SCience-INtegrated Predictive modeLing (SCINPL): a novel framework for scalable and interpretable predictive scientific modeling

科学建模正处在一个关键的、具有决定性的十字路口。随着实验技术的突破，现在可以为复杂的科学和工程问题获得高质量的数据。然而，生成如此高质量的数据需要大量的实验和计算成本，导致用于科学调查的数据有限。虽然预测建模提供了一些缓解，但最近的工作揭示了现有模型的两个关键缺陷：它们在使用有限的数据进行训练时往往产生较差的预测性能，并且可能违反既定的科学原则，这可能导致错误和虚假的科学结论。该项目将开发一种新的科学集成预测建模(SCINPL)框架，以解决这些限制。SCINPL为变革性的科学研究铺平了道路，为从业者提供了指导科学进步的准确、成本效益和可解释的预测模型。这一框架可以通过展示科学驱动的统计学习和数据驱动的科学发现的实际优势，促进科学界和数据科学界之间更密切的合作。SCINPL为广泛领域的科学发现提供了根本性的范式转变，使科学家能够通过改进的基于科学的数据科学工具推动科学知识和工程的前沿。SCINPL具有一套新的概率贝叶斯模型，能够整合广泛的先前科学领域知识作为预测建模的先验信念。科学知识与数据驱动模型的这种结合不仅提供了更好的预测性能，减少了不确定性，而且还使更好的可解释性，从而在有限的训练数据下进行了科学发现。第一种模型称为边界约束GP模型，它将响应面的已知边界信息集成在一个高斯过程(GP)框架内。第二个模型是图形化的多保真GP模型，它在科学模型之间嵌入相关性信息以进行预测建模。第三个模型是高斯过程子空间回归模型，它集成了代表主导物理的子空间信息，用于GP建模。对于每个模型，研究人员将(1)为预测建模建立坚实的理论基础，这表明通过整合科学信息提高预测性能；(2)提出一套全面的方法框架和一套有效的算法，以便将科学原理整合到概率建模中；以及(3)证明这种模型对具有成本效益、可解释和有原则的科学发现的有用性。主要的重点是展示SCINPL在解决广泛的复杂和昂贵的科学问题方面的有效性，包括3D打印的主动脉瓣的设计，重离子碰撞的研究，以及航天火箭发动机的优化。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Scientific modeling is at a critical and defining crossroads. With breakthroughs in experimental technology, high-quality data can now be obtained for complex scientific and engineering problems. However, the generation of such high-quality data entails large experimental and computational costs, resulting in limited data for scientific investigation. While predictive modeling provides some relief, recent work has revealed two key shortcomings with existing models: they often yield poor predictive performance when trained with limited data, and can violate established scientific principles, which may lead to erroneous and spurious scientific conclusions. This project will develop a novel SCience-INtegrated Predictive modeLing (SCINPL) framework which addresses these limitations. SCINPL paves the road for transformative scientific research, equipping practitioners with accurate, cost-efficient and interpretable predictive models for guiding scientific progress. This framework can catalyze closer collaborations between the scientific and data science communities, by demonstrating the practical advantages of science-driven statistical learning and data-driven scientific discovery. SCINPL provides a radical paradigm shift for scientific discovery in a broad range of fields, enabling scientists to push forward the frontiers of scientific knowledge and engineering via improved science-based data science tools.SCINPL features a suite of new probabilistic Bayesian models, which are capable of integrating a wide range of prior scientific domain knowledge as prior beliefs for predictive modeling. This integration of scientific knowledge with data-driven models not only provides improved predictive performance with reduced uncertainty, but also enables better interpretability and thus scientific discovery given limited training data. The first model, called the Boundary-constrained GP model, integrates known boundary information for the response surface within a Gaussian process (GP) framework. The second model, the Graphical Multi-fidelity GP model, embeds dependency information between scientific models for predictive modeling. The third model, the Gaussian Process Subspace regression model, integrates subspace information representing dominant physics for GP modeling. For each model, the investigators will (i) establish a solid theoretical foundation for predictive modeling, which demonstrates the improved predictive performance via the integration of scientific information, (ii) present a comprehensive methodological framework and efficient suite of algorithms for performing this desired integration of scientific principles within probabilistic modeling, and (iii) demonstrate the usefulness of such models for cost-efficient, interpretable and principled scientific discovery. Major emphasis is placed on demonstrating the effectiveness of SCINPL in tackling a broad range of complex and expensive scientific problems, including the design of 3D-printed aortic valves, the study of heavy-ion collisions, and the optimization of rocket engines for spaceflight.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.