On the Relationships between Graph Neural Networks for the Simulation of Physical Systems and Classical Numerical Methods

• URL: http://arxiv.org/abs/2304.00146v1
• Date: Fri, 31 Mar 2023 21:51:00 GMT
• Title: On the Relationships between Graph Neural Networks for the Simulation of Physical Systems and Classical Numerical Methods
• Authors: Artur P. Toshev, Ludger Paehler, Andrea Panizza and Nikolaus A. Adams
• Abstract summary: Recent developments in Machine Learning approaches for modelling physical systems have begun to mirror the past development of numerical methods in the computational sciences. We give an overview of simulation approaches, which have not yet found their way into state-of-the-art Machine Learning methods. We conclude by presenting an outlook on the potential of these approaches for making Machine Learning models for science more efficient.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Recent developments in Machine Learning approaches for modelling physical systems have begun to mirror the past development of numerical methods in the computational sciences. In this survey, we begin by providing an example of this with the parallels between the development trajectories of graph neural network acceleration for physical simulations and particle-based approaches. We then give an overview of simulation approaches, which have not yet found their way into state-of-the-art Machine Learning methods and hold the potential to make Machine Learning approaches more accurate and more efficient. We conclude by presenting an outlook on the potential of these approaches for making Machine Learning models for science more efficient.

Related papers

• Demolition and Reinforcement of Memories in Spin-Glass-like Neural Networks [0.0]
  The aim of this thesis is to understand the effectiveness of Unlearning in both associative memory models and generative models. The selection of structured data enables an associative memory model to retrieve concepts as attractors of a neural dynamics with considerable basins of attraction. A novel regularization technique for Boltzmann Machines is presented, proving to outperform previously developed methods in learning hidden probability distributions from data-sets.
  arXiv  Detail & Related papers  (2024-03-04T23:12:42Z)
• 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)
• Addressing computational challenges in physical system simulations with machine learning [0.0]
  We present a machine learning-based data generator framework tailored to aid researchers who utilize simulations to examine various physical systems or processes. Our approach involves a two-step process: first, we train a supervised predictive model using a limited simulated dataset to predict simulation outcomes. Subsequently, a reinforcement learning agent is trained to generate accurate, simulation-like data by leveraging the supervised model.
  arXiv  Detail & Related papers  (2023-05-16T17:31:50Z)
• Advancing Reacting Flow Simulations with Data-Driven Models [50.9598607067535]
  Key to effective use of machine learning tools in multi-physics problems is to couple them to physical and computer models. The present chapter reviews some of the open opportunities for the application of data-driven reduced-order modeling of combustion systems.
  arXiv  Detail & Related papers  (2022-09-05T16:48:34Z)
• 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)
• Measuring and modeling the motor system with machine learning [117.44028458220427]
  The utility of machine learning in understanding the motor system is promising a revolution in how to collect, measure, and analyze data. We discuss the growing use of machine learning: from pose estimation, kinematic analyses, dimensionality reduction, and closed-loop feedback, to its use in understanding neural correlates and untangling sensorimotor systems.
  arXiv  Detail & Related papers  (2021-03-22T12:42:16Z)
• 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)
• Using machine-learning modelling to understand macroscopic dynamics in a system of coupled maps [0.0]
  We consider a case study the macroscopic motion emerging from a system of globally coupled maps. We build a coarse-grained Markov process for the macroscopic dynamics both with a machine learning approach and with a direct numerical computation of the transition probability of the coarse-grained process. We are able to infer important information about the effective dimension of the attractor, the persistence of memory effects and the multi-scale structure of the dynamics.
  arXiv  Detail & Related papers  (2020-11-08T15:38:12Z)
• Physics-based polynomial neural networks for one-shot learning of dynamical systems from one or a few samples [0.0]
  The paper describes practical results on both a simple pendulum and one of the largest worldwide X-ray source. It is demonstrated in practice that the proposed approach allows recovering complex physics from noisy, limited, and partial observations.
  arXiv  Detail & Related papers  (2020-05-24T09:27:10Z)

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.