Related papers: RONOM: Reduced-Order Neural Operator Modeling

Model order reduction (MOR) involves offering low-dimensional models that effectively approximate the behavior of complex high-order systems. Due to potential model complexities and computational costs, designing controllers for…

Numerous cutting-edge scientific technologies originate at the laboratory scale, but transitioning them to practical industry applications is a formidable challenge. Traditional pilot projects at intermediate scales are costly and…

The predictive accuracy of operator learning frameworks depends on the quality and quantity of available training data (input-output function pairs), often requiring substantial amounts of high-fidelity data, which can be challenging to…

Simulating physical systems governed by Lagrangian dynamics often entails solving partial differential equations (PDEs) over high-resolution spatial domains, leading to significant computational expense. Reduced-order modeling (ROM)…

This paper presents a physics-informed training framework for projection-based Reduced Order Models (ROMs). We extend the PROM-ANN architecture by complementing snapshot-based training with a FEM-based, discrete physics-informed residual…

We apply reduced-order modeling (ROM) techniques to single-phase flow in faulted porous media, accounting for changing rock properties and fault geometry variations using a radial basis function mesh deformation method. This approach…

Solving complex partial differential equations is vital in the physical sciences, but often requires computationally expensive numerical methods. Reduced-order models (ROMs) address this by exploiting dimensionality reduction to create fast…

Model predictive controllers use dynamics models to solve constrained optimal control problems. However, computational requirements for real-time control have limited their use to systems with low-dimensional models. Nevertheless,…

This work proposes novel techniques for the efficient numerical simulation of parameterized, unsteady partial differential equations. Projection-based reduced order models (ROMs) such as the reduced basis method employ a (Petrov-)Galerkin…

Modeling complex dynamical systems under varying conditions is computationally intensive, often rendering high-fidelity simulations intractable. Although reduced-order models (ROMs) offer a promising solution, current methods often struggle…

Model order reduction techniques simplify high-dimensional dynamical systems by deriving lower-dimensional models that retain essential system characteristics. These techniques are crucial for the controller design of complex systems while…

Reduced order modeling lowers the computational cost of solving PDEs by learning a low-order spatial representation from data and dynamically evolving these representations using manifold projections of the governing equations. While…

Multiple model reduction techniques have been proposed to tackle linear and non linear problems. Intrusive model order reduction techniques exhibit high accuracy levels, however, they are rarely used as a standalone industrial tool, because…

A nonintrusive model order reduction method for bilinear stochastic differential equations with additive noise is proposed. A reduced order model (ROM) is designed in order to approximate the statistical properties of high-dimensional…

A nonlinear-manifold reduced order model (NM-ROM) is a great way of incorporating underlying physics principles into a neural network-based data-driven approach. We combine NM-ROMs with domain decomposition (DD) for efficient computation.…

A multi-fidelity framework is established and demonstrated for prediction of combustion instabilities in rocket engines. The major idea is to adapt appropriate fidelity modeling approaches for different components in a rocket engine to…

In the reduced order modeling (ROM) framework, the solution of a parametric partial differential equation is approximated by combining the high-fidelity solutions of the problem at hand for several properly chosen configurations. Examples…

Predictive learning for spatio-temporal processes (PL-STP) on complex spatial domains plays a critical role in various scientific and engineering fields, with its essence being the construction of operators between infinite-dimensional…

Quantum computing is an advancing area of research in which computer hardware and algorithms are developed to take advantage of quantum mechanical phenomena. In recent studies, quantum algorithms have shown promise in solving linear systems…

Deep learning-based reduced order models (DL-ROMs) have been recently proposed to overcome common limitations shared by conventional reduced order models (ROMs) - built, e.g., through proper orthogonal decomposition (POD) - when applied to…