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| Universal Differential Equations for Scientific Machine Learning (arxiv.org) | |
| 3 points by formalsystem on May 17, 2020 | hide | past | pdf | 1 comment on HN | |
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In plain words: The unknown part of a physics equation can be replaced by a neural network, trained on data while known laws stay fixed. One setup handles tasks from finding biological mechanisms to control problems, including randomness and delays, unlike pure data or pure physics models. AbstractIn the context of science, the well-known adage "a picture is worth a thousand words" might well be "a model is worth a thousand datasets." In this manuscript we introduce the SciML software ecosystem as a tool for mixing the information of physical laws and scientific models with data-driven machine learning approaches. We describe a mathematical object, which we denote universal differential equations (UDEs), as the unifying framework connecting the ecosystem. We show how a wide variety of applications, from automatically discovering biological mechanisms to solving high-dimensional Hamilton-Jacobi-Bellman equations, can be phrased and efficiently handled through the UDE formalism and its tooling. We demonstrate the generality of the software tooling to handle stochasticity, delays, and implicit constraints. This funnels the wide variety of SciML applications into a core set of training mechanisms which are highly optimized, stabilized for stiff equations, and compatible with distributed parallelism and GPU accelerators. | |
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"Incorporation of prior scientific knowledge into learnable structures could allow for a new form of machine learning that is data-efficient: thereby side stepping the issue of acquiring large expensive datasets by utilizing the condensed knowledge of the scientific literature. This manuscript develops a novel learning framework, the universal differential equation, which allows for machine-learning-augmented scientific models. We showcase the ability to incorporate prior scientific knowledge and train accurate neural architectures with small data. We demonstrate how the method is interpretable [sic] back to mechanistic equations and how it can accelerate climate simulations by 15,000x. The broad applications coupled with a software implementation demonstrates a viable path for small-data scientific machine learning."