arXiv subjects

Jean C. Ragusa

Publications and source records attributed to Jean C. Ragusa.

5 recordsLinked to original sources

arXiv2026

scikit-rom: An Open-Source Python Platform for Teaching and Prototyping Projection-Based Reduced-Order Modeling

Projection-based reduced-order modeling (ROM) has become a cornerstone technique for accelerating parameter-intensive engineering simulations, yet the methodology remains challenging to teach and prototype. The difficulty stems from its multi-stage workflow, which encompasses snapshot generation, SVD/POD basis construction, Galerkin projection, offline-online decomposition, hyper-reduction, and error assessment. Existing software frameworks either abstract these stages behind high-level interfaces or depend on compiled, monolithic solver stacks that are difficult for students and early-stage researchers to inspect or modify. This paper introduces scikit-rom, an open-source Python library designed to make the complete projection-based ROM pipeline transparent, modifiable, and suitable for interactive notebook-based exploration. Built on the lightweight finite element backend scikit-fem, scikit-rom provides modular problem templates and dedicated facilities for snapshot generation, reduced-basis construction, reduced-operator assembly, online ROM solution, hyper-reduction, and quantitative accuracy assessment within a unified workflow. Hyper-reduction is supported through four strategies: the Discrete Empirical Interpolation Method (DEIM), S-OPT sampling, the Energy-Conserving Sampling and Weighting (ECSW) scheme, and ECM-style cubature construction. Four progressive worked examples guide the reader from full-order simulation to ROM and hyper-reduced model construction across linear, nonlinear, static, and transient problem classes. The library is intended for graduate-level instruction, intensive workshops, and research prototyping in the reduced-order modeling community. Source code and examples are available at github.com/suparnob100/scikit-rom, with documentation at scikitrom.github.io.

cs.CE↗

arXiv2026

Residual-Driven Lifting Identification for Nonlinear-Manifold Reduced-Order Models of Parametrized Linear PDEs

We introduce a residual-driven procedure for training nonlinear-manifold reduced-order models for parametrized linear partial differential equations that, given prescribed latent and lifting spaces, identifies the nonlinear lifting without high-fidelity solution snapshots. The approximation is represented by a low-dimensional latent coordinate together with a nonlinear lifting into a richer reduced space. Rather than fitting the lifting to snapshot data, we determine it by minimizing a computable residual-based upper bound for the state error. For affinely parametrized operators, the resulting training objective admits an efficient offline--online decomposition, and the lifting update reduces to a sequence of low-dimensional weighted least-squares problems. Numerical evaluations on an advection--diffusion problem and a plane-strain elasticity benchmark show that the proposed approach substantially improves accuracy over linear subspaces. The resulting nonlinear models achieve accuracy comparable to snapshot-driven nonlinear-manifold training while avoiding high-fidelity snapshots in the lifting-identification stage.

math.NA↗

arXiv2022

Parametric Dynamic Mode Decomposition for Reduced Order Modeling

Dynamic Mode Decomposition (DMD) is a model-order reduction approach, whereby spatial modes of fixed temporal frequencies are extracted from numerical or experimental data sets. The DMD low-rank or reduced operator is typically obtained by singular value decomposition of the temporal data sets. For parameter-dependent models, as found in many multi-query applications such as uncertainty quantification or design optimization, the only parametric DMD technique developed was a stacked approach, with data sets at multiples parameter values were aggregated together, increasing the computational work needed to devise low-rank dynamical reduced-order models. In this paper, we present two novel approach to carry out parametric DMD: one based on the interpolation of the reduced-order DMD eigenpair and the other based on the interpolation of the reduced DMD (Koopman) operator. Numerical results are presented for diffusion-dominated nonlinear dynamical problems, including a multiphysics radiative transfer example. All three parametric DMD approaches are compared.

math.NA↗

arXiv2020

Accelerating Training in Artificial Neural Networks with Dynamic Mode Decomposition

Training of deep neural networks (DNNs) frequently involves optimizing several millions or even billions of parameters. Even with modern computing architectures, the computational expense of DNN training can inhibit, for instance, network architecture design optimization, hyper-parameter studies, and integration into scientific research cycles. The key factor limiting performance is that both the feed-forward evaluation and the back-propagation rule are needed for each weight during optimization in the update rule. In this work, we propose a method to decouple the evaluation of the update rule at each weight. At first, Proper Orthogonal Decomposition (POD) is used to identify a current estimate of the principal directions of evolution of weights per layer during training based on the evolution observed with a few backpropagation steps. Then, Dynamic Mode Decomposition (DMD) is used to learn the dynamics of the evolution of the weights in each layer according to these principal directions. The DMD model is used to evaluate an approximate converged state when training the ANN. Afterward, some number of backpropagation steps are performed, starting from the DMD estimates, leading to an update to the principal directions and DMD model. This iterative process is repeated until convergence. By fine-tuning the number of backpropagation steps used for each DMD model estimation, a significant reduction in the number of operations required to train the neural networks can be achieved. In this paper, the DMD acceleration method will be explained in detail, along with the theoretical justification for the acceleration provided by DMD. This method is illustrated using a regression problem of key interest for the scientific machine learning community: the prediction of a pollutant concentration field in a diffusion, advection, reaction problem.

cs.LG↗

arXiv2019

Accelerating PDE-constrained Inverse Solutions with Deep Learning and Reduced Order Models

Inverse problems are pervasive mathematical methods in inferring knowledge from observational and experimental data by leveraging simulations and models. Unlike direct inference methods, inverse problem approaches typically require many forward model solves usually governed by Partial Differential Equations (PDEs). This a crucial bottleneck in determining the feasibility of such methods. While machine learning (ML) methods, such as deep neural networks (DNNs), can be employed to learn nonlinear forward models, designing a network architecture that preserves accuracy while generalizing to new parameter regimes is a daunting task. Furthermore, due to the computation-expensive nature of forward models, state-of-the-art black-box ML methods would require an unrealistic amount of work in order to obtain an accurate surrogate model. On the other hand, standard Reduced-Order Models (ROMs) accurately capture supposedly important physics of the forward model in the reduced subspaces, but otherwise could be inaccurate elsewhere. In this paper, we propose to enlarge the validity of ROMs and hence improve the accuracy outside the reduced subspaces by incorporating a data-driven ML technique. In particular, we focus on a goal-oriented approach that substantially improves the accuracy of reduced models by learning the error between the forward model and the ROM outputs. Once an ML-enhanced ROM is constructed it can accelerate the performance of solving many-query problems in parametrized forward and inverse problems. Numerical results for inverse problems governed by elliptic PDEs and parametrized neutron transport equations will be presented to support our approach.

physics.comp-ph↗