Second-order AAA algorithms for structured data-driven modeling

• URL: http://arxiv.org/abs/2506.02241v1
• Date: Mon, 02 Jun 2025 20:34:18 GMT
• Title: Second-order AAA algorithms for structured data-driven modeling
• Authors: Michael S. Ackermann, Ion Victor Gosea, Serkan Gugercin, Steffen W. R. Werner,
• Abstract summary: We present three data-driven modeling approaches for the construction of dynamical systems with second-order differential structure directly from frequency domain data.<n>Based on the second-order structured barycentric form, we extend the well-known Adaptive Antoulas-Anderson algorithm to the case of second-order systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The data-driven modeling of dynamical systems has become an essential tool for the construction of accurate computational models from real-world data. In this process, the inherent differential structures underlying the considered physical phenomena are often neglected making the reinterpretation of the learned models in a physically meaningful sense very challenging. In this work, we present three data-driven modeling approaches for the construction of dynamical systems with second-order differential structure directly from frequency domain data. Based on the second-order structured barycentric form, we extend the well-known Adaptive Antoulas-Anderson algorithm to the case of second-order systems. Depending on the available computational resources, we propose variations of the proposed method that prioritize either higher computation speed or greater modeling accuracy, and we present a theoretical analysis for the expected accuracy and performance of the proposed methods. Three numerical examples demonstrate the effectiveness of our new structured approaches in comparison to classical unstructured data-driven modeling.

Related papers

• Random Matrix Theory for Deep Learning: Beyond Eigenvalues of Linear Models [51.85815025140659]
  Modern Machine Learning (ML) and Deep Neural Networks (DNNs) often operate on high-dimensional data.<n>In particular, the proportional regime where the data dimension, sample size, and number of model parameters are all large gives rise to novel and sometimes counterintuitive behaviors.<n>This paper extends traditional Random Matrix Theory (RMT) beyond eigenvalue-based analysis of linear models to address the challenges posed by nonlinear ML models.
  arXiv  Detail & Related papers  (2025-06-16T06:54:08Z)
• Generalized Factor Neural Network Model for High-dimensional Regression [50.554377879576066]
  We tackle the challenges of modeling high-dimensional data sets with latent low-dimensional structures hidden within complex, non-linear, and noisy relationships.<n>Our approach enables a seamless integration of concepts from non-parametric regression, factor models, and neural networks for high-dimensional regression.
  arXiv  Detail & Related papers  (2025-02-16T23:13:55Z)
• Hybrid Adaptive Modeling using Neural Networks Trained with Nonlinear Dynamics Based Features [5.652228574188242]
  This paper introduces a novel approach that departs from standard techniques by uncovering information from nonlinear dynamical modeling and embedding it in data-based models.<n>By explicitly incorporating nonlinear dynamic phenomena through perturbation methods, the predictive capabilities are more realistic and insightful compared to knowledge obtained from brute-force numerical simulations.
  arXiv  Detail & Related papers  (2025-01-21T02:38:28Z)
• Automatically Learning Hybrid Digital Twins of Dynamical Systems [56.69628749813084]
  Digital Twins (DTs) simulate the states and temporal dynamics of real-world systems. DTs often struggle to generalize to unseen conditions in data-scarce settings. In this paper, we propose an evolutionary algorithm ($textbfHDTwinGen$) to autonomously propose, evaluate, and optimize HDTwins.
  arXiv  Detail & Related papers  (2024-10-31T07:28:22Z)
• A parametric framework for kernel-based dynamic mode decomposition using deep learning [0.0]
  The proposed framework consists of two stages, offline and online. The online stage leverages those LANDO models to generate new data at a desired time instant. dimensionality reduction technique is applied to high-dimensional dynamical systems to reduce the computational cost of training.
  arXiv  Detail & Related papers  (2024-09-25T11:13:50Z)
• Solving Inverse Problems with Model Mismatch using Untrained Neural Networks within Model-based Architectures [14.551812310439004]
  We introduce an untrained forward model residual block within the model-based architecture to match the data consistency in the measurement domain for each instance. Our approach offers a unified solution that is less parameter-sensitive, requires no additional data, and enables simultaneous fitting of the forward model and reconstruction in a single pass.
  arXiv  Detail & Related papers  (2024-03-07T19:02:13Z)
• eXponential FAmily Dynamical Systems (XFADS): Large-scale nonlinear Gaussian state-space modeling [9.52474299688276]
  We introduce a low-rank structured variational autoencoder framework for nonlinear state-space graphical models. We show that our approach consistently demonstrates the ability to learn a more predictive generative model.
  arXiv  Detail & Related papers  (2024-03-03T02:19:49Z)
• Data-Driven Model Selections of Second-Order Particle Dynamics via Integrating Gaussian Processes with Low-Dimensional Interacting Structures [0.9821874476902972]
  We focus on the data-driven discovery of a general second-order particle-based model. We present applications to modeling two real-world fish motion datasets.
  arXiv  Detail & Related papers  (2023-11-01T23:45:15Z)
• Robust Graph Representation Learning via Predictive Coding [46.22695915912123]
  Predictive coding is a message-passing framework initially developed to model information processing in the brain. In this work, we build models that rely on the message-passing rule of predictive coding. We show that the proposed models are comparable to standard ones in terms of performance in both inductive and transductive tasks.
  arXiv  Detail & Related papers  (2022-12-09T03:58:22Z)
• Discrepancy Modeling Framework: Learning missing physics, modeling systematic residuals, and disambiguating between deterministic and random effects [4.459306403129608]
  In modern dynamical systems, discrepancies between model and measurement can lead to poor quantification. We introduce a discrepancy modeling framework to identify the missing physics and resolve the model-measurement mismatch.
  arXiv  Detail & Related papers  (2022-03-10T05:37:24Z)
• Leveraging the structure of dynamical systems for data-driven modeling [111.45324708884813]
  We consider the impact of the training set and its structure on the quality of the long-term prediction. We show how an informed design of the training set, based on invariants of the system and the structure of the underlying attractor, significantly improves the resulting models.
  arXiv  Detail & Related papers  (2021-12-15T20:09:20Z)
• Constructing Neural Network-Based Models for Simulating Dynamical Systems [59.0861954179401]
  Data-driven modeling is an alternative paradigm that seeks to learn an approximation of the dynamics of a system using observations of the true system. This paper provides a survey of the different ways to construct models of dynamical systems using neural networks. In addition to the basic overview, we review the related literature and outline the most significant challenges from numerical simulations that this modeling paradigm must overcome.
  arXiv  Detail & Related papers  (2021-11-02T10:51:42Z)
• Improved Surrogate Modeling of Fluid Dynamics with Physics-Informed Neural Networks [0.0]
  PINNs have recently shown great promise as a way of incorporating physics-based domain knowledge, including fundamental governing equations, into neural network models. Here, we explore the use of this modeling methodology to surrogate modeling of a fluid dynamical system. We show that the inclusion of a physics-based regularization term can substantially improve the equivalent data-driven surrogate model.
  arXiv  Detail & Related papers  (2021-05-05T02:23:20Z)
• Model-Based Deep Learning [155.063817656602]
  Signal processing, communications, and control have traditionally relied on classical statistical modeling techniques. Deep neural networks (DNNs) use generic architectures which learn to operate from data, and demonstrate excellent performance. We are interested in hybrid techniques that combine principled mathematical models with data-driven systems to benefit from the advantages of both approaches.
  arXiv  Detail & Related papers  (2020-12-15T16:29:49Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.