Related papers: On the representation of energy-preserving quadrat…
Many-query computations, in which a computational model for an engineering system must be evaluated many times, are crucial in design and control. For systems governed by partial differential equations (PDEs), typical high-fidelity…
Scientific machine learning for inferring dynamical systems combines data-driven modeling, physics-based modeling, and empirical knowledge. It plays an essential role in engineering design and digital twinning. In this work, we primarily…
This paper proposes a novel approach for learning a data-driven quadratic manifold from high-dimensional data, then employing this quadratic manifold to derive efficient physics-based reduced-order models. The key ingredient of the approach…
We propose neural network operator inference (NN-OpInf): a structure-preserving, composable, and minimally restrictive operator inference framework for the non-intrusive reduced-order modeling of dynamical systems. The approach learns…
This work explores the physics-driven machine learning technique Operator Inference (OpInf) for predicting the state of chaotic dynamical systems. OpInf provides a non-intrusive approach to infer approximations of polynomial operators in…
In this paper, we develop a novel class of linear energy-preserving integrating factor methods for the 2D nonlinear Schr\"odinger equation with wave operator (NLSW), combining the scalar auxiliary variable approach and the integrating…
This work develops a non-intrusive, data-driven surrogate modeling framework based on Operator Inference (OpInf) for rapidly solving parameter-dependent matrix equations in many-query settings. Motivated by the requirements of the OpInf…
This work formulates a new approach to reduced modeling of parameterized, time-dependent partial differential equations (PDEs). The method employs Operator Inference, a scientific machine learning framework combining data-driven learning…
Mechanical systems are often characterized only by their response to certain loads known from experiments or simulations. The obtained data can be used for various purposes: system analysis, design of mathematical models, or construction of…
Existing model reduction techniques for high-dimensional models of conservative partial differential equations (PDEs) encounter computational bottlenecks when dealing with systems featuring non-polynomial nonlinearities. This work presents…
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…
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 a new scientific machine learning method that learns from data a computationally inexpensive surrogate model for predicting the evolution of a system governed by a time-dependent nonlinear partial differential equation (PDE), an…
Recently, a whole class of evergy-preserving integrators has been derived for the numerical solution of Hamiltonian problems. In the mainstream of this research, we have defined a new family of symplectic integrators depending on a real…
This paper investigates convex quadratic optimization problems involving $n$ indicator variables, each associated with a continuous variable, particularly focusing on scenarios where the matrix $Q$ defining the quadratic term is positive…
This paper presents a data-driven, nested Operator Inference (OpInf) approach for learning physics-informed reduced-order models (ROMs) from snapshot data of high-dimensional dynamical systems. The approach exploits the inherent hierarchy…
Thus far, sparse representations have been exploited largely in the context of robustly estimating functions in a noisy environment from a few measurements. In this context, the existence of a basis in which the signal class under…
This paper derives predictive reduced-order models for rocket engine combustion dynamics via Operator Inference, a scientific machine learning approach that blends data-driven learning with physics-based modeling. The non-intrusive nature…
In this paper, we investigate projection-based intrusive and data-driven non-intrusive model order reduction methods in numerical simulation of rotating thermal shallow water equation (RTSWE) in parametric and non-parametric form.…
Hamiltonian Operator Inference has been introduced 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. This approach…