2022/07/15 by Jos Stam, Stam, Jos
Computer Science · Mathematics · Physics and Astronomy · #FOS: Computer and information sciences #Graphics (cs.GR) #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Numerical Methods and Algorithms #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2207.07695
openalex publication_date 2022/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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).