Related papers: Data-driven reduced-order models via regularized o…
Reduced-order modeling lies at the interface of numerical analysis and data-driven scientific computing, providing principled ways to compress high-fidelity simulations in science and engineering. We propose a training framework that…
Although projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems have demonstrated exciting results across a range of applications, their broad adoption has been limited by their intrusivity: implementing…
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…
Noise poses a challenge for learning dynamical-system models because already small variations can distort the dynamics described by trajectory data. This work builds on operator inference from scientific machine learning to infer…
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…
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…
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…
We consider data-driven reduced-order models of partial differential equations with shift equivariance. Shift-equivariant systems typically admit traveling solutions, and the main idea of our approach is to represent the solution in a…
Constrained mechanical systems occur in many applications, such as modeling of robots and other multibody systems. In this case, the motion is governed by a system of differential-algebraic equations (DAE), often with large and sparse…
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…
This paper focuses on the construction of accurate and predictive data-driven reduced models of large-scale numerical simulations with complex dynamics and sparse training datasets. In these settings, standard, single-domain approaches may…
Optimal operation of chemical processes is vital for energy, resource, and cost savings in chemical engineering. The problem of optimal operation can be tackled with reinforcement learning, but traditional reinforcement learning methods…
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…
Data-driven control algorithms use observations of system dynamics to construct an implicit model for the purpose of control. However, in practice, data-driven techniques often require excessive sample sizes, which may be infeasible in…
This work introduces a non-intrusive model reduction approach for learning reduced models from partially observed state trajectories of high-dimensional dynamical systems. The proposed approach compensates for the loss of information due to…
Accurate modeling of personalized cardiovascular dynamics is crucial for non-invasive monitoring and therapy planning. State-of-the-art physics-informed neural network (PINN) approaches employ deep, multi-branch architectures with…
The present study focuses on a subject of significant interest in fluid dynamics: the identification of a model with decreased computational complexity from numerical code output using Koopman operator theory. A reduced-order modelling…
This work presents a non-intrusive reduced-order modeling framework for dynamical systems with spatially localized features characterized by slow singular value decay. The proposed approach builds upon two existing methodologies for reduced…
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…
This paper develops an interpretable, non-intrusive reduced-order modeling technique using regularized kernel interpolation. Existing non-intrusive approaches approximate the dynamics of a reduced-order model (ROM) by solving a data-driven…