Learning task-specific predictive models for scientific computing

2025-06-04

AI Summary

In scientific computing applications—such as trajectory prediction, optimal control, and minimum energy path computation—downstream algorithms critically depend on accurate model evaluations. Conventional mean-squared-error-based supervised learning often induces task-specific performance degradation due to misalignment between the loss function and the ultimate algorithmic objective. Method: We propose a task-oriented predictive modeling paradigm that replaces standard regression losses with a surrogate objective: the maximum prediction error over a downstream task support set. Our framework integrates sampling measure modeling, empirical risk discretization, and iterative optimization to directly optimize downstream algorithmic performance. Contribution/Results: This is the first approach to explicitly embed downstream robustness requirements into the training objective. Evaluated across multiple scientific computing benchmarks, it consistently improves both predictive accuracy and algorithmic stability, demonstrating superior generalization under task-relevant perturbations.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs

Abstract

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.

Problem

• Learning predictive models for non-prediction scientific tasks
• Addressing limitations of mean square error in task-specific learning
• Developing iterative algorithms for task-specific supervised learning

Innovation

• Task-specific predictive models for scientific computing
• Maximum prediction error for downstream task performance
• Iterative algorithm for task-specific supervised learning