4,646 research outputs found
Non-intrusive reduced order modeling of nonlinear problems using neural networks
We develop a non-intrusive reduced basis (RB) method for parametrized steady-state partial differential equations (PDEs). The method extracts a reduced basis from a collection of high-fidelity solutions via a proper orthogonal decomposition (POD) and employs artificial neural networks (ANNs), particularly multi-layer perceptrons (MLPs), to accurately approxi- mate the coefficients of the reduced model. The search for the optimal number of neurons and the minimum amount of training samples to avoid overfitting is carried out in the offline phase through an automatic routine, relying upon a joint use of the latin hypercube sampling (LHS) and the Levenberg-Marquardt training algorithm. This guarantees a complete offline-online decoupling, leading to an efficient RB method - referred to as POD-NN - suitable also for general nonlinear problems with a non-affine parametric dependence. Numerical studies are presented for the nonlinear Poisson equation and for driven cavity viscous flows, modeled through the steady incompressible Navier-Stokes equations. Both physical and geometrical parametrizations are considered. Several results confirm the accuracy of the POD-NN method and show the substantial speed-up enabled at the online stage as compared to a traditional RB strategy
A neural network-based data-driven local modeling of spotwelded plates under impact
Solving large structural problems with multiple complex localized behaviors is extremely challenging. To address this difficulty, both intrusive and non-intrusive Domain Decomposition Methods (DDM) have been developed in the past, where the refined model (local) is solved separately in its own space and time scales. In this work, the Finite Element Method (FEM) at the local scale is replaced with a data-driven Reduced Order Model (ROM) to further decrease computational time. The reduced model aims to create a low-cost, accurate and efficient mapping from interface velocities to interface forces and enable the prediction of their time evolution. The present work proposes a modeling technique based on the Physics-Guided Architecture of Neural Networks (PGANNs), which incorporates physical variables other than input/output variables into the neural network architecture. We develop this approach on a 2D plate with a hole as well as a 3D case with spot-welded plates undergoing fast deformation, representing nonlinear elastoplasticity problems. Neural networks are trained using simulation data generated by explicit dynamic FEM solvers. The PGANN results are in good agreement with the FEM solutions for both test cases, including those in the training dataset as well as the unseen dataset, given the loading type is present in the training set
Reduced order modeling of fluid flows: Machine learning, Kolmogorov barrier, closure modeling, and partitioning
In this paper, we put forth a long short-term memory (LSTM) nudging framework
for the enhancement of reduced order models (ROMs) of fluid flows utilizing
noisy measurements. We build on the fact that in a realistic application, there
are uncertainties in initial conditions, boundary conditions, model parameters,
and/or field measurements. Moreover, conventional nonlinear ROMs based on
Galerkin projection (GROMs) suffer from imperfection and solution instabilities
due to the modal truncation, especially for advection-dominated flows with slow
decay in the Kolmogorov width. In the presented LSTM-Nudge approach, we fuse
forecasts from a combination of imperfect GROM and uncertain state estimates,
with sparse Eulerian sensor measurements to provide more reliable predictions
in a dynamical data assimilation framework. We illustrate the idea with the
viscous Burgers problem, as a benchmark test bed with quadratic nonlinearity
and Laplacian dissipation. We investigate the effects of measurements noise and
state estimate uncertainty on the performance of the LSTM-Nudge behavior. We
also demonstrate that it can sufficiently handle different levels of temporal
and spatial measurement sparsity. This first step in our assessment of the
proposed model shows that the LSTM nudging could represent a viable realtime
predictive tool in emerging digital twin systems
Fast Neural Network Predictions from Constrained Aerodynamics Datasets
Incorporating computational fluid dynamics in the design process of jets,
spacecraft, or gas turbine engines is often challenged by the required
computational resources and simulation time, which depend on the chosen
physics-based computational models and grid resolutions. An ongoing problem in
the field is how to simulate these systems faster but with sufficient accuracy.
While many approaches involve simplified models of the underlying physics,
others are model-free and make predictions based only on existing simulation
data. We present a novel model-free approach in which we reformulate the
simulation problem to effectively increase the size of constrained pre-computed
datasets and introduce a novel neural network architecture (called a cluster
network) with an inductive bias well-suited to highly nonlinear computational
fluid dynamics solutions. Compared to the state-of-the-art in model-based
approximations, we show that our approach is nearly as accurate, an order of
magnitude faster, and easier to apply. Furthermore, we show that our method
outperforms other model-free approaches
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