为科学计算任务定制预测模型，提升下游算法性能。
Learning task-specific predictive models for scientific computing
- 基于下游任务的采样分布构建特定损失函数
- 最大预测误差控制可有效提升任务表现
- 适用于轨迹预测、最优控制等科学计算场景
我们研究学习一个预测模型，该模型将用于后续特定下游任务（由某算法定义），且该任务需访问模型输出。此任务不一定是预测，常见于机器学习增强的科学计算中。我们指出，该设定不同于经典监督学习，通常无法通过最小化预测均方误差来解决。相反，我们发现：下游任务支持集上的最大预测误差可作为任务性能的有效估计。基于此，我们提出一种基于给定采样测度的任务特定监督学习问题，其解可作为下游任务的可靠代理模型。随后，我们对经验风险进行离散化，并开发了迭代算法求解该问题。三个数值示例——轨迹预测、最优控制和最小能量路径计算——验证了该方法的有效性。
原文摘要 · Abstract (English)
We consider learning a predictive model to be subsequently used for a given downstream task (described by an algorithm) that requires access to the model evaluation. This task need not be prediction, and this situation is frequently encountered in machine-learning-augmented scientific computing. We show that this setting differs from classical supervised learning, and in general it cannot be solved by minimizing the mean square error of the model predictions as is frequently performed in the literature. Instead, we find that the maximum prediction error on the support of the downstream task algorithm can serve as an effective estimate for the subsequent task performance. With this insight, we formulate a task-specific supervised learning problem based on the given sampling measure, whose solution serves as a reliable surrogate model for the downstream task. Then, we discretize the empirical risk based on training data, and develop an iterative algorithm to solve the task-specific supervised learning problem. Three illustrative numerical examples on trajectory prediction, optimal control and minimum energy path computation demonstrate the effectiveness of the approach.
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