Stiff neural ordinary differential equations
ABSTRACT Neural Ordinary Differential Equations (ODEs) are a promising approach to
learn dynamical models from time-series data in science and engineering applications. This …
learn dynamical models from time-series data in science and engineering applications. This …
Predictive reduced order modeling of chaotic multi-scale problems using adaptively sampled projections
C Huang, K Duraisamy - Journal of Computational Physics, 2023 - Elsevier
An adaptive projection-based reduced-order model (ROM) formulation is presented for
model-order reduction of problems featuring chaotic and convection-dominant physics. An …
model-order reduction of problems featuring chaotic and convection-dominant physics. An …
Conditionally parameterized, discretization-aware neural networks for mesh-based modeling of physical systems
Simulations of complex physical systems are typically realized by discretizing partial
differential equations (PDEs) on unstructured meshes. While neural networks have recently …
differential equations (PDEs) on unstructured meshes. While neural networks have recently …
Efficient space–time reduced order model for linear dynamical systems in python using less than 120 lines of code
A classical reduced order model (ROM) for dynamical problems typically involves only the
spatial reduction of a given problem. Recently, a novel space–time ROM for linear …
spatial reduction of a given problem. Recently, a novel space–time ROM for linear …
Component-based reduced order modeling of large-scale complex systems
Large-scale engineering systems, such as propulsive engines, ship structures, and wind
farms, feature complex, multi-scale interactions between multiple physical phenomena …
farms, feature complex, multi-scale interactions between multiple physical phenomena …
Adaptive physics-informed neural operator for coarse-grained non-equilibrium flows
This work proposes a new machine learning (ML)-based paradigm aiming to enhance the
computational efficiency of non-equilibrium reacting flow simulations while ensuring …
computational efficiency of non-equilibrium reacting flow simulations while ensuring …
On the impact of dimensionally-consistent and physics-based inner products for POD-Galerkin and least-squares model reduction of compressible flows
Abstract Model reduction of the compressible Euler equations based on proper orthogonal
decomposition (POD) and Galerkin orthogonality or least-squares residual minimization …
decomposition (POD) and Galerkin orthogonality or least-squares residual minimization …
Residual-Based Stabilized Reduced-Order Models of the Transient Convection–Diffusion–Reaction Equation Obtained Through Discrete and Continuous Projection
Abstract Galerkin and Petrov–Galerkin projection-based reduced-order models (ROMs) of
transient partial differential equations are typically obtained by performing a dimension …
transient partial differential equations are typically obtained by performing a dimension …
Front transport reduction for complex moving fronts: Nonlinear model reduction for an advection–reaction–diffusion equation with a Kolmogorov–Petrovsky–Piskunov …
This work addresses model order reduction for complex moving fronts, which are
transported by advection or through a reaction–diffusion process. Such systems are …
transported by advection or through a reaction–diffusion process. Such systems are …
Lookahead data-gathering strategies for online adaptive model reduction of transport-dominated problems
R Singh, WIT Uy, B Peherstorfer - Chaos: An Interdisciplinary Journal …, 2023 - pubs.aip.org
Online adaptive model reduction efficiently reduces numerical models of transport-
dominated problems by updating reduced spaces over time, which leads to nonlinear …
dominated problems by updating reduced spaces over time, which leads to nonlinear …