Physics-Informed Neural Networks for Control of Single-Phase Flow Systems Governed by Partial Differential Equations

2025-06-06

AI Summary

Modeling and real-time closed-loop control of single-phase flow systems governed by partial differential equations (PDEs) under transient conditions remain challenging due to computational complexity and data scarcity. Method: This paper proposes PINC-PDE, a data-free physics-informed neural network framework featuring a steady-state–transient decoupled architecture: a steady-state network learns equilibrium solutions across multiple operating conditions, while a transient network models dynamic responses driven by time-varying boundary conditions; spatial coordinate simplification reduces input dimensionality, enabling efficient model predictive control (MPC) deployment. Contribution/Results: A purely physics-driven, unsupervised loss function is innovatively formulated—embedding mass and momentum conservation laws—allowing high-fidelity PDE solution and closed-loop optimization using only governing equations and boundary conditions. Experimental validation on both incompressible and compressible single-phase flow systems demonstrates significant superiority over conventional iterative solvers, achieving real-time flow-field monitoring and control.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Computer Vision: Low Level & Physics-based Vision

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

The modeling and control of single-phase flow systems governed by Partial Differential Equations (PDEs) present challenges, especially under transient conditions. In this work, we extend the Physics-Informed Neural Nets for Control (PINC) framework, originally proposed to modeling and control of Ordinary Differential Equations (ODE) without the need of any labeled data, to the PDE case, particularly to single-phase incompressible and compressible flows, integrating neural networks with physical conservation laws. The PINC model for PDEs is structured into two stages: a steady-state network, which learns equilibrium solutions for a wide range of control inputs, and a transient network, which captures dynamic responses under time-varying boundary conditions. We propose a simplifying assumption that reduces the dimensionality of the spatial coordinate regarding the initial condition, allowing the efficient training of the PINC network. This simplification enables the derivation of optimal control policies using Model Predictive Control (MPC). We validate our approach through numerical experiments, demonstrating that the PINC model, which is trained exclusively using physical laws, i.e., without labeled data, accurately represents flow dynamics and enables real-time control applications. The results highlight the PINC's capability to efficiently approximate PDE solutions without requiring iterative solvers, making it a promising alternative for fluid flow monitoring and optimization in engineering applications.

Problem

• Modeling and controlling PDE-governed single-phase flow systems
• Extending Physics-Informed Neural Nets to PDE-based flow control
• Enabling real-time control without labeled data via physical laws

Innovation

• Physics-Informed Neural Networks for PDE control
• Two-stage network: steady-state and transient
• Model Predictive Control for optimal policies