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Data-driven algorithms are developed to fully automate sensor fault detection in systems governed by underlying physics, with a particular focus on the flight test setting. The proposed machine lea...

Generation and analysis of time-series data is relevant to many quantitative fields ranging from economics to fluid mechanics. In the physical sciences, structures such as metastable and coherent sets, slow relaxation processes, collective variables, dominant transition pathways or manifolds and channels of probability flow can be of great importance for understanding and characterizing the kinetic, thermodynamic and mechanistic properties of the system. Deeptime is a general purpose Python library offering various tools to estimate dynamical models based on time-series data including conventional linear learning methods, such as Markov state models (MSMs), Hidden Markov Models and Koopman models, as well as kernel and deep learning approaches such as VAMPnets and deep MSMs. The library is largely compatible with scikit-learn, having a range of Estimator classes for these different models, but in contrast to scikit-learn also provides deep Model classes, e.g. in the case of an MSM, which provide a multitude of analysis methods to compute interesting thermodynamic, kinetic and dynamical quantities, such as free energies, relaxation times and transition paths. The library is designed for ease of use but also easily maintainable and extensible code. In this paper we introduce the main features and structure of the deeptime software. Deeptime can be found under https://deeptime-ml.github.io/.

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.

Authors of papers retaincopyright and release the workunder a Creative CommonsAttribution 4.0 InternationalLicense (CC-BY) Scientists have long quantified empirical observations by developing mathematical models that characterize the observations, have some measure of interpretability, and are capable of making predictions. Dynamical systems models in particular have been widely used to study, explain, and predict system behavior in a wide range of application areas, with examples ranging from Newton’s laws of classical mechanics to the Michaelis-Menten kinetics for modeling enzyme kinetics. While governing laws and equations were traditionally derived by hand, the current growth of available measurement data and resulting emphasis on data-driven modeling motivates algorithmic approaches for model discovery. A number of such approaches have been developed in recent years and have generated widespread interest, including Eureqa (Schmidt & Lipson, 2009), sure independence screening and sparsifying operator (Ouyang, Curtarolo, Ahmetcik, Scheffler, & Ghiringhelli, 2018), and the sparse identification of nonlinear dynamics (SINDy) (Brunton, Proctor, & Kutz, 2016). Maximizing the impact of these model discovery methods requires tools to make them widely accessible to scientists across domains and at various levels of mathematical expertise. This project is a fork of sparsereg( Quade, 2018). SLB acknowledges funding supportfrom the Air Force Office of Scientific Research (AFOSR FA9550-18-1-0200) and the ArmyResearch Office (ARO W911NF-19-1-0045). JNK acknowledges support from the Air ForceOffice of Scientific Research (AFOSR FA9550-17-1-0329). This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under GrantNumber DGE-1256082.

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 non-linear 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.

Microscopy imaging of mouse growth plates is extensively used in biology to understand the effect of specific molecules on various stages of normal bone development and on bone disease. Until now, such image analysis has been conducted by manual detection. In fact, when existing automated detection techniques were applied, morphological variations across the growth plate and heterogeneity of image background color, including the faint presence of cells (chondrocytes) located deeper in tissue away from the image's plane of focus, and lack of cell-specific features, interfered with identification of cell. We propose the first method of automated detection and morphometry applicable to images of cells in the growth plate of long bone. Through ad hoc sequential application of the Retinex method, anisotropic diffusion and thresholding, our new cell detection algorithm (CDA) addresses these challenges on bright-field microscopy images of mouse growth plates. Five parameters, chosen by the user in respect of image characteristics, regulate our CDA. Our results demonstrate effectiveness of the proposed numerical method relative to manual methods. Our CDA confirms previously established results regarding chondrocytes' number, area, orientation, height and shape of normal growth plates. Our CDA also confirms differences previously found between the genetic mutated mouse Smad1/5(CKO) and its control mouse on fluorescence images. The CDA aims to aid biomedical research by increasing efficiency and consistency of data collection regarding arrangement and characteristics of chondrocytes. Our results suggest that automated extraction of data from microscopy imaging of growth plates can assist in unlocking information on normal and pathological development, key to the underlying biological mechanisms of bone growth.