Physical Modeling using Recurrent Neural Networks with Fast Convolutional Layers

• URL: http://arxiv.org/abs/2204.10125v1
• Date: Thu, 21 Apr 2022 14:22:44 GMT
• Title: Physical Modeling using Recurrent Neural Networks with Fast Convolutional Layers
• Authors: Julian D. Parker and Sebastian J. Schlecht and Rudolf Rabenstein and Maximilian Sch\"afer
• Abstract summary: We describe several novel recurrent neural network structures and show how they can be thought of as an extension of modal techniques. As a proof of concept, we generate synthetic data for three physical systems and show that the proposed network structures can be trained with this data to reproduce the behavior of these systems.
• Score: 1.7013938542585922
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Discrete-time modeling of acoustic, mechanical and electrical systems is a prominent topic in the musical signal processing literature. Such models are mostly derived by discretizing a mathematical model, given in terms of ordinary or partial differential equations, using established techniques. Recent work has applied the techniques of machine-learning to construct such models automatically from data for the case of systems which have lumped states described by scalar values, such as electrical circuits. In this work, we examine how similar techniques are able to construct models of systems which have spatially distributed rather than lumped states. We describe several novel recurrent neural network structures, and show how they can be thought of as an extension of modal techniques. As a proof of concept, we generate synthetic data for three physical systems and show that the proposed network structures can be trained with this data to reproduce the behavior of these systems.

Related papers

• Learning Governing Equations of Unobserved States in Dynamical Systems [0.0]
  We employ a hybrid neural ODE structure to learn governing equations of partially-observed dynamical systems. We demonstrate that the method is capable of successfully learning the true underlying governing equations of unobserved states within these systems.
  arXiv  Detail & Related papers  (2024-04-29T10:28:14Z)
• Mechanistic Neural Networks for Scientific Machine Learning [58.99592521721158]
  We present Mechanistic Neural Networks, a neural network design for machine learning applications in the sciences. It incorporates a new Mechanistic Block in standard architectures to explicitly learn governing differential equations as representations. Central to our approach is a novel Relaxed Linear Programming solver (NeuRLP) inspired by a technique that reduces solving linear ODEs to solving linear programs.
  arXiv  Detail & Related papers  (2024-02-20T15:23:24Z)
• Algebraic Dynamical Systems in Machine Learning [0.1843404256219181]
  We show that a function applied to the output of an iterated rewriting system defines a formal class of models. We also show that these algebraic models are a natural language for describing the compositionality of dynamic models. These models provide a template for the generalisation of the above dynamic models to learning problems on structured or non-numerical data.
  arXiv  Detail & Related papers  (2023-11-06T14:10:40Z)
• A Recursive Bateson-Inspired Model for the Generation of Semantic Formal Concepts from Spatial Sensory Data [77.34726150561087]
  This paper presents a new symbolic-only method for the generation of hierarchical concept structures from complex sensory data. The approach is based on Bateson's notion of difference as the key to the genesis of an idea or a concept. The model is able to produce fairly rich yet human-readable conceptual representations without training.
  arXiv  Detail & Related papers  (2023-07-16T15:59:13Z)
• 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)
• 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)
• Artificial neural network as a universal model of nonlinear dynamical systems [0.0]
  The map is built as an artificial neural network whose weights encode a modeled system. We consider the Lorenz system, the Roessler system and also Hindmarch-Rose neuron. High similarity is observed for visual images of attractors, power spectra, bifurcation diagrams and Lyapunovs exponents.
  arXiv  Detail & Related papers  (2021-03-06T16:02:41Z)
• Using Data Assimilation to Train a Hybrid Forecast System that Combines Machine-Learning and Knowledge-Based Components [52.77024349608834]
  We consider the problem of data-assisted forecasting of chaotic dynamical systems when the available data is noisy partial measurements. We show that by using partial measurements of the state of the dynamical system, we can train a machine learning model to improve predictions made by an imperfect knowledge-based model.
  arXiv  Detail & Related papers  (2021-02-15T19:56:48Z)
• 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)
• Learning Queuing Networks by Recurrent Neural Networks [0.0]
  We propose a machine-learning approach to derive performance models from data. We exploit a deterministic approximation of their average dynamics in terms of a compact system of ordinary differential equations. This allows for an interpretable structure of the neural network, which can be trained from system measurements to yield a white-box parameterized model.
  arXiv  Detail & Related papers  (2020-02-25T10:56:47Z)

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.