Gradient-free training of neural ODEs for system identification and control using ensemble Kalman inversion

• URL: http://arxiv.org/abs/2307.07882v1
• Date: Sat, 15 Jul 2023 20:45:50 GMT
• Title: Gradient-free training of neural ODEs for system identification and control using ensemble Kalman inversion
• Authors: Lucas B\"ottcher
• Abstract summary: Ensemble Kalman inversion (EKI) is a sequential Monte Carlo method used to solve inverse problems within a Bayesian framework. In this study, we examine the effectiveness of EKI in training neural ordinary differential equations (neural ODEs) for system identification and control tasks.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Ensemble Kalman inversion (EKI) is a sequential Monte Carlo method used to solve inverse problems within a Bayesian framework. Unlike backpropagation, EKI is a gradient-free optimization method that only necessitates the evaluation of artificial neural networks in forward passes. In this study, we examine the effectiveness of EKI in training neural ordinary differential equations (neural ODEs) for system identification and control tasks. To apply EKI to optimal control problems, we formulate inverse problems that incorporate a Tikhonov-type regularization term. Our numerical results demonstrate that EKI is an efficient method for training neural ODEs in system identification and optimal control problems, with runtime and quality of solutions that are competitive with commonly used gradient-based optimizers.

Related papers

• A Simulation-Free Deep Learning Approach to Stochastic Optimal Control [12.699529713351287]
  We propose a simulation-free algorithm for the solution of generic problems in optimal control (SOC) Unlike existing methods, our approach does not require the solution of an adjoint problem.
  arXiv  Detail & Related papers  (2024-10-07T16:16:53Z)
• Score-based Neural Ordinary Differential Equations for Computing Mean Field Control Problems [13.285775352653546]
  This paper proposes a system of neural differential equations representing first- and second-order score functions along trajectories based on deep neural networks. We reformulate the mean viscous field control (MFC) problem with individual noises into an unconstrained optimization problem framed by the proposed neural ODE system.
  arXiv  Detail & Related papers  (2024-09-24T21:45:55Z)
• A minimax optimal control approach for robust neural ODEs [44.99833362998488]
  We address the adversarial training of neural ODEs from a robust control perspective. We derive first order optimality conditions in the form of Pontryagin's Maximum Principle.
  arXiv  Detail & Related papers  (2023-10-26T17:07:43Z)
• Application of deep and reinforcement learning to boundary control problems [0.6906005491572401]
  The aim is to find the optimal values for the domain boundaries such that the enclosed domain attains the desired state values. This project explores possibilities using deep learning and reinforcement learning to solve boundary control problems.
  arXiv  Detail & Related papers  (2023-10-21T10:56:32Z)
• An Optimization-based Deep Equilibrium Model for Hyperspectral Image Deconvolution with Convergence Guarantees [71.57324258813675]
  We propose a novel methodology for addressing the hyperspectral image deconvolution problem. A new optimization problem is formulated, leveraging a learnable regularizer in the form of a neural network. The derived iterative solver is then expressed as a fixed-point calculation problem within the Deep Equilibrium framework.
  arXiv  Detail & Related papers  (2023-06-10T08:25:16Z)
• Implicit Stochastic Gradient Descent for Training Physics-informed Neural Networks [51.92362217307946]
  Physics-informed neural networks (PINNs) have effectively been demonstrated in solving forward and inverse differential equation problems. PINNs are trapped in training failures when the target functions to be approximated exhibit high-frequency or multi-scale features. In this paper, we propose to employ implicit gradient descent (ISGD) method to train PINNs for improving the stability of training process.
  arXiv  Detail & Related papers  (2023-03-03T08:17:47Z)
• On Robust Numerical Solver for ODE via Self-Attention Mechanism [82.95493796476767]
  We explore training efficient and robust AI-enhanced numerical solvers with a small data size by mitigating intrinsic noise disturbances. We first analyze the ability of the self-attention mechanism to regulate noise in supervised learning and then propose a simple-yet-effective numerical solver, Attr, which introduces an additive self-attention mechanism to the numerical solution of differential equations.
  arXiv  Detail & Related papers  (2023-02-05T01:39:21Z)
• Experimental study of Neural ODE training with adaptive solver for dynamical systems modeling [72.84259710412293]
  Some ODE solvers called adaptive can adapt their evaluation strategy depending on the complexity of the problem at hand. This paper describes a simple set of experiments to show why adaptive solvers cannot be seamlessly leveraged as a black-box for dynamical systems modelling.
  arXiv  Detail & Related papers  (2022-11-13T17:48:04Z)
• A memory-efficient neural ODE framework based on high-level adjoint differentiation [4.063868707697316]
  We present a new neural ODE framework, PNODE, based on high-level discrete algorithmic differentiation. We show that PNODE achieves the highest memory efficiency when compared with other reverse-accurate methods.
  arXiv  Detail & Related papers  (2022-06-02T20:46:26Z)
• Meta-Solver for Neural Ordinary Differential Equations [77.8918415523446]
  We investigate how the variability in solvers' space can improve neural ODEs performance. We show that the right choice of solver parameterization can significantly affect neural ODEs models in terms of robustness to adversarial attacks.
  arXiv  Detail & Related papers  (2021-03-15T17:26:34Z)
• Neural Control Variates [71.42768823631918]
  We show that a set of neural networks can face the challenge of finding a good approximation of the integrand. We derive a theoretically optimal, variance-minimizing loss function, and propose an alternative, composite loss for stable online training in practice. Specifically, we show that the learned light-field approximation is of sufficient quality for high-order bounces, allowing us to omit the error correction and thereby dramatically reduce the noise at the cost of negligible visible bias.
  arXiv  Detail & Related papers  (2020-06-02T11:17:55Z)

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.