Data-driven Model Reduction Research Articles

Data-Driven Reduced Model Construction with Time-Domain Loewner Models

This work presents a data-driven nonintrusive model reduction approach for large-scale time-dependent systems with linear state dependence. Traditionally, model reduction is performed in an intrusi...

Dynamic data-driven model reduction: adapting reduced models from incomplete data

This work presents a data-driven online adaptive model reduction approach for systems that undergo dynamic changes. Classical model reduction constructs a reduced model of a large-scale system in an offline phase and then keeps the reduced model unchanged during the evaluations in an online phase; however, if the system changes online, the reduced model may fail to predict the behavior of the changed system. Rebuilding the reduced model from scratch is often too expensive in time-critical and real-time environments. We introduce a dynamic data-driven adaptation approach that adapts the reduced model from incomplete sensor data obtained from the system during the online computations. The updates to the reduced models are derived directly from the incomplete data, without recourse to the full model. Our adaptivity approach approximates the missing values in the incomplete sensor data with gappy proper orthogonal decomposition. These approximate data are then used to derive low-rank updates to the reduced basis and the reduced operators. In our numerical examples, incomplete data with 30–40 % known values are sufficient to recover the reduced model that would be obtained via rebuilding from scratch.

Dynamic data-driven reduced-order models

Abstract Data-driven model reduction constructs reduced-order models of large-scale systems by learning the system response characteristics from data. Existing methods build the reduced-order models in a computationally expensive offline phase and then use them in an online phase to provide fast predictions of the system. In cases where the underlying system properties are not static but undergo dynamic changes, repeating the offline phase after each system change to rebuild the reduced-order model from scratch forfeits the savings gained in the online phase. This paper proposes dynamic reduced-order models that break with this classical but rigid approach. Dynamic reduced-order models exploit the opportunity presented by dynamic sensor data and adaptively incorporate sensor data during the online phase. This permits online adaptation to system changes while circumventing the expensive rebuilding of the model. A computationally cheap adaptation is achieved by constructing low-rank updates to the reduced operators. With these updates and with sufficient and accurate data, our approach recovers the same model that would be obtained by rebuilding from scratch. We demonstrate dynamic reduced-order models on a structural assessment example in the context of real-time decision making. We consider a plate in bending where the dynamic reduced-order model quickly adapts to changes in structural properties and achieves speedups of four orders of magnitude compared to rebuilding a model from scratch.

Data-driven model reduction for weakly nonlinear systems: A summary

Model reduction seeks to replace complex dynamical systems with simpler ones, having similar characteristics. One approach is data-driven reduction based on system data which are either measured or computed. In this regard the Loewner framework is a powerful tool for dealing with the reduction of both linear and nonlinear systems.

Thermal Response Variability of Random Polycrystalline Microstructures

AbstractA data-driven model reduction strategy is presented for the representation of random polycrystal microstructures. Given a set of microstructure snapshots that satisfy certain statistical constraints such as given low-order moments of the grain size distribution, using a non-linear manifold learning approach, we identify the intrinsic low-dimensionality of the microstructure manifold. In addition to grain size, a linear dimensionality reduction technique (Karhunun-Loéve Expansion) is used to reduce the texture representation. The space of viable microstructures is mapped to a low-dimensional region thus facilitating the analysis and design of polycrystal microstructures. This methodology allows us to sample microstructure features in the reduced-order space thus making it a highly efficient, low-dimensional surrogate for representing microstructures (grain size and texture). We demonstrate the model reduction approach by computing the variability of homogenized thermal properties using sparse grid collocation in the reduced-order space that describes the grain size and orientation variability.

Identification and data-driven model reduction of state-space representations of lossless and dissipative systems from noise-free data

We illustrate procedures to identify a state-space representation of a lossless or dissipative system from a given noise-free trajectory; important special cases are passive systems and bounded-real systems. Computing a rank-revealing factorization of a Gramian-like matrix constructed from the data, a state sequence can be obtained; the state-space equations are then computed by solving a system of linear equations. This idea is also applied to perform model reduction by obtaining a balanced realization directly from data and truncating it to obtain a reduced-order model.

The effect of multiple sources of uncertainty on the convex hull of material properties of polycrystals

Quantification and propagation of uncertainty in process conditions and initial microstructure on the final product properties in a deformation process are presented. The stochastic deformation problem is modeled using a sparse grid collocation approach that allows the utilization of a deterministic simulator to build interpolants of the main solution variables in the stochastic support space. The ability of the method in estimating the statistics of the macro-scale microstructure-sensitive properties and constructing the convex hull of these properties is shown through examples featuring randomness in initial texture and process parameters. A data-driven model reduction methodology together with a maximum entropy approach are used for representing randomness in initial texture in Rodrigues space. Comparisons are made with the results obtained from the Monte-Carlo method.