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 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.

Automated Cell Detection and Morphometry on Growth Plate Images of Mouse Bone.

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 Smad1/5CKO 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.