mlsanityData to 14 Oct 2026

Learning task-specific predictive models for scientific computing

arXiv 2506.03835 ↗First posted 4 Jun 2025cs.LGcited by 0

Not on the map. Why?

Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 24 of its 39 references that are in the map. First posted on arXiv 4 Jun 2025.

Builds on

24 of 39 references.

References · 24

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2015Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)cited by 1,070
  3. 2018Learning to Reweight Examples for Robust Deep Learningcited by 675
  4. 2017MoDL: Model Based Deep Learning Architecture for Inverse Problemscited by 387
  5. 2017Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanicscited by 214
  6. 2020Machine Learning Force Fieldscited by 207
  7. 2019Adversarial Training and Robustness for Multiple Perturbationscited by 183
  8. 2019Stable Learning via Sample Reweightingcited by 70
  9. 2020TorchMD: A deep learning framework for molecular simulationscited by 55
  10. 2021Optimal control of PDEs using physics-informed neural networkscited by 52
  11. 2018Active Learning of Uniformly Accurate Inter-atomic Potentials for Materials Simulationcited by 37
  12. 2020OnsagerNet: Learning Stable and Interpretable Dynamics using a Generalized Onsager Principlecited by 37
12 more
  1. 2020Why resampling outperforms reweighting for correcting sampling bias with stochastic gradientscited by 34
  2. 2015Understanding Adversarial Training: Increasing Local Stability of Neural Nets through Robust Optimizationcited by 32
  3. 2019Adversarial Attack Generation Empowered by Min-Max Optimizationcited by 32
  4. 2020Active learning of deep surrogates for PDEs: Application to metasurface designcited by 28
  5. 2020Iterative Surrogate Model Optimization (ISMO): An active learning algorithm for PDE constrained optimization with deep neural networkscited by 27
  6. 2022DPA-1: Pretraining of Attention-based Deep Potential Model for Molecular Simulationcited by 15
  7. 2020A Data Driven Method for Computing Quasipotentialscited by 11
  8. 2023AI-Lorenz: A physics-data-driven framework for black-box and gray-box identification of chaotic systems with symbolic regressioncited by 9
  9. 2024Polynomial Chaos Expansions on Principal Geodesic Grassmannian Submanifolds for Surrogate Modeling and Uncertainty Quantificationcited by 6
  10. 2022Progressive Optimal Path Sampling for Closed-Loop Optimal Control Design with Deep Neural Networkscited by 3
  11. 2024Mitigating distribution shift in machine learning-augmented hybrid simulationcited by 2
  12. 2024Leveraging Interpolation Models and Error Bounds for Verifiable Scientific Machine Learningcited by 2

Built on by

Not cited yet.