The measured spatiotemporal response of various physical processes is utilized to infer the governing partial differential equations (PDEs). We propose SimultaNeous Basis Function Approximation and Parameter Estimation (SNAPE), a technique…