# Data-Driven Adaptive PID Control Based on Physics-Informed Neural Networks

arXiv: https://arxiv.org/abs/2510.04591 · HTML: https://mlsanity.com/paper/2510.04591/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 38 references that are in the map.
- First posted on arXiv 6 Oct 2025.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Enhancing Computational Fluid Dynamics with Machine Learning](https://mlsanity.com/paper/2110.02085/) (2021)
- [From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning](https://mlsanity.com/paper/2410.13228/) (2024)
- [Data-Enabled Predictive Control: In the Shallows of the DeePC](https://mlsanity.com/paper/1811.05890/) (2018)
- [Physics-Informed Neural Nets for Control of Dynamical Systems](https://mlsanity.com/paper/2104.02556/) (2021)
- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
- [Physics-informed Neural Networks-based Model Predictive Control for Multi-link Manipulators](https://mlsanity.com/paper/2109.10793/) (2021)
- [Physics-informed Neural Networks to Model and Control Robots: a Theoretical and Experimental Investigation](https://mlsanity.com/paper/2305.05375/) (2023)
- [Deep Learning Explicit Differentiable Predictive Control Laws for Buildings](https://mlsanity.com/paper/2107.11843/) (2021)
- [Learning Exactly Linearizable Deep Dynamics Models](https://mlsanity.com/paper/2311.18261/) (2023)
- [Neural Horizon Model Predictive Control -- Increasing Computational Efficiency with Neural Networks](https://mlsanity.com/paper/2408.09781/) (2024)

## Built on by (most cited first, 1 of 1)

- [Model Predictive Path Integral PID Control for Learning-Based Path Following](https://mlsanity.com/paper/2603.29499/) (2026)

## Abstract (arXiv)

This article proposes a data-driven PID controller design based on the principle of adaptive gain optimization, leveraging Physics-Informed Neural Networks (PINNs) generated for predictive modeling purposes. The proposed control design method utilizes gradients of the PID gain optimization, achieved through the automatic differentiation of PINNs, to apply model predictive control using a cost function based on tracking error and control inputs. By optimizing PINNs-based PID gains, the method achieves adaptive gain tuning that ensures stability while accounting for system nonlinearities. The proposed method features a systematic framework for integrating PINNs-based models of dynamical control systems into closed-loop control systems, enabling direct application to PID control design. A series of numerical experiments is conducted to demonstrate the effectiveness of the proposed method from the control perspectives based on both time and frequency domains.