# Learning task-specific predictive models for scientific computing

arXiv: https://arxiv.org/abs/2506.03835 · HTML: https://mlsanity.com/paper/2506.03835/

## 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 (most cited first, 24 of 24)

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- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics](https://mlsanity.com/paper/1707.09571/) (2017)
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- [Adversarial Training and Robustness for Multiple Perturbations](https://mlsanity.com/paper/1904.13000/) (2019)
- [Stable Learning via Sample Reweighting](https://mlsanity.com/paper/1911.12580/) (2019)
- [TorchMD: A deep learning framework for molecular simulations](https://mlsanity.com/paper/2012.12106/) (2020)
- [Optimal control of PDEs using physics-informed neural networks](https://mlsanity.com/paper/2111.09880/) (2021)
- [Active Learning of Uniformly Accurate Inter-atomic Potentials for Materials Simulation](https://mlsanity.com/paper/1810.11890/) (2018)
- [OnsagerNet: Learning Stable and Interpretable Dynamics using a Generalized Onsager Principle](https://mlsanity.com/paper/2009.02327/) (2020)
- [Why resampling outperforms reweighting for correcting sampling bias with stochastic gradients](https://mlsanity.com/paper/2009.13447/) (2020)
- [Understanding Adversarial Training: Increasing Local Stability of Neural Nets through Robust Optimization](https://mlsanity.com/paper/1511.05432/) (2015)
- [Adversarial Attack Generation Empowered by Min-Max Optimization](https://mlsanity.com/paper/1906.03563/) (2019)
- [Active learning of deep surrogates for PDEs: Application to metasurface design](https://mlsanity.com/paper/2008.12649/) (2020)
- [Iterative Surrogate Model Optimization (ISMO): An active learning algorithm for PDE constrained optimization with deep neural networks](https://mlsanity.com/paper/2008.05730/) (2020)
- [DPA-1: Pretraining of Attention-based Deep Potential Model for Molecular Simulation](https://mlsanity.com/paper/2208.08236/) (2022)
- [A Data Driven Method for Computing Quasipotentials](https://mlsanity.com/paper/2012.09111/) (2020)
- [AI-Lorenz: A physics-data-driven framework for black-box and gray-box identification of chaotic systems with symbolic regression](https://mlsanity.com/paper/2312.14237/) (2023)
- [Polynomial Chaos Expansions on Principal Geodesic Grassmannian Submanifolds for Surrogate Modeling and Uncertainty Quantification](https://mlsanity.com/paper/2401.16683/) (2024)
- [Progressive Optimal Path Sampling for Closed-Loop Optimal Control Design with Deep Neural Networks](https://mlsanity.com/paper/2209.04078/) (2022)
- [Mitigating distribution shift in machine learning-augmented hybrid simulation](https://mlsanity.com/paper/2401.09259/) (2024)
- [Leveraging Interpolation Models and Error Bounds for Verifiable Scientific Machine Learning](https://mlsanity.com/paper/2404.03586/) (2024)

## 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.