1,288 research outputs found
Operator inference for non-intrusive model reduction with quadratic manifolds
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 is a polynomial mapping between high-dimensional states and a
low-dimensional embedding. This mapping consists of two parts: a representation
in a linear subspace (computed in this work using the proper orthogonal
decomposition) and a quadratic component. The approach can be viewed as a form
of data-driven closure modeling, since the quadratic component introduces
directions into the approximation that lie in the orthogonal complement of the
linear subspace, but without introducing any additional degrees of freedom to
the low-dimensional representation. Combining the quadratic manifold
approximation with the operator inference method for projection-based model
reduction leads to a scalable non-intrusive approach for learning reduced-order
models of dynamical systems. Applying the new approach to transport-dominated
systems of partial differential equations illustrates the gains in efficiency
that can be achieved over approximation in a linear subspace
Non-Intrusive Reduced Models based on Operator Inference for Chaotic Systems
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 reduced space without having access to the full order operators
appearing in discretized models. Datasets for the physics systems are generated
using conventional numerical solvers and then projected to a low-dimensional
space via Principal Component Analysis (PCA). In latent space, a least-squares
problem is set to fit a quadratic polynomial operator, which is subsequently
employed in a time-integration scheme in order to produce extrapolations in the
same space. Once solved, the inverse PCA operation is applied to reconstruct
the extrapolations in the original space. The quality of the OpInf predictions
is assessed via the Normalized Root Mean Squared Error (NRMSE) metric from
which the Valid Prediction Time (VPT) is computed. Numerical experiments
considering the chaotic systems Lorenz 96 and the Kuramoto-Sivashinsky equation
show promising forecasting capabilities of the OpInf reduced order models with
VPT ranges that outperform state-of-the-art machine learning methods such as
backpropagation and reservoir computing recurrent neural networks [1], as well
as Markov neural operators [2].Comment: 16 pages, 37 figures, accepted for publication in the IEEE-TAI-PIM
Canonical and Noncanonical Hamiltonian Operator Inference
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
straightforward linear solve given snapshot data and gray-box knowledge of the
system Hamiltonian. Examples involving several hyperbolic partial differential
equations show that the proposed method yields reduced models which, in
addition to being accurate and stable with respect to the addition of basis
modes, preserve conserved quantities well outside the range of their training
data
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