The use of computational models and simulations to predict events that take place in our physical universe, or to predict the behaviour of engineered systems, has significantly advanced the pace of scientific discovery and the creation of new technologies for the benefit of humankind over recent decades, at least up to a point. That ‘point’ in recent history occurred around the time that the scientific community began to realize that true predictive science must deal with many formidable obstacles, including the determination of the reliability of the models in the presence of many uncertainties. To develop meaningful predictions one needs relevant data, itself possessing uncertainty due to experimental noise; in addition, one must determine model parameters, and concomitantly, there is the overriding need to select and validate models given the data and the goals of the simulation.This article provides a broad overview of predictive computational science within the framework of what is often called the science of uncertainty quantification. The exposition is divided into three major parts. In Part 1, philosophical and statistical foundations of predictive science are developed within a Bayesian framework. There the case is made that the Bayesian framework provides, perhaps, a unique setting for handling all of the uncertainties encountered in scientific prediction. In Part 2, general frameworks and procedures for the calculation and validation of mathematical models of physical realities are given, all in a Bayesian setting. But beyond Bayes, an introduction to information theory, the maximum entropy principle, model sensitivity analysis and sampling methods such as MCMC are presented. In Part 3, the central problem of predictive computational science is addressed: the selection, adaptive control and validation of mathematical and computational models of complex systems. The Occam Plausibility Algorithm, OPAL, is introduced as a framework for model selection, calibration and validation. Applications to complex models of tumour growth are discussed.

中文翻译：

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自适应多尺度预测建模

近几十年来，使用计算模型和模拟来预测我们物理宇宙中发生的事件，或预测工程系统的行为，显着加快了科学发现和新技术创造的步伐，以造福人类，至少在一定程度上。近代历史上的那个“点”发生在科学界开始意识到真正的预测科学必须处理许多可怕的障碍的时候，包括在存在许多不确定性的情况下确定模型的可靠性。要进行有意义的预测，需要相关数据，由于实验噪声本身具有不确定性；此外，必须确定模型参数，同时，在给定数据和模拟目标的情况下，最重要的是选择和验证模型。本文在通常称为不确定性量化科学的框架内提供了预测计算科学的广泛概述。展览分为三个主要部分。在第 1 部分中，预测科学的哲学和统计基础是在贝叶斯框架内开发的。那里的情况是，贝叶斯框架可能提供了一个独特的设置来处理科学预测中遇到的所有不确定性。在第 2 部分中，给出了计算和验证物理现实数学模型的一般框架和程序，所有这些都在贝叶斯环境中进行。但是除了贝叶斯，信息论的介绍，最大熵原理，提出了模型敏感性分析和采样方法，例如 MCMC。在第 3 部分中，解决了预测计算科学的核心问题：复杂系统的数学和计算模型的选择、自适应控制和验证。引入奥卡姆合理性算法 OPAL 作为模型选择、校准和验证的框架。讨论了在复杂的肿瘤生长模型中的应用。