Abstract
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.
Highlights
The ability to derive governing equations and physical principles has been a hallmark feature of scientific discovery and technological progress throughout human history
We demonstrate that a sparse regression framework is well-suited for physics discovery, while highlighting both the need for principled methods to extract parsimonious physics models and the challenges associated with the naive application of machine learning (ML)/artificial intelligence (AI) techniques
The algorithm can be reformulated to include integral terms for noisy data (Schaeffer and McCalla, 2017) or handle incomplete or limited data (Tran and Ward, 2016; Schaeffer et al, 2018). In this manuscript we show that group sparsity (Rudy et al, 2019) may be used to enforce that the same model terms explain all of the observed trajectories, which is essential in identifying the correct model terms without overfitting
Summary
The ability to derive governing equations and physical principles has been a hallmark feature of scientific discovery and technological progress throughout human history. Even before the scientific revolution, the Ptolemaic doctrine of the perfect circle (Peters and Knobel, 1915; Ptolemy, 2014) provided a principled decomposition of planetary motion into a hierarchy of circles, i.e., a bona fide theory for planetary motion. With advances in data science over the past few decades, principled methods are emerging for such scientific discovery from time-series measurements alone. Across the engineering, physical and biological sciences, significant advances in sensor and measurement technologies have afforded unprecedented new opportunities for scientific exploration. Despite its rapid advancements and wide-spread deployment, machine learning (ML) and artificial intelligence (AI) algorithms for scientific discovery face significant challenges and limitations, including noisy and corrupt data, Frontiers in Artificial Intelligence | www.frontiersin.org de Silva et al
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