Constrained Block Nonlinear Neural Dynamical Models

TL;DR

This paper introduces a novel neural dynamical modeling approach that embeds local structure and constraints, enabling data-efficient learning and accurate long-term simulation of nonlinear systems with minimal data.

Contribution

It proposes a constrained block-structured neural network framework for nonlinear dynamical systems, improving data efficiency and simulation accuracy over traditional neural models.

Findings

Achieves accurate system representation with few thousand observations.

Reduces open-loop simulation error by an order of magnitude.

Effective on diverse nonlinear systems like reactors and aerodynamics.

Abstract

Neural network modules conditioned by known priors can be effectively trained and combined to represent systems with nonlinear dynamics. This work explores a novel formulation for data-efficient learning of deep control-oriented nonlinear dynamical models by embedding local model structure and constraints. The proposed method consists of neural network blocks that represent input, state, and output dynamics with constraints placed on the network weights and system variables. For handling partially observable dynamical systems, we utilize a state observer neural network to estimate the states of the system's latent dynamics. We evaluate the performance of the proposed architecture and training methods on system identification tasks for three nonlinear systems: a continuous stirred tank reactor, a two tank interacting system, and an aerodynamics body. Models optimized with a few thousand system state observations accurately represent system dynamics in open loop simulation over thousands of time steps from a single set of initial conditions. Experimental results demonstrate an order of magnitude reduction in open-loop simulation mean squared error for our constrained, block-structured neural models when compared to traditional unstructured and unconstrained neural network models.