OAC Core: Toward a Rigorous and Reliable Scientific Deep Learning Framework for Forward, Inverse, and UQ Problems

虽然深度学习是机器学习的一个子集，在计算机科学的许多领域已经被证明是最先进的方法，但它在计算科学和工程界仍处于初级阶段。与解决方案的准确性和可靠性得到保证的计算应用数学方法不同，深度学习-在其目前的状态-往往远不能为工程和科学应用提供准确的预测。对于作为设计、控制、发现和决策基础的机器学习方法，其解决方案必须配备有置信度。然而，量化机器学习解决方案中的不确定性仍然是一个具有挑战性的问题。因此，迫切需要开发可靠、健壮和模型感知的深度学习方法来处理复杂的、自然的、工程的和科学的系统，以继续科学发现的步伐和促进科学的进步。该项目在机器学习、计算工程和科学界都具有直接的实用价值。它旨在解决现实世界中由数据驱动的问题，这些问题可以导致原创性的科学发现，促进科学的进步。该项目是在TensorFlow、JAX和FENICS/FireDrake之上开发的开源软件，可供计算机、计算科学和工程研究人员、科学家、教职员工和学生组成的不同社区访问。建议的研究将直接纳入国际和平协会每年在德克萨斯大学奥斯汀分校开设的机器学习入门课程。该项目的学生为高级科学家的培养做出了贡献，以保持美国在科学和技术领域的竞争力和领先地位。PI研究计划的长期目标是为科学机器学习开发可扩展的不确定性量化、优化、数学和并行计算方法。这个项目的目标是：1)为深度学习提供基本的数学模型，以改善泛化误差，特别是在低数据区；2)在获得与传统正/逆计算方法相当的精度的同时，只需花费一小部分成本；以及3)量化深度学习中正/反问题解的不确定性。为此，该项目开发了1)严格的自适应体系结构设计方法，2)可解释的模型约束方法，将数学模型编码为深层神经网络，用于解决正问题和反问题以及科学和工程问题，以及3)模型约束统计方法，用于量化神经网络预测中的不确定性。实际的正反向地震波传播-NSF投资组合中的一个问题-被选为开发的苛刻试验台。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。

While Deep Learning, a subset of machine learning, has proved to be state-of-the-art approach in many fields of computersciences, it is still in its infancy in computational science and engineering communities. Unlike computational applied math methods in which solution accuracy and reliability are guaranteed, deep learning---in its present state---is often far from providing accuratepredictions for engineering and science applications. For machine learning methods that serve as a basis for design,control, discovery, and decision-making, their solutions must be equipped with the degree of confidence. However, quantifying the uncertainty in machine learning solution remains challenging and an open problem. Thus, there is a critical need to develop reliable, robust, and model-aware deep learning methods to tackle complex, natural, engineered, and science systems in order to continue the pace of scientific discoveries and to promote the progress of science. This project is of immediate practical utility in both machine learning and computational engineering and sciences communities. It aims at solving real-world data-driven problems, which can lead to original scientific discoveries and promote the progress of science. The project open-sourced software developed on top of TensorFlow, Jax, and FEniCS/FireDrake is accessible to a diverse community of computer and computational science and engineering researchers, scientists, faculty, and students. Proposed research will be directly incorporated into the Introduction to machine learning course offered by the PI annually at the University of Texas at Austin. Students from the project contributes to the pipeline of advanced scientists to maintain US competitiveness and leadership in sciences and technologies.The long-term goal of the PI's research program is to develop scalable uncertainty quantification, optimization, mathematical, and parallel computational methods for scientific machine learning. The objective of this project is to: 1) equip deep learning with the underlying mathematical models to improve generalization error, especially for low data regime, 2) achieve comparable accuracy with traditional forward/inverse computational methods while taking a fraction of the cost; and 3) quantify the uncertainty in deep learning for forward/inverse solutions. To that end, the project develops 1) rigorous adaptive architecture design methods, 2) interpretable model-constrained methods to encode mathematical models into deep neural networks for solving forward and inverse problems and science and engineering, and 3) model-constrained statistical approaches for quantifying the uncertainty in neural network predictions. Practical forward and inverse seismic wave propagation---a problem in NSF portfolio---is chosen as the demanding testbed for the developments.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.