Data-Driven Model Reduction via Non-intrusive Optimization of Projection Operators and Reduced-Order Dynamics

SIAM Journal on Applied Dynamical Systems, Journal Year: 2024, Volume and Issue: 23(4), P. 3052 - 3076

Published: Dec. 11, 2024

Language: Английский

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Reconstructing attractors with autoencoders

Chaos An Interdisciplinary Journal of Nonlinear Science, Journal Year: 2025, Volume and Issue: 35(1)

Published: Jan. 1, 2025

We propose a method based on autoencoders to reconstruct attractors from recorded footage, preserving the topology of underlying phase space. provide theoretical support and test with (i) footage temperature stream function fields involved in Lorenz atmospheric convection problem (ii) time series obtained by integrating Rössler equations.

Language: Английский

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Stability analysis of chaotic systems in latent spaces

Nonlinear Dynamics, Journal Year: 2025, Volume and Issue: unknown

Published: Feb. 4, 2025

Partial differential equations, and their chaotic solutions, are pervasive in the modelling of complex systems engineering, science, beyond. Data-driven methods can find solutions to partial equations with a divide-and-conquer strategy: The solution is sought latent space, on which temporal dynamics inferred ("latent-space" approach). This achieved by, first, compressing data an autoencoder, and, second, inferring recurrent neural networks. overarching goal this paper show that latent-space approach not only infer equation, but it also predict stability properties physical system. First, we employ convolutional autoencoder echo state network (CAE-ESN) Kuramoto-Sivashinsky equation for various regimes. We CAE-ESN (i) finds low-dimensional representation observations (ii) accurately infers Lyapunov exponents covariant vectors (CLVs) manifold different attractors. Second, extend turbulent flow, comparing spectrum estimates obtained from Jacobian-free methods. A based effectively produces space preserves key system, such as CLVs, thus retaining geometric structure attractor. reduced-order model predicts or, alternatively, be used data.

Language: Английский

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Entropy-Stable Model Reduction of One-Dimensional Hyperbolic Systems using Rational Quadratic Manifolds

Journal of Computational Physics, Journal Year: 2025, Volume and Issue: unknown, P. 113817 - 113817

Published: Feb. 1, 2025

Language: Английский

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Data-driven nonlinear model reduction to spectral submanifolds via oblique projection

Chaos An Interdisciplinary Journal of Nonlinear Science, Journal Year: 2025, Volume and Issue: 35(4)

Published: April 1, 2025

The dynamics in a primary spectral submanifold (SSM) constructed over the slowest modes of dynamical system provide an ideal reduced-order model for nearby trajectories. Modeling trajectories further away from SSM, however, is difficult if linear part exhibits strong non-normal behavior. Such non-normality implies that simply projecting onto SSMs along directions normal to slow will not pair those correctly with their reduced counterparts on SSMs. In principle, well-defined nonlinear projection stable invariant foliation exists and would exactly match full SSM-reduced dynamics. This foliation, cannot realistically be practically feasible amounts distributions experimental data. Here, we develop oblique technique able approximate this efficiently, even single trajectory significantly beam.

Language: Английский

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Nonlinear model reduction from equations and data

Chaos An Interdisciplinary Journal of Nonlinear Science, Journal Year: 2024, Volume and Issue: 34(9)

Published: Sept. 1, 2024

Modeling in applied science and engineering targets increasingly ambitious objectives, which typically yield complex models. Despite major advances computations, simulating such models with exceedingly high dimensions remains a challenge. Even if technically feasible, numerical simulations on high-dimensional problems do not necessarily give the simplified insight into these phenomena that motivated their initial Reduced-order hold more promise for quick assessment of changes under parameters uncertainties, as well effective prediction control. Such are also highly desirable systems only known form data sets. This focus issue will survey latest trends nonlinear model reduction equations sets across various fields applications, ranging from computational to theoretical aspects.

Language: Английский

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A multi-task learning framework for aerodynamic computation of two-dimensional airfoils

Physics of Fluids, Journal Year: 2024, Volume and Issue: 36(11)

Published: Nov. 1, 2024

Accurate and efficient prediction of airfoil aerodynamic coefficients is essential for improving aircraft performance. However, current research often encounters significant challenges in balancing accuracy with computational efficiency when predicting complex coefficients. In this paper, a Multi-Task Learning framework Aerodynamic parameters Computation (MTL4AC) two-dimensional (2D) airfoils proposed. The MTL4AC processes two key subtasks: flow field pressure coefficient prediction. These subtasks complement each other to reveal both global local changes around the airfoil. provides coarse-grained perspective, which focuses on velocity variations surface. offers fine-grained concentrates distribution surface accurately calculate lift drag demonstrated substantial improvements experiments conducted public dataset, achieving enhancements stability. This contributes an accurate computation, integrating geometric features advanced multi-task learning techniques achieve superior performance

Language: Английский

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Model reduction on manifolds: A differential geometric framework

Physica D Nonlinear Phenomena, Journal Year: 2024, Volume and Issue: 468, P. 134299 - 134299

Published: July 25, 2024

Using nonlinear projections and preserving structure in model order reduction (MOR) are currently active research fields. In this paper, we provide a novel differential geometric framework for on smooth manifolds, which emphasizes the nature of objects involved. The crucial ingredient is construction an embedding low-dimensional submanifold compatible map, discuss several options. Our general allows capturing generalizing existing MOR techniques, such as preservation Lagrangian- or Hamiltonian dynamics, using that are, instance, relevant transport-dominated problems. joint abstraction can be used to derive shared theoretical properties different methods, exact reproduction result. To connect our work field, demonstrate various techniques data-driven included framework.

Language: Английский

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An adaptive learning strategy for surrogate modeling of high-dimensional functions - Application to unsteady hypersonic flows in chemical nonequilibrium

Computer Physics Communications, Journal Year: 2024, Volume and Issue: unknown, P. 109404 - 109404

Published: Oct. 1, 2024

Language: Английский

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Machine Learning in Viscoelastic Fluids Via Energy-Based Kernel Embedding

Published: Jan. 1, 2024

The ability to measure differences in collected data is of fundamental importance for quantitative science and machine learning, motivating the establishment metrics grounded physical principles. In this study, we focus on development such viscoelastic fluid flows governed by a large class linear nonlinear stress models. To do this, introduce kernel function corresponding given model that implicitly embeds flowfield snapshots into Reproducing Kernel Hilbert Space (RKHS) whose squared norm equals total mechanical energy.Working with lifted representations RKHS via provides natural unambiguous distances angles between flowfields without need hyperparameter tuning.Additionally, present solution preimage problem our kernels, enabling accurate reconstruction from their representations.Through numerical experiments an unsteady lid-driven cavity flow, demonstrate utility kernels extracting energetically-dominant coherent structures across range Reynolds Weissenberg numbers.Specifically, features extracted Principal Component Analysis (KPCA) using functions yield reconstructions superior accuracy terms energy compared conventional methods as ordinary (PCA) naively-defined state vectors or KPCA ad-hoc choices functions.Our findings underscore principled both scientific learning investigations complex systems.

Language: Английский

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