# Program

The full-day workshop will be organized into a morning and an afternoon session, split by a lunch break. The morning session starts with a general introduction and an overview of the challenges and potential opportunities for the control community. Afterwards, special topics and applications of physics-informed learning and a series of exciting research questions are presented by contributing speakers.

Tentative Schedule

09:00 - 09:10

### Warming up: Welcome, motivation, and introduction

09:10 - 09:30

### Introduction to Physics-Informed Machine Learning:

Challenges and Opportunities

Challenges and Opportunities

Thomas Beckers (Vanderbilt University) [slides]

09:30 - 10:15

### Integrating Physics in Gaussian Process and Neural-Networks for Model Based Control

Rolf Findeisen (TU Darmstadt) [slides]

Coffee Break 10:15 - 10:45

10:45 - 11:30

### A Physics-Informed Composable Learning Framework

Thomas Beckers (Vanderbilt University) [slides]

Data-driven approaches achieve remarkable results for modeling nonlinear electromechanical systems based on collected data. However, these models often neglect basic physical principles which determine the behavior of any real-world system. This omission is unfavorable in two ways: The models are not as data-efficient as they could be by incorporating physical prior knowledge, and the model itself might not be physically correct.

In this talk, I will present our results on physics-enhanced Gaussian processes for learning of dynamical system with a focus on the class of electromechanical systems. I will propose Gaussian Process Port-Hamiltonian systems (GP-PHS) as a physics-informed, nonparametric Bayesian learning approach with uncertainty quantification. In contrast to many physics-informed techniques that impose physics by penalty, the proposed data-driven model is physically correct by design. The Bayesian nature of GP-PHS uses collected data to form a distribution over all possible Port-Hamiltonian systems instead of a single point estimate. The framework is in particular suitable for composable learning as its structure can be preserved under interconnection. Finally, the model can be used in a robust control setting to establish safe learning-based control.

11:30 - 12:15

### Combining Data and Physics Knowledge for Demand Response Forecast in Energy Systems

Yuanyuan Shi (University of California, San Diego) [slides]

In this talk, I will present our recent works [1, 2] that combines physics knowledge and operational data for modeling and predicting the user behaviors of demand response (DR) in energy systems. Specially, we model the DR agent as a private optimization problem, with unknown model parameters. We encode the prior knowledge as a differentiable optimization layer in neural network (OptNet), and propose a gradient-based method to identify the private parameters and predict agent behavior to future price signals. We prove convergence to the ground-truth parameters under equality-constrained quadratic problems. We compare our approach against pure data-driven approaches and a benchmark inverse optimization model that are commonly used in the literature. The results show that our proposed method achieves orders of magnitude improvements in the prediction accuracy, in both simulation and real-world datasets. We envision the proposed framework can be adopted by future energy system operators to design incentives in anticipation of strategic agent behavior, with the objective to reduce total system operating cost and system volatility.

References

[1] Bian, Yuexin, Ningkun Zheng, Yang Zheng, Bolun Xu, and Yuanyuan Shi. "Demand response model identification and behavior forecast with OptNet: a gradient-based approach." In Proceedings of the Thirteenth ACM International Conference on Future Energy Systems (ACM e-Energy), 2022.

[2] Bian, Yuexin, Ningkun Zheng, Yang Zheng, Bolun Xu, and Yuanyuan Shi. "Predicting Strategic Energy Storage Behaviors." IEEE Transactions on Smart Grid, 2023.

Lunch Break 12:15 - 01:45

01:45 - 02:30

### A Physics-Informed Neural-Network-based Simulator for Power System Dynamics

Spyros Chatzivasileiadis / Rahul Nellikkath (Technical University of Denmark) [slides]

Machine Learning (ML) has been proposed as a fast and efficient method to predict the response of non-linear dynamic systems, such as power systems. Considering that simulating the electromagnetic transient dynamics of a power system following a short-circuit fault is an extremely computationally expensive procedure, which is, however, essential in converter-dominated power systems, alternative methods are necessary. Traditional ML algorithms require large amounts of labeled data for training, which becomes prohibitive considering the time required to generate a rich enough dataset of electromagnetic transient (EMT) simulations. In this talk, we introduce a Physics-Informed Neural Network (PINN) architecture that accurately predicts the nonlinear electromagnetic transient dynamics, achieving a 100x speedup while requiring a very limited amount of simulation data for training. In contrast with conventional EMT solvers, which require 2 days to assess 5 million scenarios, we show how our proposed PINN algorithm can both be trained and evaluate the same scenarios within only 30 minutes. The proposed PINN algorithm can be incorporated into conventional simulation tools, accelerating EMT simulations by over 100 times.

