Department of Animal Science, Texas A&M University, College Station, TX.
J Anim Sci. 2019 Apr 29;97(5):1921-1944. doi: 10.1093/jas/skz092.
This paper outlines typical terminology for modeling and highlights key historical and forthcoming aspects of mathematical modeling. Mathematical models (MM) are mental conceptualizations, enclosed in a virtual domain, whose purpose is to translate real-life situations into mathematical formulations to describe existing patterns or forecast future behaviors in real-life situations. The appropriateness of the virtual representation of real-life situations through MM depends on the modeler's ability to synthesize essential concepts and associate their interrelationships with measured data. The development of MM paralleled the evolution of digital computing. The scientific community has only slightly accepted and used MM, in part because scientists are trained in experimental research and not systems thinking. The scientific advancements in ruminant production have been tangible but incipient because we are still learning how to connect experimental research data and concepts through MM, a process that is still obscure to many scientists. Our inability to ask the right questions and to define the boundaries of our problem when developing models might have limited the breadth and depth of MM in agriculture. Artificial intelligence (AI) has been developed in tandem with the need to analyze big data using high-performance computing. However, the emergence of AI, a computational technology that is data-intensive and requires less systems thinking of how things are interrelated, may further reduce the interest in mechanistic, conceptual MM. Artificial intelligence might provide, however, a paradigm shift in MM, including nutrition modeling, by creating novel opportunities to understand the underlying mechanisms when integrating large amounts of quantifiable data. Associating AI with mechanistic models may eventually lead to the development of hybrid mechanistic machine-learning modeling. Modelers must learn how to integrate powerful data-driven tools and knowledge-driven approaches into functional models that are sustainable and resilient. The successful future of MM might rely on the development of redesigned models that can integrate existing technological advancements in data analytics to take advantage of accumulated scientific knowledge. However, the next evolution may require the creation of novel technologies for data gathering and analyses and the rethinking of innovative MM concepts rather than spending resources in collecting futile data or amending old technologies.
本文概述了建模的典型术语，并重点介绍了数学建模的关键历史和未来方面。数学模型（MM）是一种心理概念化，包含在虚拟领域中，其目的是将现实生活中的情况转化为数学公式，以描述现实生活中的现有模式或预测未来行为。通过 MM 对现实生活情况的虚拟表示的适当性取决于建模者将重要概念综合起来并将它们之间的关系与测量数据联系起来的能力。MM 的发展与数字计算的发展并行不悖。科学界只是在一定程度上接受和使用了 MM，部分原因是科学家接受的是实验研究方面的培训，而不是系统思维方面的培训。反刍动物生产方面的科学进步是实实在在的，但也是初步的，因为我们仍在学习如何通过 MM 将实验研究数据和概念联系起来，而这一过程对许多科学家来说仍然很模糊。在开发模型时，我们无法提出正确的问题并定义问题的范围，这可能限制了 MM 在农业中的广度和深度。人工智能（AI）的发展是为了满足使用高性能计算分析大数据的需求。然而，人工智能的出现是一种计算技术，它需要大量的数据，并且对事物之间的关系的系统思维要求较低，这可能会进一步降低人们对机械的、概念性的 MM 的兴趣。然而，人工智能可能会通过在整合大量可量化数据时创造理解潜在机制的新机会，为营养建模等 MM 带来范式转变。将 AI 与机械模型结合使用最终可能会导致开发混合机械机器学习建模。建模者必须学会如何将强大的数据驱动工具和知识驱动方法集成到可持续和有弹性的功能模型中。MM 的成功未来可能依赖于开发能够利用现有数据分析技术进步的重新设计的模型，以利用积累的科学知识。然而，下一个发展阶段可能需要为数据收集和分析创建新的技术，并重新思考创新的 MM 概念，而不是浪费资源收集无用的数据或修改旧技术。
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