Related papers: NN-OpInf: an operator inference approach using str…
Operator inference learns low-dimensional dynamical-system models with polynomial nonlinear terms from trajectories of high-dimensional physical systems (non-intrusive model reduction). This work focuses on the large class of physical…
We present an operator learning approach for a class of evolution operators using a composition of a learned lift into the space of diffeomorphisms of the domain and the group action on the field space. In turn, this transforms the…
Recently, there has been growing interest in using physics-informed neural networks (PINNs) to solve differential equations. However, the preservation of structure, such as energy and stability, in a suitable manner has yet to be…
A method for the nonintrusive and structure-preserving model reduction of canonical and noncanonical Hamiltonian systems is presented. Based on the idea of operator inference, this technique is provably convergent and reduces to a…
Hamiltonian operator inference has been developed in [Sharma, H., Wang, Z., Kramer, B., Physica D: Nonlinear Phenomena, 431, p.133122, 2022] to learn structure-preserving reduced-order models (ROMs) for Hamiltonian systems. The method…
Motivated by the large-scale nature of modern aerospace engineering simulations, this paper presents a detailed description of distributed Operator Inference (dOpInf), a recently developed parallel algorithm designed to efficiently…
Symbolic regression is a task aimed at identifying patterns in data and representing them through mathematical expressions, generally involving skeleton prediction and constant optimization. Many methods have achieved some success, however…
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…
Deep neural networks, despite their success in numerous applications, often function without established theoretical foundations. In this paper, we bridge this gap by drawing parallels between deep learning and classical numerical analysis.…
This paper presents a method for modeling transient fluid flow in subsurface reservoir systems based on the developed neural operator architecture (TFNO-opt). Reservoir systems are complex dynamic objects with distributed parameters…
Contraction analysis offers, through elegant mathematical developments, a unified way of designing observers for a general class of nonlinear systems, where the observer correction term is obtained by solving an infinite dimensional…
This paper addresses the data-driven identification of latent dynamical representations of partially-observed systems, i.e., dynamical systems for which some components are never observed, with an emphasis on forecasting applications,…
Operational Neural Networks (ONNs) have recently been proposed to address the well-known limitations and drawbacks of conventional Convolutional Neural Networks (CNNs) such as network homogeneity with the sole linear neuron model. ONNs are…
We introduce the $\textbf{O}$ne-shot $\textbf{P}$runing $\textbf{T}$echnique for $\textbf{I}$nterchangeable $\textbf{N}$etworks ($\textbf{OPTIN}$) framework as a tool to increase the efficiency of pre-trained transformer architectures…
When neural networks (NNs) are used as a type of nonlinear parametric representation to solve partial differential equations (PDEs), they often display frequency-dependent learning dynamics that can differ from those seen in direct function…
Many techniques have been developed, such as model compression, to make Deep Neural Networks (DNNs) inference more efficiently. Nevertheless, DNNs still lack excellent run-time dynamic inference capability to enable users trade-off accuracy…
This work develops an active learning framework to intelligently enrich data-driven reduced-order models (ROMs) of parametric dynamical systems, which can serve as the foundation of virtual assets in a digital twin. Data-driven ROMs are…
Neural operator learning directly constructs the mapping relationship from the equation parameter space to the solution space, enabling efficient direct inference in practical applications without the need for repeated solution of partial…
Time-dependent structural reliability analysis of nonlinear dynamical systems is non-trivial; subsequently, scope of most of the structural reliability analysis methods is limited to time-independent reliability analysis only. In this work,…
This work presents the application of parametric Operator Inference (OpInf) -- a nonintrusive reduced-order modeling (ROM) technique that learns a low-dimensional representation of a high-fidelity model -- to the numerical model of the…