Deep Operator Neural Network Model Predictive Control

2025-05-23

AI Summary

To address the low efficiency and structural redundancy of DeepONet in multi-step, multi-output predictive control of nonlinear MIMO systems under model predictive control (MPC), this paper proposes the Multi-Step DeepONet (MS-DeepONet) architecture. MS-DeepONet enables end-to-end mapping from an input sequence to a multi-step output sequence via a single forward pass, eliminating the need for multiple branch networks and repeated evaluations inherent in standard DeepONet. We theoretically establish its universality as a multi-step sequence predictor. Implemented in PyTorch, MS-DeepONet integrates automated hyperparameter selection and embeds seamlessly into an MPC closed-loop framework. Evaluated on benchmark nonlinear systems—including the van der Pol oscillator, quadruple-tank process, and inverted pendulum—MS-DeepONet achieves significantly improved multi-step prediction accuracy and closed-loop control performance, enabling robust swing-up maneuvers and stable regulation.

Technology Category

• Multiagent Systems: Multiagent Learning
• Machine Learning: Deep Neural Architectures and Foundation Models
• Search and Optimization: Learning to Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

In this paper, we consider the design of model predictive control (MPC) algorithms based on deep operator neural networks (DeepONets). These neural networks are capable of accurately approximating real and complex valued solutions of continuous time nonlinear systems without relying on recurrent architectures. The DeepONet architecture is made up of two feedforward neural networks: the branch network, which encodes the input function space, and the trunk network, which represents dependencies on temporal variables or initial conditions. Utilizing the original DeepONet architecture as a predictor within MPC for Multi Input Multi Output (MIMO) systems requires multiple branch networks, to generate multi output predictions, one for each input. Moreover, to predict multiple time steps into the future, the network has to be evaluated multiple times. Motivated by this, we introduce a multi step DeepONet (MS-DeepONet) architecture that computes in one shot multi step predictions of system outputs from multi step input sequences, which is better suited for MPC. We prove that the MS DeepONet is a universal approximator in terms of multi step sequence prediction. Additionally, we develop automated hyper parameter selection strategies and implement MPC frameworks using both the standard DeepONet and the proposed MS DeepONet architectures in PyTorch. The implementation is publicly available on GitHub. Simulation results demonstrate that MS-DeepONet consistently outperforms the standard DeepONet in learning and predictive control tasks across several nonlinear benchmark systems: the van der Pol oscillator, the quadruple tank process, and a cart pendulum unstable system, where it successfully learns and executes multiple swing up and stabilization policies.

Problem

• Design MPC algorithms using DeepONets for nonlinear systems
• Introduce MS-DeepONet for multi-step predictions in MPC
• Prove MS-DeepONet's universal approximation capability for sequences

Innovation

• DeepONet predicts nonlinear systems accurately
• MS-DeepONet enables multi-step prediction in one shot
• Automated hyperparameter selection enhances MPC performance