Transfer Learning for Monte Carlo Methods

英国政府的布莱克特评估报告传递出的一个关键信息是：“未来，我们将更需要可靠的预测性模型，这些模型与我们想要理解或希望构建的大规模复杂系统相关。”如果模型可以用于预测，如果围绕这些预测的不确定性可以量化，则建模主要是有用的，这通常需要先进的计算工具。随着我们的模型规模的扩大，也带来了巨大的计算挑战。新奇之处不在于计算任务本身，而在于我们模型的巨大规模，以及处理这些任务的计算成本。例如，海啸模型每次运行需要几个小时的计算时间，而用于预测风力发电场发电量的大型涡流模拟模型每次运行需要数千小时的计算时间。这些庞大的计算成本严重限制了这些模型对未来做出准确预测的实际应用。一套可以帮助应对这一挑战的技术是“转移学习”，这是机器学习的一个子领域，它建议在类似的任务中共享数据，以提高预测能力。例如，在海啸模型中，我们可能对波浪在接近给定地区的两个沿海城市时的预期能量感兴趣。在这种情况下，对城市1进行预测的海啸模型的运行可以合理地重复使用，以提高我们对城市2的预测的准确性。在这个项目中，建议使用迁移学习来转换统计学和机器学习中最广泛使用的计算方法之一：蒙特卡罗方法。它们通常用于计算某些感兴趣的量的期望值，不仅应用于海啸模型，而且几乎应用于科学、社会科学和人文科学的所有领域。转移学习在蒙特卡罗方法中的使用目前非常有限，该项目将为其广泛采用奠定必要的基础。

A key message from the UK government's Blackett review was that 'In the future, there will be a greater need for reliable, predictive models that are relevant to the large-scale, complex systems that we want to understand or wish to construct'. Modelling is primarily useful if the model can be used for prediction and if uncertainty around these predictions can be quantified, which typically requires advanced computational tools. As our models grow in scale, significant computational challenges are created. The novelty is not the computational tasks in and of themselves, but the sheer scale of our models, and hence the computational cost of tackling these tasks. For example, tsunami models require several hours of compute time per run, whilst large eddy simulation models for predicting the energy production of wind farms require thousands of hours of compute time per run. These large compute costs are severely limiting the practical use of these models for making accurate predictions about the future.One set of techniques which can help tackle this challenge is 'transfer learning', a sub-field of machine learning which proposes to share data across similar tasks to improve predictions. For example, in tsunami modelling, we might be interested in the expected energy of a wave as it approaches two coastal cities in a given region. In this case, runs of the tsunami models to make predictions for city 1 could reasonably be re-used to improve the accuracy of our predictions for city 2.In this project, propose to use transfer learning to transform one of the most widely used class of computational methods in statistics and machine learning: Monte Carlo methods. These are commonly use to compute the expected value of some quantity of interest, and have been applied not just to tsunami models, but virtually all areas of science, social science and humanities. The use of transfer learning in Monte Carlo methods is currently very limited, and this project will set the foundations needed to pave the way for its widespread adoption.