Machine learning and serving of discrete field theories -- when artificial intelligence meets the discrete universe

Abstract

A method for machine learning and serving of discrete field theories in physics is developed. The learning algorithm trains a discrete field theory from a set of observational data on a spacetime lattice, and the serving algorithm uses the learned discrete field theory to predict new observations of the field for new boundary and initial conditions. The approach to learn discrete field theories overcomes the difficulties associated with learning continuous theories by artificial intelligence. The serving algorithm of discrete field theories belongs to the family of structure-preserving geometric algorithms, which have been proven to be superior to the conventional algorithms based on discretization of differential equations. The effectiveness of the method and algorithms developed is demonstrated using the examples of nonlinear oscillations and the Kepler problem. In particular, the learning algorithm learns a discrete field theory from a set of data of planetary orbits similar to what Kepler inherited from Tycho Brahe in 1601, and the serving algorithm correctly predicts other planetary orbits, including parabolic and hyperbolic escaping orbits, of the solar system without learning or knowing Newton's laws of motion and universal gravitation. The proposed algorithms are also applicable when effects of special relativity and general relativity are important. The illustrated advantages of discrete field theories relative to continuous theories in terms of machine learning compatibility are consistent with Bostrom's simulation hypothesis.

arXiv comment25 pages, 12 figures

References in corpus (38)

• Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
• Artificial Neural Networks for Solving Ordinary and Partial Differential Equations
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Low Dose CT Image Denoising Using a Generative Adversarial Network with Wasserstein Distance and Perceptual Loss
• Multisymplectic geometry, variational integrators, and nonlinear PDEs
• PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Network
• Learning data driven discretizations for partial differential equations
• A Comprehensive Physics-Informed Machine Learning Framework for Predictive Turbulence Modeling
• Physics-Informed Machine Learning Approach for Augmenting Turbulence Models: A Comprehensive Framework
• Stable Architectures for Deep Neural Networks
• Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems
• Generative Adversarial Networks recover features in astrophysical images of galaxies beyond the deconvolution limit
• GEMPIC: Geometric ElectroMagnetic Particle-In-Cell Methods
• Variational Autoencoders for New Physics Mining at the Large Hadron Collider
• On Learning Hamiltonian Systems from Data
• Geometric integration of the Vlasov-Maxwell system with a variational particle-in-cell scheme
• Uniformly Accurate Machine Learning Based Hydrodynamic Models for Kinetic Equations
• Branes with Brains: Exploring String Vacua with Deep Reinforcement Learning
• Canonical symplectic particle-in-cell method for long-term large-scale simulations of the Vlasov-Maxwell system
• Restoration of Rotational Symmetry in the Continuum Limit of Lattice Field Theories
• Machine learning action parameters in lattice quantum chromodynamics
• Multidimensional approximation of nonlinear dynamical systems
• Structure-Preserving Geometric Particle-in-Cell Methods for Vlasov-Maxwell Systems
• Explicit symplectic algorithms based on generating functions for charged particle dynamics
• Hamiltonian integration methods for Vlasov-Maxwell equations
• Constraints on the Universe as a Numerical Simulation
• Variational integration for ideal magnetohydrodynamics with built-in advection equations
• Hamiltonian particle-in-cell methods for Vlasov-Maxwell equations
• Finite-dimensional collisionless kinetic theory
• Explicit high-order noncanonical symplectic algorithms for ideal two-fluid systems
• Toroidal regularization of the guiding center Lagrangian
• Degenerate Variational Integrators for Magnetic Field Line Flow and Guiding Center Trajectories
• Canonical symplectic structure and structure-preserving geometric algorithms for Schrödinger-Maxwell systems
• The geometric theory of charge conservation in particle-in-cell simulations
• Explicit High-Order Gauge-Independent Symplectic Algorithms for Relativistic Charged Particle Dynamics
• Field theory and structure-preserving geometric particle-in-cell algorithm for drift wave instability and turbulence
• Lorentz Covariant Canonical Symplectic Algorithms for Dynamics of Charged Particles
• Local Energy Conservation Law for Spatially-Discretized Hamiltonian Vlasov-Maxwell System