Identifying latent state transition in non-linear dynamical systems

• URL: http://arxiv.org/abs/2406.03337v2
• Date: Thu, 6 Jun 2024 06:27:57 GMT
• Title: Identifying latent state transition in non-linear dynamical systems
• Authors: Çağlar Hızlı, Çağatay Yıldız, Matthias Bethge, ST John, Pekka Marttinen,
• Abstract summary: This work aims to improve generalization and interpretability of dynamical systems by recovering the underlying lower-dimensional latent states and their time evolutions. Inspired by the advances in nonlinear ICA, we propose a state-space modeling framework in which we can identify not just the latent states but also the unknown transition function that maps the past states to the present.
• Score: 12.875635969116683
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This work aims to improve generalization and interpretability of dynamical systems by recovering the underlying lower-dimensional latent states and their time evolutions. Previous work on disentangled representation learning within the realm of dynamical systems focused on the latent states, possibly with linear transition approximations. As such, they cannot identify nonlinear transition dynamics, and hence fail to reliably predict complex future behavior. Inspired by the advances in nonlinear ICA, we propose a state-space modeling framework in which we can identify not just the latent states but also the unknown transition function that maps the past states to the present. We introduce a practical algorithm based on variational auto-encoders and empirically demonstrate in realistic synthetic settings that we can (i) recover latent state dynamics with high accuracy, (ii) correspondingly achieve high future prediction accuracy, and (iii) adapt fast to new environments.

Related papers

• Automated Global Analysis of Experimental Dynamics through Low-Dimensional Linear Embeddings [3.825457221275617]
  We introduce a data-driven computational framework to derive low-dimensional linear models for nonlinear dynamical systems. This framework enables global stability analysis through interpretable linear models that capture the underlying system structure. Our method offers a promising pathway to analyze complex dynamical behaviors across fields such as physics, climate science, and engineering.
  arXiv  Detail & Related papers  (2024-11-01T19:27:47Z)
• Latent Space Energy-based Neural ODEs [73.01344439786524]
  This paper introduces novel deep dynamical models designed to represent continuous-time sequences. We train the model using maximum likelihood estimation with Markov chain Monte Carlo. Experimental results on oscillating systems, videos and real-world state sequences (MuJoCo) demonstrate that our model with the learnable energy-based prior outperforms existing counterparts.
  arXiv  Detail & Related papers  (2024-09-05T18:14:22Z)
• 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)
• A Poisson-Gamma Dynamic Factor Model with Time-Varying Transition Dynamics [51.147876395589925]
  A non-stationary PGDS is proposed to allow the underlying transition matrices to evolve over time. A fully-conjugate and efficient Gibbs sampler is developed to perform posterior simulation. Experiments show that, in comparison with related models, the proposed non-stationary PGDS achieves improved predictive performance.
  arXiv  Detail & Related papers  (2024-02-26T04:39:01Z)
• A Priori Denoising Strategies for Sparse Identification of Nonlinear Dynamical Systems: A Comparative Study [68.8204255655161]
  We investigate and compare the performance of several local and global smoothing techniques to a priori denoise the state measurements. We show that, in general, global methods, which use the entire measurement data set, outperform local methods, which employ a neighboring data subset around a local point.
  arXiv  Detail & Related papers  (2022-01-29T23:31:25Z)
• Likelihood-Free Inference in State-Space Models with Unknown Dynamics [71.94716503075645]
  We introduce a method for inferring and predicting latent states in state-space models where observations can only be simulated, and transition dynamics are unknown. We propose a way of doing likelihood-free inference (LFI) of states and state prediction with a limited number of simulations.
  arXiv  Detail & Related papers  (2021-11-02T12:33:42Z)
• Physics-guided Deep Markov Models for Learning Nonlinear Dynamical Systems with Uncertainty [6.151348127802708]
  We propose a physics-guided framework, termed Physics-guided Deep Markov Model (PgDMM) The proposed framework takes advantage of the expressive power of deep learning, while retaining the driving physics of the dynamical system.
  arXiv  Detail & Related papers  (2021-10-16T16:35:12Z)
• Value Iteration in Continuous Actions, States and Time [99.00362538261972]
  We propose a continuous fitted value iteration (cFVI) algorithm for continuous states and actions. The optimal policy can be derived for non-linear control-affine dynamics. Videos of the physical system are available at urlhttps://sites.google.com/view/value-iteration.
  arXiv  Detail & Related papers  (2021-05-10T21:40:56Z)
• Physics-aware, probabilistic model order reduction with guaranteed stability [0.0]
  We propose a generative framework for learning an effective, lower-dimensional, coarse-grained dynamical model. We demonstrate its efficacy and accuracy in multiscale physical systems of particle dynamics.
  arXiv  Detail & Related papers  (2021-01-14T19:16:51Z)
• Active Learning for Nonlinear System Identification with Guarantees [102.43355665393067]
  We study a class of nonlinear dynamical systems whose state transitions depend linearly on a known feature embedding of state-action pairs. We propose an active learning approach that achieves this by repeating three steps: trajectory planning, trajectory tracking, and re-estimation of the system from all available data. We show that our method estimates nonlinear dynamical systems at a parametric rate, similar to the statistical rate of standard linear regression.
  arXiv  Detail & Related papers  (2020-06-18T04:54:11Z)
• Neural Physicist: Learning Physical Dynamics from Image Sequences [0.6445605125467573]
  We present a novel architecture named Neural Physicist (NeurPhy) to learn physical dynamics directly from image sequences using deep neural networks. Our model can not only extract the physically meaningful state representations, but also learn the state transition dynamics enabling long-term predictions for unseen image sequences.
  arXiv  Detail & Related papers  (2020-06-09T04:36:51Z)

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.