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

TL;DR

This paper extends Physics-Informed Neural Networks to control single-phase flow systems governed by PDEs, enabling real-time control without labeled data by integrating physical laws into neural network models.

Contribution

The work introduces a PDE-specific PINC framework with a two-stage structure and a spatial dimensionality reduction, facilitating efficient training and control policy derivation.

Findings

Accurately models flow dynamics using physics-based training.

Enables real-time control without iterative PDE solvers.

Demonstrates effectiveness in numerical experiments.

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.