An Exact Bitwise Reversible Integrator

At a fundamental level most physical equations are time reversible. In this paper we propose an integrator that preserves this property at the discrete computational level. Our simulations can be run forward and backwards and trace the same path exactly bitwise. We achieve this by implementing theor...

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Bibliographic Details
Published in:arXiv.org 2022-07
Main Author: Stam, Jos
Format: Article
Language:English
Subjects:
Back propagation
Floating point arithmetic
Integrators
Machine learning
Optimization
Online Access:Get full text
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Summary:At a fundamental level most physical equations are time reversible. In this paper we propose an integrator that preserves this property at the discrete computational level. Our simulations can be run forward and backwards and trace the same path exactly bitwise. We achieve this by implementing theoretically reversible integrators using a mix of fixed and floating point arithmetic. Our main application is in efficiently implementing the reverse step in the adjoint method used in optimization. Our integrator has applications in differential simulations and machine learning (backpropagation).
ISSN:2331-8422