Neural Autoencoder-Based Structure-Preserving Model Order Reduction and Control Design for High-Dimensional Physical Systems

• URL: http://arxiv.org/abs/2312.06256v1
• Date: Mon, 11 Dec 2023 09:52:25 GMT
• Title: Neural Autoencoder-Based Structure-Preserving Model Order Reduction and Control Design for High-Dimensional Physical Systems
• Abstract summary: This work concerns control-oriented and structure-preserving learning of low-dimensional approximations of high-dimensional physical systems. We introduce a model-based controller that exploits the mathematical structure of the compressed model to regulate the configuration of heavily under mechanical systems.
• Score: 17.430588392066333
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This work concerns control-oriented and structure-preserving learning of low-dimensional approximations of high-dimensional physical systems, with a focus on mechanical systems. We investigate the integration of neural autoencoders in model order reduction, while at the same time preserving Hamiltonian or Lagrangian structures. We focus on extensively evaluating the considered methodology by performing simulation and control experiments on large mass-spring-damper networks, with hundreds of states. The empirical findings reveal that compressed latent dynamics with less than 5 degrees of freedom can accurately reconstruct the original systems' transient and steady-state behavior with a relative total error of around 4\%, while simultaneously accurately reconstructing the total energy. Leveraging this system compression technique, we introduce a model-based controller that exploits the mathematical structure of the compressed model to regulate the configuration of heavily underactuated mechanical systems.

