Główne pojęcia
Superior efficacy of trust region method in improving generalization errors for regression tasks in scientific machine learning.
Streszczenie
The article discusses the emergence of scientific machine learning, focusing on training problems with a large volume of smooth data. It introduces PETScML as a framework to bridge deep-learning software and conventional solvers. Empirical evidence shows the effectiveness of second-order solvers like L-BFGS and trust region methods in improving generalization errors for regression tasks.
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Introduction
- Scientific machine learning (SciML) integrates data-driven approaches into computational science.
- Neural network models handle high-dimensional function approximations effectively.
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Background
- Non-convex minimization challenges training deep-learning models.
- Stochastic first-order methods are preferred due to overfitting tendencies with second-order optimization methods.
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Related Work
- Second-order methods have been adapted for deep-learning contexts but face efficiency challenges.
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Contributions
- PETScML offers a lightweight Python interface to expose neural networks to PETSc solvers.
- Demonstrates superior efficacy of trust region method based on Gauss-Newton approximation in improving generalization errors.
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Deep-learning Training
- Supervised learning problem involves minimizing non-convex scalar functions using stochastic gradient descent methods.
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Software Architecture
- PETScML provides an abstract class with basic optimization solver methods.
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Numerical Results
- Evaluation of L-BFGS, trust region, and inexact Newton solvers on test cases from recent literature.
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Further Questions
How can the findings from this study be applied to real-world applications?
What are potential drawbacks or limitations of using second-order solvers in practice?
How might advancements in hardware technology impact the efficiency of these solvers?