Neural Network Surrogate Models: A Step-by-Step Tutorial from NumPy Basics to Deep Ensemble Learning for Optimization Assistance

This project is a step-by-step Python tutorial that systematically explains surrogate-assisted optimization techniques, from basic NumPy implementations to neural network surrogate models (MC Dropout and deep ensembles), and validates model performance on the COCO/BBOB benchmark test suite. It helps learners understand and build neural network surrogate models for optimization assistance from scratch.

Surrogate-assisted optimization is a strategy for solving complex optimization problems in scenarios with limited computational resources. When the cost of evaluating the objective function is extremely high, direct use of traditional optimization algorithms is not feasible. Surrogate models replace the original expensive functions by building low-cost approximate models. Neural networks are ideal choices due to their nonlinear fitting capabilities, as they can quickly predict objective function values to reduce optimization overhead.

The tutorial is divided into three stages: 1. Basic NumPy Implementation: Manually build neural networks and understand forward/backward propagation, gradient descent, etc.; 2. Neural Network Surrogate Construction: Covers data sampling strategies (Latin hypercube, adaptive sampling), model architecture design, and uncertainty quantification; 3. MC Dropout and Deep Ensembles: Explains MC Dropout (approximate Bayesian neural networks) that keeps Dropout enabled during inference, deep ensembles trained with multiple independent networks, and their applications in optimization.

The project validates performance on the BBOB test suite of the COCO platform, which contains 24 functions covering characteristics such as multimodality and separability. Significance of the test: A unified environment ensures comparable results, comprehensively tests the model's scope of application, and uses BBOB standard metrics to facilitate comparison with literature.

Highlights include: Equal emphasis on theory and practice (code and visualization follow concepts), progressive complexity (from basics to cutting-edge technologies), coverage of frontier methods such as MC Dropout and deep ensembles, and standardized evaluation (COCO/BBOB validation ensures rigor).

Surrogate-assisted optimization can be applied in scenarios such as hyperparameter optimization (accelerating ML model tuning), engineering design optimization (shortening simulation cycles in aerospace, etc.), experimental design (reducing the number of experiments in materials/chemistry fields), and reinforcement learning (transfer to environment model construction).

Suitable for learners with Python basics and understanding of basic ML concepts. Prerequisites: Linear algebra, calculus, probability theory; familiarity with NumPy operations; understanding of supervised learning and neural network basics. It is recommended not to skip the NumPy implementation stage to deepen understanding of framework principles.