Related papers: Data-driven Model Reduction for Parameter-Dependen…

This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that…

This work presents a non-intrusive model reduction method to learn low-dimensional models of dynamical systems with non-polynomial nonlinear terms that are spatially local and that are given in analytic form. In contrast to state-of-the-art…

Reduced-order models are indispensable for multi-query or real-time problems. However, there are still many challenges to constructing efficient ROMs for time-dependent parametrized problems. Using a linear reduced space is inefficient for…

In this work, we consider wave propagation in materials characterized by nonlinear properties or damage. To accelerate the simulations of the resulting high-dimensional problems, we apply model order reduction methods. Depending on the…

Driven by increased complexity of dynamical systems, the solution of system of differential equations through numerical simulation in optimization problems has become computationally expensive. This paper provides a smart data driven…

Reduced-order modeling has a long tradition in computational fluid dynamics. The ever-increasing significance of data for the synthesis of low-order models is well reflected in the recent successes of data-driven approaches such as Dynamic…

The central task in modeling complex dynamical systems is parameter estimation. This task involves numerous evaluations of a computationally expensive objective function. Surrogate-based optimization introduces a computationally efficient…

We present an efficient data-driven regression approach for constructing reduced-order models (ROMs) of reaction-diffusion systems exhibiting pattern formation. The ROMs are learned non-intrusively from available training data of physically…

In this work, we address the challenge of efficiently modeling dynamical systems in process engineering. We use reduced-order model learning, specifically operator inference. This is a non-intrusive, data-driven method for learning…

A modeling methodology and matrix formalism is presented that permits analysis of arbitrarily complex interferometric waveguide systems, including polarization and backreflection effects. Considerable improvement results from separation of…

Providing efficient and accurate parametrizations for model reduction is a key goal in many areas of science and technology. Here we present a strong link between data-driven and theoretical approaches to achieving this goal. Formal…

Parameter inference in ordinary differential equations is an important problem in many applied sciences and in engineering, especially in a data-scarce setting. In this work, we introduce a novel generative modeling approach based on…

In order to optimally design materials, it is crucial to understand the structure-property relations in the material by analyzing the effect of microstructure parameters on the macroscopic properties. In computational homogenization, the…

Nonlinear parametric inverse problems appear in many applications and are typically very expensive to solve, especially if they involve many measurements. These problems pose huge computational challenges as evaluating the objective…

Parametric reduced-order modelling often serves as a surrogate method for hemodynamics simulations to improve the computational efficiency in many-query scenarios or to perform real-time simulations. However, the snapshots of the method…

The existing physical-informed Deep Operator Networks are mostly based on either the well-known mathematical formula of the system or huge amounts of data for different scenarios. However, in some cases, it is difficult to get the exact…

Numerical simulations of complex multiphysics systems, such as char combustion considered herein, yield numerous state variables that inherently exhibit physical constraints. This paper presents a new approach to augment Operator Inference…

The dominant paradigm for power system dynamic simulation is to build system-level simulations by combining physics-based models of individual components. The sheer size of the system along with the rapid integration of inverter-based…

Data-driven modeling can suffer from a constant demand for data, leading to reduced accuracy and impractical for engineering applications due to the high cost and scarcity of information. To address this challenge, we propose a progressive…

Solving diverse partial differential equations (PDEs) is fundamental in science and engineering. Large language models (LLMs) have demonstrated strong capabilities in code generation, symbolic reasoning, and tool use, but reliably solving…