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1. Discovering sparse interpretable dynamics from partial observations

   https://doi.org/10.1038/s42005-022-00987-z  

   Lu, Peter Y.; Ariño Bernad, Joan; Soljačić, Marin (August 2022, Communications Physics)

   Abstract Identifying the governing equations of a nonlinear dynamical system is key to both understanding the physical features of the system and constructing an accurate model of the dynamics that generalizes well beyond the available data. Achieving this kind of interpretable system identification is even more difficult for partially observed systems. We propose a machine learning framework for discovering the governing equations of a dynamical system using only partial observations, combining an encoder for state reconstruction with a sparse symbolic model. The entire architecture is trained end-to-end by matching the higher-order symbolic time derivatives of the sparse symbolic model with finite difference estimates from the data. Our tests show that this method can successfully reconstruct the full system state and identify the equations of motion governing the underlying dynamics for a variety of ordinary differential equation (ODE) and partial differential equation (PDE) systems. 

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2. A Comparative Study of Surrogate Based Learning Methods in Solving Power Flow Problem

   https://doi.org/10.1109/PESGM41954.2020.9281640  

   Ceylan, Oguzhan; Taskin, Gulsen; Paudyal, Sumit (December 2020, IEEE Power and Energy Society General Meeting)

   null (Ed.)

   Due to increasing volume of measurements in smart grids, surrogate based learning approaches for modeling the power grids are becoming popular. This paper uses regression based models to find the unknown state variables on power systems. Generally, to determine these states, nonlinear systems of power flow equations are solved iteratively. This study considers that the power flow problem can be modeled as an data driven type of a model. Then, the state variables, i.e., voltage magnitudes and phase angles are obtained using machine learning based approaches, namely, Extreme Learning Machine (ELM), Gaussian Process Regression (GPR), and Support Vector Regression (SVR). Several simulations are performed on the IEEE 14 and 30-Bus test systems to validate surrogate based learning based models. Moreover, input data was modified with noise to simulate measurement errors. Numerical results showed that all three models can find state variables reasonably well even with measurement noise. 

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3. Physics-informed learning of governing equations from scarce data

   https://doi.org/10.1038/s41467-021-26434-1  

   Chen, Zhao; Liu, Yang; Sun, Hao (December 2021, Nature Communications)

   Abstract Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and engineering disciplines. This work introduces a novel approach called physics-informed neural network with sparse regression to discover governing partial differential equations from scarce and noisy data for nonlinear spatiotemporal systems. In particular, this discovery approach seamlessly integrates the strengths of deep neural networks for rich representation learning, physics embedding, automatic differentiation and sparse regression to approximate the solution of system variables, compute essential derivatives, as well as identify the key derivative terms and parameters that form the structure and explicit expression of the equations. The efficacy and robustness of this method are demonstrated, both numerically and experimentally, on discovering a variety of partial differential equation systems with different levels of data scarcity and noise accounting for different initial/boundary conditions. The resulting computational framework shows the potential for closed-form model discovery in practical applications where large and accurate datasets are intractable to capture. 

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4. Dynamic Response Recovery Using Ambient Synchrophasor Data: A Synthetic Texas Interconnection Case Study

   https://doi.org/10.24251/HICSS.2023.327  

   Liu, Shaohui; Zhu, Hao; Kekatos, Vassilis (January 2023, Proceedings of the 56th Hawaii International Conference on System Sciences)

   Wide-area dynamic studies are of paramount importance to ensure the stability and reliability of power grids. This paper puts forth a comprehensive framework for inferring the dynamic responses in the small-signal regime using ubiquitous fast-rate ambient data collected during normal grid operations. We have shown that the impulse response between any pair of locations can be recovered in a model-free fashion by cross-correlating angle and power flow data streams collected only at these two locations, going beyond previous work based on frequency data only. The result has been established via model-based analysis of linearized second-order swing dynamics under certain conditions. Numerical validations demonstrate its applicability to realistic power system models including nonlinear, higher-order dynamics. In particular, the case study using synthetic PMU data on a synthetic Texas Interconnection (TI) system strongly corroborates the benefit of using angle PMU data over frequency one for real-world power system dynamic modeling. 

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5. Global, Unified Representation of Heterogenous Robot Dynamics Using Composition Operators: A Koopman Direct Encoding Method

   https://doi.org/10.1109/TMECH.2023.3253599  

   Asada, H. Harry (May 2023, IEEE/ASME Transactions on Mechatronics)

   The dynamic complexity of robots and mechatronic systems often pertains to the hybrid nature of dynamics, where governing equations consist of heterogenous equations that are switched depending on the state of the system. Legged robots and manipulator robots experience contact-noncontact discrete transitions, causing switching of governing equations. Analysis of these systems have been a challenge due to the lack of a global, unified model that is amenable to analysis of the global behaviors. Composition operator theory has the potential to provide a global, unified representation by converting them to linear dynamical systems in a lifted space. The current work presents a method for encoding nonlinear heterogenous dynamics into a high dimensional space of observables in the form of Koopman operator. First, a new formula is established for representing the Koopman operator in a Hilbert space by using inner products of observable functions and their composition with the governing state transition function. This formula, called Direct Encoding, allows for converting a class of heterogenous systems directly to a global, unified linear model. Unlike prevalent data-driven methods, where results can vary depending on numerical data, the proposed method is globally valid, not requiring numerical simulation of the original dynamics. A simple example validates the theoretical results, and the method is applied to a multi-cable suspension system. 

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