使用校准驱动的深度模型为科学过程设计精确的仿真器
Designing Accurate Emulators for Scientific Processes using Calibration-Driven Deep Models
摘要：
准确模拟复杂科学过程的预测模型可以在数值模拟器或实验上实现指数加速，同时为改进后续分析提供替代。因此，最近出现了利用现代机器学习（ML）方法（例如深度神经网络）来构建数据驱动仿真器的热潮。虽然大多数现有的努力都集中在定制现成的ML解决方案，以更好地适应手头的科学问题，但我们研究了一个经常被忽视但很重要的问题，即选择损失函数来衡量观测数据与模型预测之间的差异。由于缺乏对期望残差结构的更好的先验，在实践中，做出简单的选择，例如均方误差和平均绝对误差。然而，固有的对称噪声的假设，这些损失函数，使他们不适当的情况下，数据是异构的或噪声分布是不对称的。我们提出了校准学习（LbC），这是一种基于区间校准的新型深度学习方法，用于设计科学应用中的仿真器，即使使用异构数据也有效，并且对离群值具有鲁棒性。使用大量的用例，我们表明LbC在广泛采用的损失函数选择上提供了泛化误差的显着改进，即使在小数据情况下也能实现高质量的仿真器，更重要的是，在没有任何显式先验的情况下恢复了固有的噪声结构。
英文摘要：
Predictive models that accurately emulate complex scientific processes can achieve exponential speed-ups over numerical simulators or experiments, and at the same time provide surrogates for improving the subsequent analysis. Consequently, there is a recent surge in utilizing modern machine learning (ML) methods, such as deep neural networks, to build data-driven emulators. While the majority of existing efforts has focused on tailoring off-the-shelf ML solutions to better suit the scientific problem at hand, we study an often overlooked, yet important, problem of choosing loss functions to measure the discrepancy between observed data and the predictions from a model. Due to lack of better priors on the expected residual structure, in practice, simple choices such as the mean squared error and the mean absolute error are made. However, the inherent symmetric noise assumption made by these loss functions makes them inappropriate in cases where the data is heterogeneous or when the noise distribution is asymmetric. We propose Learn-by-Calibrating (LbC), a novel deep learning approach based on interval calibration for designing emulators in scientific applications, that are effective even with heterogeneous data and are robust to outliers. Using a large suite of use-cases, we show that LbC provides significant improvements in generalization error over widely-adopted loss function choices, achieves high-quality emulators even in small data regimes and more importantly, recovers the inherent noise structure without any explicit priors.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
