arXiv subjects

Brian M. de Silva

Publications and source records attributed to Brian M. de Silva.

6 recordsLinked to original sources

arXiv2023

PyKoopman: A Python Package for Data-Driven Approximation of the Koopman Operator

PyKoopman is a Python package for the data-driven approximation of the Koopman operator associated with a dynamical system. The Koopman operator is a principled linear embedding of nonlinear dynamics and facilitates the prediction, estimation, and control of strongly nonlinear dynamics using linear systems theory. In particular, PyKoopman provides tools for data-driven system identification for unforced and actuated systems that build on the equation-free dynamic mode decomposition (DMD) and its variants. In this work, we provide a brief description of the mathematical underpinnings of the Koopman operator, an overview and demonstration of the features implemented in PyKoopman (with code examples), practical advice for users, and a list of potential extensions to PyKoopman. Software is available at http://github.com/dynamicslab/pykoopman

eess.SY↗

arXiv2022

PySINDy: A comprehensive Python package for robust sparse system identification

Automated data-driven modeling, the process of directly discovering the governing equations of a system from data, is increasingly being used across the scientific community. PySINDy is a Python package that provides tools for applying the sparse identification of nonlinear dynamics (SINDy) approach to data-driven model discovery. In this major update to PySINDy, we implement several advanced features that enable the discovery of more general differential equations from noisy and limited data. The library of candidate terms is extended for the identification of actuated systems, partial differential equations (PDEs), and implicit differential equations. Robust formulations, including the integral form of SINDy and ensembling techniques, are also implemented to improve performance for real-world data. Finally, we provide a range of new optimization algorithms, including several sparse regression techniques and algorithms to enforce and promote inequality constraints and stability. Together, these updates enable entirely new SINDy model discovery capabilities that have not been reported in the literature, such as constrained PDE identification and ensembling with different sparse regression optimizers.

eess.SY↗

arXiv2021

PySensors: A Python Package for Sparse Sensor Placement

PySensors is a Python package for selecting and placing a sparse set of sensors for classification and reconstruction tasks. Specifically, PySensors implements algorithms for data-driven sparse sensor placement optimization for reconstruction (SSPOR) and sparse sensor placement optimization for classification (SSPOC). In this work we provide a brief description of the mathematical algorithms and theory for sparse sensor optimization, along with an overview and demonstration of the features implemented in PySensors (with code examples). We also include practical advice for user and a list of potential extensions to PySensors. Software is available at https://github.com/dynamicslab/pysensors.

eess.SP↗

arXiv2020

Physics-informed machine learning for sensor fault detection with flight test data

We develop data-driven algorithms to fully automate sensor fault detection in systems governed by underlying physics. The proposed machine learning method uses a time series of typical behavior to approximate the evolution of measurements of interest by a linear time-invariant system. Given additional data from related sensors, a Kalman observer is used to maintain a separate real-time estimate of the measurement of interest. Sustained deviation between the measurements and the estimate is used to detect anomalous behavior. A decision tree, informed by integrating other sensor measurement values, is used to determine the amount of deviation required to identify a sensor fault. We validate the method by applying it to three test systems exhibiting various types of sensor faults: commercial flight test data, an unsteady aerodynamics model with dynamic stall, and a model for longitudinal flight dynamics forced by atmospheric turbulence. In the latter two cases we test fault detection for several prototypical failure modes. The combination of a learned dynamical model with the automated decision tree accurately detects sensor faults in each case.

eess.SY↗

arXiv2020

PySINDy: A Python package for the Sparse Identification of Nonlinear Dynamics from Data

PySINDy is a Python package for the discovery of governing dynamical systems models from data. In particular, PySINDy provides tools for applying the sparse identification of nonlinear dynamics (SINDy) (Brunton et al. 2016) approach to model discovery. In this work we provide a brief description of the mathematical underpinnings of SINDy, an overview and demonstration of the features implemented in PySINDy (with code examples), practical advice for users, and a list of potential extensions to PySINDy. Software is available at https://github.com/dynamicslab/pysindy.

math.DS↗

arXiv2020

Discovery of Physics from Data: Universal Laws and Discrepancies

Machine learning (ML) and artificial intelligence (AI) algorithms are now being used to automate the discovery of physics principles and governing equations from measurement data alone. However, positing a universal physical law from data is challenging without simultaneously proposing an accompanying discrepancy model to account for the inevitable mismatch between theory and measurements. By revisiting the classic problem of modeling falling objects of different size and mass, we highlight a number of nuanced issues that must be addressed by modern data-driven methods for automated physics discovery. Specifically, we show that measurement noise and complex secondary physical mechanisms, like unsteady fluid drag forces, can obscure the underlying law of gravitation, leading to an erroneous model. We use the sparse identification of nonlinear dynamics (SINDy) method to identify governing equations for real-world measurement data and simulated trajectories. Incorporating into SINDy the assumption that each falling object is governed by a similar physical law is shown to improve the robustness of the learned models, but discrepancies between the predictions and observations persist due to subtleties in drag dynamics. This work highlights the fact that the naive application of ML/AI will generally be insufficient to infer universal physical laws without further modification.

cs.LG↗