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This paper studies continuous-time stochastic control problems whose controlled states are fully non-Markovian and depend on unknown model parameters. Such problems arise naturally in path-dependent stochastic differential equations,…

Machine Learning · Statistics 2026-05-29 Dorival Leão , Alberto Ohashi , Simone Scotti , Adolfo M. D da Silva

The popularity of deep convolutional autoencoders (CAEs) has engendered new and effective reduced-order models (ROMs) for the simulation of large-scale dynamical systems. Despite this, it is still unknown whether deep CAEs provide superior…

Machine Learning · Computer Science 2022-03-14 Anthony Gruber , Max Gunzburger , Lili Ju , Zhu Wang

We propose an efficient retraining strategy for a parameterized Reduced Order Model (ROM) that attains accuracy comparable to full retraining while requiring only a fraction of the computational time and relying solely on sparse…

Machine Learning · Computer Science 2026-02-27 Ismaël Zighed , Andrea Nóvoa , Luca Magri , Taraneh Sayadi

Hamiltonian operator inference has been developed in [Sharma, H., Wang, Z., Kramer, B., Physica D: Nonlinear Phenomena, 431, p.133122, 2022] to learn structure-preserving reduced-order models (ROMs) for Hamiltonian systems. The method…

Numerical Analysis · Mathematics 2025-07-21 Yuwei Geng , Lili Ju , Boris Kramer , Zhu Wang

System identification has greatly benefited from deep learning techniques, particularly for modeling complex, nonlinear dynamical systems with partially unknown physics where traditional approaches may not be feasible. However, deep…

Machine Learning · Computer Science 2025-04-17 Marco Forgione , Ankush Chakrabarty , Dario Piga , Matteo Rufolo , Alberto Bemporad

Generally, reduced order models of fluid flows are obtained by projecting the Navier-Stokes equations onto a reduced subspace spanned by vector functions that carry the meaningful information of the dynamics. A common method to generate…

Fluid Dynamics · Physics 2023-09-22 M. Oulghelou , A. Ammar , R. Ayoub

Forecasting atmospheric flows with traditional discretization methods, also called full order methods (e.g., finite element methods or finite volume methods), is computationally expensive. We propose to reduce the computational cost with a…

Numerical Analysis · Mathematics 2025-04-03 Arash Hajisharifi , Michele Girfoglio , Annalisa Quaini , Gianluigi Rozza

Computationally cheap yet accurate dynamical models are a key requirement for real-time capable nonlinear optimization and model-based control. When given a computationally expensive high-order prediction model, a reduction to a lower-order…

Systems and Control · Electrical Eng. & Systems 2026-02-20 Jan C. Schulze , Alexander Mitsos

We apply the Proper Orthogonal Decomposition (POD) method for the efficient simulation of several scenarios undergone by Micro-Electro-Mechanical-Systems, involving nonlinearites of geometric and electrostatic nature. The former type of…

Numerical Analysis · Mathematics 2022-02-22 Gobat G. , Opreni A. , Fresca S. , Manzoni A. , Frangi A

Nonlinear reduced-order models (ROMs), represented by manifold learning (ML), can effectively improve the modeling accuracy of nonlinear flow fields with discontinuities. However, the inverse mapping from low-dimensional manifold…

Fluid Dynamics · Physics 2025-07-24 Weiji Wang , Chunlin Gong , Xuyi Jia , Chunna Li

This work investigates a two-stage method for constructing projection-based reduced-order models (ROMs) of parameterized partial differential equations (PDEs). Based on established tensorial ROM methodology, the proposed approach reduces…

Numerical Analysis · Mathematics 2026-04-30 Arjun Vijaywargia , Eric C. Cyr , Anthony Gruber

We describe an efficient domain decomposition-based framework for nonlinear multiscale PDE problems. The framework is inspired by manifold learning techniques and exploits the tangent spaces spanned by the nearest neighbors to compress…

Numerical Analysis · Mathematics 2021-11-10 Shi Chen , Qin Li , Jianfeng Lu , Stephen J. Wright

Construction of reduced-order models (ROMs) for hyperbolic conservation laws is notoriously challenging mainly due to the translational property and nonlinearity of the governing equations. While the Lagrangian framework for ROM…

Numerical Analysis · Mathematics 2020-03-30 Hannah Lu , Daniel M. Tartakovsky

Reduced-order models are central to motion planning and control of quadruped robots, yet existing templates are often hand-crafted for a specific locomotion modality. This motivates the need for automatic methods that extract task-specific,…

Robotics · Computer Science 2026-01-14 Gioele Buriani , Jingyue Liu , Maximilian Stölzle , Cosimo Della Santina , Jiatao Ding

This paper focuses on a new framework for reduced order modelling of non-intrusive data with application to 2D flows. To overcome the shortcomings of intrusive model order reduction usually derived by combining the POD and the Galerkin…

Numerical Analysis · Mathematics 2016-11-16 D. A. Bistrian , I. M. Navon

State estimation aims at approximately reconstructing the solution $u$ to a parametrized partial differential equation from $m$ linear measurements, when the parameter vector $y$ is unknown. Fast numerical recovery methods have been…

Numerical Analysis · Mathematics 2020-11-25 Albert Cohen , Wolfgang Dahmen , Olga Mula , James Nichols

High-dimensional nonlinear systems pose considerable challenges for modeling and control across many domains, from fluid mechanics to advanced robotics. Such systems are typically approximated with reduced-order models, which often rely on…

Systems and Control · Electrical Eng. & Systems 2025-09-05 Hugo Buurmeijer , Luis A. Pabon , John Irvin Alora , Roshan S. Kaundinya , George Haller , Marco Pavone

Scientific and engineering processes deliver massive high-dimensional data sets that are generated as non-linear transformations of an initial state and few process parameters. Mapping such data to a low-dimensional manifold facilitates…

Machine Learning · Statistics 2018-08-07 Frank Schoeneman , Varun Chandola , Nils Napp , Olga Wodo , Jaroslaw Zola

In recent years, deep learning has gained increasing popularity in the fields of Partial Differential Equations (PDEs) and Reduced Order Modeling (ROM), providing domain practitioners with new powerful data-driven techniques such as…

Numerical Analysis · Mathematics 2024-06-25 Nicola Rares Franco , Simone Brugiapaglia

Model order reduction provides low-complexity high-fidelity surrogate models that allow rapid and accurate solutions of parametric differential equations. The development of reduced order models for parametric \emph{nonlinear} Hamiltonian…

Numerical Analysis · Mathematics 2024-09-30 Cecilia Pagliantini , Federico Vismara