Neural Integration of Continuous Dynamics
Neural dynamical systems are dynamical systems that are described at least in part by neural networks. The class of continuous-time neural dynamical systems must, however, be numerically integrated for simulation and learning. Here, we present a compact neural circuit for two common numerical integrators: the explicit fixed-step Runge-Kutta method of any order and the semi-implicit/predictor-corrector Adams-Bashforth-Moulton method. Modeled as constant-sized recurrent networks embedding a continuous neural differential equation, they achieve fully neural temporal output. Using the polynomial class of dynamical systems, we demonstrate the equivalence of neural and numerical integration.
Code (0)
등록된 구현이 없습니다.
Tasks
Numerical IntegrationSimilar Papers 제목 키워드 기반
Discretization of Linear Systems using the Matrix Exponential
Discretizing continuous-time linear systems typically requires numerical integration. This document presents a convenient method for discretizing the dynamics, input, and process noise state-space matrices of a continuou…
Numerical IntegrationCENIC: Convex Error-controlled Numerical Integration for Contact
State-of-the-art robotics simulators operate in discrete time. This requires users to choose a time step, which is both critical and challenging: large steps can produce non-physical artifacts, while small steps force th…
Training Generative Adversarial Networks by Solving Ordinary Differential Equations
The instability of Generative Adversarial Network (GAN) training has frequently been attributed to gradient descent. Consequently, recent methods have aimed to tailor the models and training procedures to stabilise the d…
Generative Adversarial NetworkAccelerated Mixing Time of Randomized Hamiltonian Monte Carlo
We show the Randomized Hamiltonian Monte Carlo (RHMC) algorithm has accelerated mixing time guarantees for sampling from log-concave probability distributions. RHMC proceeds by repeatedly simulating the continuous-time H…
CFO: Learning Continuous-Time PDE Dynamics via Flow-Matched Neural Operators
Neural operator surrogates for time-dependent partial differential equations (PDEs) conventionally employ autoregressive prediction schemes, which accumulate error over long rollouts and require uniform temporal discreti…