Composite bayesian optimization in function spaces ising NEON-Neural Epistemic Operator Networks.

Area of Science:

• Scientific Computing
• Machine Learning
• Operator Learning

Background:

• Operator learning models functions in infinite-dimensional spaces.
• Deep ensembles are common for uncertainty but computationally expensive.
• Bayesian Optimization (BO) is crucial for sequential decision-making.

Purpose of the Study:

• Introduce Neon (Neural Epistemic Operator Networks), an efficient architecture for operator learning.
• Enable uncertainty quantification with fewer trainable parameters than deep ensembles.
• Demonstrate Neon's effectiveness in composite Bayesian Optimization.

Main Methods:

• Developed Neon, a single operator network backbone for uncertainty predictions.
• Applied Neon to composite Bayesian Optimization problems.
• Compared Neon against state-of-the-art methods on various scenarios.

Main Results:

• Neon achieves state-of-the-art performance in Bayesian Optimization.
• Neon requires orders of magnitude fewer trainable parameters than deep ensembles.
• The architecture effectively generates predictions with uncertainty.

Conclusions:

• Neon offers a computationally efficient and high-performing alternative for operator learning and uncertainty quantification.
• The method shows significant promise for complex sequential decision-making tasks like Bayesian Optimization.
• Neon advances the field of scientific computing by reducing model complexity without sacrificing performance.