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

2025/06/06 by Luis Kin Miyatake, Eduardo Camponogara, Miyatake, Luis Kin +5
Computer Science · Physics and Astronomy · #Adaptive Dynamic Programming Control #Artificial neural network #Boundary (topology) #Control theory (sociology) #Curse of dimensionality #FOS: Computer and information sciences #Flow (mathematics) #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Neural Networks and Reservoir Computing #Ordinary differential equation #Partial differential equation #Range (aeronautics) #Transient (computer programming)

paper · pdf · doi:10.48550/arxiv.2506.06188

openalex publication_date 2025/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

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Related

• Learning to Control PDEs with Differentiable Physics
• Physics-informed neural networks for PDE-constrained optimization and control
• Physics-Informed Neural Networks: Bridging the Divide Between Conservative and Non-Conservative Equations
• An analysis and solution of ill-conditioning in physics-informed neural networks
• Optimal control of PDEs using physics-informed neural networks