Related papers

• Controlled Dynamics Attractor Transformer [58.15454173718687]
  Transformer architectures have advanced representation learning and inference in deep models through self-attention mechanisms.<n>In parallel,associative memory (AM) frameworks map representations onto energy landscapes, offering interpretable retrieval mechanisms.<n>We propose Controlled Dynamics Attractor Transformer (CCAT), which couples a mixture von Mises-Fisher (Mo-vMF) attention energy with a Hopfield refinement energy.<n>CCAT achieves state-of-the-art performance across multiple benchmarks in graph anomaly detection and graph classification.
  arXiv  Detail & Related papers  (2026-06-13T09:04:22Z)
• Shape Control of a Planar Hyper-Redundant Robot via Hybrid Kinematics-Informed and Learning-based Approach [42.55947704321053]
  Hyper-redundant robots offer high dexterity, making them good at operating in confined and unstructured environments.<n>To extend the reachable workspace, we built a multi-segment flexible rack actuated planar robot.<n>We propose a hybrid kinematics-informed and learning-based shape control method, named SpatioCoupledNet.
  arXiv  Detail & Related papers  (2026-03-11T04:35:06Z)
• Learning Hamiltonians for solid-state quantum simulators [0.0]
  We introduce a generalizable framework for learning to identify effective Hamiltonians directly from experimental data in solid-state quantum systems.<n>Our approach is based on a physics-informed neural network architecture that embeds physical constraints directly into the model structure.
  arXiv  Detail & Related papers  (2026-03-03T11:37:43Z)
• Reduced-order Control and Geometric Structure of Learned Lagrangian Latent Dynamics [16.958692029614994]
  This paper introduces a latent control framework based on learned structure-preserving reduced-order dynamics for high-dimensional Lagrangian systems.<n>By quantifying the sources of modeling error, we derive interpretable conditions for stability and convergence.<n>We extend the proposed controller and analysis to underactuated systems by introducing learned actuation patterns.
  arXiv  Detail & Related papers  (2026-02-09T18:00:04Z)
• Efficiency of Dynamical Decoupling for (Almost) Any Spin-Boson Model [44.99833362998488]
  We analytically study the dynamical decoupling of a two-level system coupled with a structured bosonic environment.<n>We find sufficient conditions under which dynamical decoupling works for such systems.<n>Our bounds reproduce the correct scaling in various relevant system parameters.
  arXiv  Detail & Related papers  (2024-09-24T04:58:28Z)
• Symplectic Autoencoders for Model Reduction of Hamiltonian Systems [0.0]
  It is crucial to preserve the symplectic structure associated with the system in order to ensure long-term numerical stability. We propose a new neural network architecture in the spirit of autoencoders, which are established tools for dimension reduction. In order to train the network, a non-standard gradient descent approach is applied.
  arXiv  Detail & Related papers  (2023-12-15T18:20:25Z)
• TANGO: Time-Reversal Latent GraphODE for Multi-Agent Dynamical Systems [43.39754726042369]
  We propose a simple-yet-effective self-supervised regularization term as a soft constraint that aligns the forward and backward trajectories predicted by a continuous graph neural network-based ordinary differential equation (GraphODE) It effectively imposes time-reversal symmetry to enable more accurate model predictions across a wider range of dynamical systems under classical mechanics. Experimental results on a variety of physical systems demonstrate the effectiveness of our proposed method.
  arXiv  Detail & Related papers  (2023-10-10T08:52:16Z)
• From NeurODEs to AutoencODEs: a mean-field control framework for width-varying Neural Networks [68.8204255655161]
  We propose a new type of continuous-time control system, called AutoencODE, based on a controlled field that drives dynamics. We show that many architectures can be recovered in regions where the loss function is locally convex.
  arXiv  Detail & Related papers  (2023-07-05T13:26:17Z)
• Capturing dynamical correlations using implicit neural representations [85.66456606776552]
  We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data. In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
  arXiv  Detail & Related papers  (2023-04-08T07:55:36Z)
• Physics-Inspired Temporal Learning of Quadrotor Dynamics for Accurate Model Predictive Trajectory Tracking [76.27433308688592]
  Accurately modeling quadrotor's system dynamics is critical for guaranteeing agile, safe, and stable navigation. We present a novel Physics-Inspired Temporal Convolutional Network (PI-TCN) approach to learning quadrotor's system dynamics purely from robot experience. Our approach combines the expressive power of sparse temporal convolutions and dense feed-forward connections to make accurate system predictions.
  arXiv  Detail & Related papers  (2022-06-07T13:51:35Z)
• End-to-End Learning of Hybrid Inverse Dynamics Models for Precise and Compliant Impedance Control [16.88250694156719]
  We present a novel hybrid model formulation that enables us to identify fully physically consistent inertial parameters of a rigid body dynamics model. We compare our approach against state-of-the-art inverse dynamics models on a 7 degree of freedom manipulator.
  arXiv  Detail & Related papers  (2022-05-27T07:39:28Z)
• Real-time Neural-MPC: Deep Learning Model Predictive Control for Quadrotors and Agile Robotic Platforms [59.03426963238452]
  We present Real-time Neural MPC, a framework to efficiently integrate large, complex neural network architectures as dynamics models within a model-predictive control pipeline. We show the feasibility of our framework on real-world problems by reducing the positional tracking error by up to 82% when compared to state-of-the-art MPC approaches without neural network dynamics.
  arXiv  Detail & Related papers  (2022-03-15T09:38:15Z)
• 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)
• Using scientific machine learning for experimental bifurcation analysis of dynamic systems [2.204918347869259]
  This study focuses on training universal differential equation (UDE) models for physical nonlinear dynamical systems with limit cycles. We consider examples where training data is generated by numerical simulations, whereas we also employ the proposed modelling concept to physical experiments. We use both neural networks and Gaussian processes as universal approximators alongside the mechanistic models to give a critical assessment of the accuracy and robustness of the UDE modelling approach.
  arXiv  Detail & Related papers  (2021-10-22T15:43:03Z)
• Sparsity in Partially Controllable Linear Systems [56.142264865866636]
  We study partially controllable linear dynamical systems specified by an underlying sparsity pattern. Our results characterize those state variables which are irrelevant for optimal control.
  arXiv  Detail & Related papers  (2021-10-12T16:41:47Z)
• Constrained Block Nonlinear Neural Dynamical Models [1.3163098563588727]
  Neural network modules conditioned by known priors can be effectively trained and combined to represent systems with nonlinear dynamics. The proposed method consists of neural network blocks that represent input, state, and output dynamics with constraints placed on the network weights and system variables. We evaluate the performance of the proposed architecture and training methods on system identification tasks for three nonlinear systems.
  arXiv  Detail & Related papers  (2021-01-06T04:27:54Z)
• Prediction with Approximated Gaussian Process Dynamical Models [7.678864239473703]
  We present approximated GPDMs which are Markov and analyze their control theoretical properties. The outcomes are illustrated with numerical examples that show the power of the approximated models.
  arXiv  Detail & Related papers  (2020-06-25T16:51:17Z)

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.