Efficient Learning Method to Connect Observables

Area of Science:

• Computational Physics
• Scientific Computing
• Machine Learning

Background:

• Accurate surrogate models are crucial for efficient predictions in complex scientific domains.
• Existing methods for surrogate modeling face challenges in speed and direct observable-to-observable prediction.
• Multiparameter eigenvalue problems (MEPs) are common in physics and engineering, requiring efficient solution techniques.

Purpose of the Study:

• Introduce a novel multiparameter eigenvalue problem (MEP) emulator for constructing fast and accurate surrogate models.
• Enable direct predictions from observables to observables by connecting different emulation techniques.
• Demonstrate the MEP emulator's performance and utility in scientific applications.

Main Methods:

• Developed a new MEP emulator capable of connecting existing emulation frameworks.
• Trained the MEP emulator using data generated from eigenvector continuation and parametric matrix model emulators.
• Validated the emulator's performance through simulations on a one-dimensional lattice.

Main Results:

• The MEP emulator demonstrates high performance in constructing fast and accurate surrogate models.
• The method successfully connects different types of emulators, allowing direct observable-to-observable predictions.
• A case study using ^{28}O showcases the straightforward derivation of predictive probability distributions for target observables.

Conclusions:

• The MEP emulator offers a significant advancement in surrogate modeling for computational physics and related fields.
• This approach enhances prediction accuracy and computational efficiency, particularly for problems involving MEPs.
• The ability to obtain predictive probability distributions directly from the emulator opens new avenues for uncertainty quantification.