Towards Efficient Modelling of String Dynamics: A Comparison of State Space and Koopman based Deep Learning Methods

• URL: http://arxiv.org/abs/2408.16650v1
• Date: Thu, 29 Aug 2024 15:55:27 GMT
• Title: Towards Efficient Modelling of String Dynamics: A Comparison of State Space and Koopman based Deep Learning Methods
• Authors: Rodrigo Diaz, Carlos De La Vega Martin, Mark Sandler,
• Abstract summary: State Space Models (SSM) and Koopman-based deep learning methods for modelling the dynamics of both linear and non-linear stiff strings. Our findings indicate that our proposed Koopman-based model performs as well as or better than other existing approaches in non-linear cases for long-sequence modelling. This research contributes insights into the physical modelling of dynamical systems by offering a comparative overview of these and previous methods and introducing innovative strategies for model improvement.
• Score: 8.654571696634825
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: This paper presents an examination of State Space Models (SSM) and Koopman-based deep learning methods for modelling the dynamics of both linear and non-linear stiff strings. Through experiments with datasets generated under different initial conditions and sample rates, we assess the capacity of these models to accurately model the complex behaviours observed in string dynamics. Our findings indicate that our proposed Koopman-based model performs as well as or better than other existing approaches in non-linear cases for long-sequence modelling. We inform the design of these architectures with the structure of the problems at hand. Although challenges remain in extending model predictions beyond the training horizon (i.e., extrapolation), the focus of our investigation lies in the models' ability to generalise across different initial conditions within the training time interval. This research contributes insights into the physical modelling of dynamical systems (in particular those addressing musical acoustics) by offering a comparative overview of these and previous methods and introducing innovative strategies for model improvement. Our results highlight the efficacy of these models in simulating non-linear dynamics and emphasise their wide-ranging applicability in accurately modelling dynamical systems over extended sequences.

Related papers

• Deep Learning for Koopman Operator Estimation in Idealized Atmospheric Dynamics [2.2489531925874013]
  Deep learning is revolutionizing weather forecasting, with new data-driven models achieving accuracy on par with operational physical models for medium-term predictions. These models often lack interpretability, making their underlying dynamics difficult to understand and explain. This paper proposes methodologies to estimate the Koopman operator, providing a linear representation of complex nonlinear dynamics to enhance the transparency of data-driven models.
  arXiv  Detail & Related papers  (2024-09-10T13:56:54Z)
• Latent Space Energy-based Neural ODEs [73.01344439786524]
  This paper introduces a novel family of deep dynamical models designed to represent continuous-time sequence data. We train the model using maximum likelihood estimation with Markov chain Monte Carlo. Experiments on oscillating systems, videos and real-world state sequences (MuJoCo) illustrate that ODEs with the learnable energy-based prior outperform existing counterparts.
  arXiv  Detail & Related papers  (2024-09-05T18:14:22Z)
• Towards Learning Stochastic Population Models by Gradient Descent [0.0]
  We show that simultaneous estimation of parameters and structure poses major challenges for optimization procedures. We demonstrate accurate estimation of models but find that enforcing the inference of parsimonious, interpretable models drastically increases the difficulty.
  arXiv  Detail & Related papers  (2024-04-10T14:38:58Z)
• 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)
• Latent Variable Representation for Reinforcement Learning [131.03944557979725]
  It remains unclear theoretically and empirically how latent variable models may facilitate learning, planning, and exploration to improve the sample efficiency of model-based reinforcement learning. We provide a representation view of the latent variable models for state-action value functions, which allows both tractable variational learning algorithm and effective implementation of the optimism/pessimism principle. In particular, we propose a computationally efficient planning algorithm with UCB exploration by incorporating kernel embeddings of latent variable models.
  arXiv  Detail & Related papers  (2022-12-17T00:26:31Z)
• Homotopy-based training of NeuralODEs for accurate dynamics discovery [0.0]
  We develop a new training method for NeuralODEs, based on synchronization and homotopy optimization. We show that synchronizing the model dynamics and the training data tames the originally irregular loss landscape. Our method achieves competitive or better training loss while often requiring less than half the number of training epochs.
  arXiv  Detail & Related papers  (2022-10-04T06:32:45Z)
• Learning continuous models for continuous physics [94.42705784823997]
  We develop a test based on numerical analysis theory to validate machine learning models for science and engineering applications. Our results illustrate how principled numerical analysis methods can be coupled with existing ML training/testing methodologies to validate models for science and engineering applications.
  arXiv  Detail & Related papers  (2022-02-17T07:56:46Z)
• 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)
• Learning Dynamics Models for Model Predictive Agents [28.063080817465934]
  Model-Based Reinforcement Learning involves learning a textitdynamics model from data, and then using this model to optimise behaviour. This paper sets out to disambiguate the role of different design choices for learning dynamics models, by comparing their performance to planning with a ground-truth model.
  arXiv  Detail & Related papers  (2021-09-29T09:50:25Z)
• Autoregressive Dynamics Models for Offline Policy Evaluation and Optimization [60.73540999409032]
  We show that expressive autoregressive dynamics models generate different dimensions of the next state and reward sequentially conditioned on previous dimensions. We also show that autoregressive dynamics models are useful for offline policy optimization by serving as a way to enrich the replay buffer.
  arXiv  Detail & Related papers  (2021-04-28T16:48:44Z)
• Improving the Reconstruction of Disentangled Representation Learners via Multi-Stage Modeling [54.94763543386523]
  Current autoencoder-based disentangled representation learning methods achieve disentanglement by penalizing the ( aggregate) posterior to encourage statistical independence of the latent factors. We present a novel multi-stage modeling approach where the disentangled factors are first learned using a penalty-based disentangled representation learning method. Then, the low-quality reconstruction is improved with another deep generative model that is trained to model the missing correlated latent variables.
  arXiv  Detail & Related papers  (2020-10-25T18:51:15Z)

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.