Proper Orthogonal Decomposition

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Evaluating Hybrid Quantum-Classical Models for Reduced-Order Brain Deformation Dynamics
Sep 30, 2026Tao Liu, Ge He, Dongyu Liang +1Time Series Forecasting Proper Orthogonal Decomposition
Lawrence Technological University · North Carolina State University
The balance between compactness and forecast accuracy of data-driven latent-space reduced-order models in controlled wake flows
Jul 27, 2026Alberto Solera-Rico, Patricia García-Caspueñas, Carlos Sanmiguel Vila +1Variational Autoencoders Latent Dynamics Modeling
Sub-directorate general of aeronautical systems, Spanish National Institute for Aerospace Technology (INTA), ctra. M-301, km. 10.5, 28330 San Mart´ın de la Vega, Madrid, Spain. · Departamento de Ingenier´ıa Aeroespacial, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Legan´es, Madrid, Spain. · Department of Mechanical Engineering, University of Washington, 1410 NE Campus Parkway, Seattle, WA 98195, USA.
Reduced-Order Models: The Mother of World Models
Jul 3, 2026Rajat GhoshWorld Models Action-Conditioned World Models
Independent Researcher
Patch-PODiff-ViT: Structured Latent Diffusion with Patchwise POD for Super-Resolution and Uncertainty Quantification
Jun 30, 2026Onkar Jadhav, Tim French, Matthew Rayson +1Diffusion Models for Image Restoration Uncertainty Quantification
School of Earth and Oceans, UWA Oceans Institute University of Western Australia Crawley, WA, Australia · School of Physics, Mathematics and Computing, Computer Science and Software Engineering University of Western Australia Crawley, WA, Australia
Multiscale POD of Transformer Attention Fields: Scale-Selective Analysis via Morlet Scalogram
Jun 4, 2026Athanasios ZerisTransformer Interpretability Proper Orthogonal Decomposition
Independent Researcher, Athens, Greece.
CFDTwin: An open-source GUI and Python toolkit for POD-NN surrogate modeling of ANSYS Fluent simulations
May 26, 2026Daniel Curl, Han HuPDE Surrogate Modeling Proper Orthogonal Decomposition
Department of Mechanical Engineering, University of Arkansas, Fayetteville, AR 72701, USA
NSPOD: Accelerating Krylov solvers via DeepONet-learned POD subspaces
May 8, 2026Francesc Levrero-Florencio, Youngkyu Lee, Jay Pathak +1PDE Solving Structural Mechanics
Synopsys UK Ltd, UK · Division of Applied Mathematics, Brown University, Rhode Island, USA · Synopsys Inc, California, USA
PODiff: Latent Diffusion in Proper Orthogonal Decomposition Space for Scientific Super-Resolution
May 5, 2026Onkar Jadhav, Tim French, Matthew Rayson +1Uncertainty Quantification Proper Orthogonal Decomposition
School of Earth and Oceans, UWA Oceans Institute, University of Western Australia, Crawley, WA, Australia · School of Physics, Mathematics and Computing, Computer Science and Software Engineering, University of Western Australia, Crawley, WA, Australia.

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Evaluating Hybrid Quantum-Classical Models for Reduced-Order Brain Deformation Dynamics

Tao Liu, Ge He, Dongyu Liang, Wujie Wen

Lawrence Technological University · North Carolina State University

Time Series Forecasting Proper Orthogonal Decomposition Hybrid Quantum-Classical ML Reduced-Order Modeling Variational Quantum Circuits

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We evaluate hybrid quantum-classical machine learning for the reduced-order prediction of spatiotemporal brain deformation fields. To mitigate the computational intractability of high-dimensional displacement fields, we employ Proper Orthogonal Decomposition (POD) to project the data into a compact latent space. Within this framework, we formulate two distinct learning objectives: static temporal-to-latent regression and autoregressive latent state forecasting. We systematically benchmark compact classical baselines against both minimal and enhanced hybrid quantum architectures. Our results demonstrate that classical networks provide the strongest baselines in the present setting. For static regression, a classical POD-MLP outperforms all evaluated quantum variants, although an enhanced Variational Quantum Circuit (VQC) substantially improves upon a minimal VQC baseline. For temporal forecasting, a classical POD-LSTM delivers superior predictive accuracy and statistical robustness compared to an enhanced Quantum LSTM (QLSTM) across varying history windows and random initializations. Overall, this study establishes reduced-order physical field learning as a rigorous testbed for near-term QML, highlighting that while hybrid enhancements successfully recover expressivity in weak quantum circuits, classical architectures retain a definitive advantage in both fidelity and stability.