02:30 - 03:15

### Data-driven Identification of Dissipative Models for Nonlinear Systems

Sivaranjani Seetharaman (Purdue University)

Assume that we have a priori information that a nonlinear system satisfies a physical property that makes it easy to design a controller and obtain a desired performance or stability guarantee on the closed loop system. Can we identify a system model that satisfies this property? In particular, we consider the property to be that of dissipativity. Dissipativity is an important input-output property of dynamical systems which encompasses many important special cases like L2 stability, passivity and conicity. Dissipativity, thus, finds application in various domains ranging from robotics, electromechanical systems, and aerospace systems to process control, networked control, cyber-physical systems, and energy. To address this problem, we will discuss a two-stage approach where we first learn an approximate linear models of the nonlinear system using classical or Koopman operator approaches, and then perturb the system matrices of the linear model to enforce dissipativity, while closely approximating the dynamical behavior of the nonlinear system. Further, we provide an analytical relationship between the size of the perturbation and the radius in which the dissipativity of the linear model guarantees local dissipativity of the unknown nonlinear system. We demonstrate the application of this identification technique to the problem of learning dissipative models of power systems.

Coffee Break 03:15 - 03:45

03:45 - 04:30

### Physics-informed Learning with Gaussian Processes and its Application to Robotics

Sandra Hirche / Giulio Evangelisti (Technical University of Munich)

The formulation of Gaussian Processes and other learning frameworks consistent with the relevant physical laws and mathematical models holds great promise for learning-based control of uncertain systems, improving data efficiency and reliability via their physical integrity. Classical parametric identification techniques also profit from exploiting physical priors but are limited to dynamical systems with low complexity since they require linearity in the parameters. Thus, with the increasing uncertainty in physical systems, developing reliable yet tractable models is still a crucial ongoing issue.

This talk will address these issues by focusing on a common methodology behind different learning methods applied to control uncertain systems: integrating physical knowledge and other structural priors into the learning framework on the one hand and enforcing structure via control with learning on the other hand. In particular, we introduce the concept of physically consistent GPs for data-driven modeling of uncertain Lagrangian systems, which constrain the function space according to the energy components of the Lagrangian and the differential equation structure, analytically guaranteeing properties such as energy conservation and quadratic form. We demonstrate and compare performances in simulations and physical experiments.

04:30 - 05:15

### Fusing Pre-existing Knowledge and Machine Learning for Enhanced Building Thermal Modeling and Control

Colin Jones / Loris Di Natale (École polytechnique fédérale de Lausanne) [slides]

In the first part of this talk, we will analyze some shortcomings of classical Neural Networks (NNs) and Physics-inspired NNs (PiNNs), which cannot guarantee compliance with the underlying physical laws. To remedy to that problem, we will introduce the Physically Consistent NN (PCNN) architecture that we developed in previous work, which simultaneously achieved state-of-the-art accuracy and physical consistency for building thermal modeling.

We will then turn to Deep Reinforcement Learning (DRL), where NN control policies learn to minimize the energy consumption of buildings. We will discuss various possibilities to ensure DRL agents behave as expected and propose computationally inexpensive modifications to accelerate their convergence to well-performing policies.

In the last part of the talk, we will take a step back from NNs and reflect how to use open-source Machine Learning libraries to help scale traditional System Identification (SI) methods. We will introduce SIMBa, an open-source SI toolbox leveraging backpropagation. SIMBa often significantly outperforms traditional SI methods, and often significantly, while ensuring desired system properties – like stability or sparsity – are respected.

05:15 - 05:30