134,149 research outputs found
Reduced-Order Modeling of Hidden Dynamics
International audienceThe objective of this paper is to investigate how noisy and incomplete observations can be integrated in the process of building a reduced-order model. This problematic arises in many scientific domains where there exists a need for accurate low-order descriptions of highly-complex phenomena, which can not be directly and/or deterministically observed. Within this context, the paper proposes a probabilistic framework for the construction of "POD-Galerkin" reduced-order models. Assuming a hidden Markov chain, the inference integrates the uncertainty of the hidden states relying on their posterior distribution. Simulations show the benefits obtained by exploiting the proposed framework
Data-driven recovery of hidden physics in reduced order modeling of fluid flows
In this article, we introduce a modular hybrid analysis and modeling (HAM)
approach to account for hidden physics in reduced order modeling (ROM) of
parameterized systems relevant to fluid dynamics. The hybrid ROM framework is
based on using the first principles to model the known physics in conjunction
with utilizing the data-driven machine learning tools to model remaining
residual that is hidden in data. This framework employs proper orthogonal
decomposition as a compression tool to construct orthonormal bases and Galerkin
projection (GP) as a model to built the dynamical core of the system. Our
proposed methodology hence compensates structural or epistemic uncertainties in
models and utilizes the observed data snapshots to compute true modal
coefficients spanned by these bases. The GP model is then corrected at every
time step with a data-driven rectification using a long short-term memory
(LSTM) neural network architecture to incorporate hidden physics. A
Grassmannian manifold approach is also adapted for interpolating basis
functions to unseen parametric conditions. The control parameter governing the
system's behavior is thus implicitly considered through true modal coefficients
as input features to the LSTM network. The effectiveness of the HAM approach is
discussed through illustrative examples that are generated synthetically to
take hidden physics into account. Our approach thus provides insights
addressing a fundamental limitation of the physics-based models when the
governing equations are incomplete to represent underlying physical processes
An evolve-then-correct reduced order model for hidden fluid dynamics
In this paper, we put forth an evolve-then-correct reduced order modeling
approach that combines intrusive and nonintrusive models to take hidden
physical processes into account. Specifically, we split the underlying dynamics
into known and unknown components. In the known part, we first utilize an
intrusive Galerkin method projected on a set of basis functions obtained by
proper orthogonal decomposition. We then formulate a recurrent neural network
emulator based on the assumption that observed data is a manifestation of all
relevant processes. We further enhance our approach by using an orthonormality
conforming basis interpolation approach on a Grassmannian manifold to address
off-design conditions. The proposed framework is illustrated here with the
application of two-dimensional co-rotating vortex simulations under modeling
uncertainty. The results demonstrate highly accurate predictions underlining
the effectiveness of the evolve-then-correct approach toward realtime
simulations, where the full process model is not known a priori
Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks
We introduce a data-driven forecasting method for high-dimensional chaotic
systems using long short-term memory (LSTM) recurrent neural networks. The
proposed LSTM neural networks perform inference of high-dimensional dynamical
systems in their reduced order space and are shown to be an effective set of
nonlinear approximators of their attractor. We demonstrate the forecasting
performance of the LSTM and compare it with Gaussian processes (GPs) in time
series obtained from the Lorenz 96 system, the Kuramoto-Sivashinsky equation
and a prototype climate model. The LSTM networks outperform the GPs in
short-term forecasting accuracy in all applications considered. A hybrid
architecture, extending the LSTM with a mean stochastic model (MSM-LSTM), is
proposed to ensure convergence to the invariant measure. This novel hybrid
method is fully data-driven and extends the forecasting capabilities of LSTM
networks.Comment: 31 page
- …