今天有點空閒的時間， 想要看看Bingqing老師的文章， 結果發現有好多的東西， 一頭霧水。 我想有好幾個不清楚的東西， 第一個就是圖神經網絡，還沒有學會。 說到圖這種結構我就蒙了。 那第一個要解決的問題應該是圖神經網絡。 理解了之後應該就會很優雅， 有趣。 有些東西確實不簡單， 但真正掌握了應該會很有成就感吧。 要想人前優雅， 就要人後把改學的東西學了才可以。 讓AI給我寫了一個Roadmap。

Roadmap: Building a Machine Learning Potential (MLP) for Atomistic Simulations

This roadmap guides you through the stages of learning required to develop a machine learning interatomic potential from scratch. It starts with fundamental concepts and progresses to advanced integration into simulation tools. Each stage lists key topics, recommended resources, and what you should be able to achieve before moving on.

Stage 1: Foundational Machine Learning Knowledge (Beginner)

• Core ML Concepts (Regression & Optimization):
  Understand supervised learning for regression, gradient descent, loss functions.
  Goal: Train and evaluate a simple regression model.
  Resources: Andrew Ng’s ML course, “Hands-On ML with Scikit-Learn and TensorFlow”.

• Neural Networks and Backpropagation:
  Learn how feedforward neural networks work.
  Goal: Build and train a 2-3 layer neural network using PyTorch or TensorFlow.
  Resources: Michael Nielsen’s book, CS231n notes, PyTorch tutorials.

• Practical ML Skills:
  Learn model evaluation, train/validation split, overfitting, and regularization.
  Goal: Train ML models on regression datasets and track performance.

Stage 2: Atomistic Simulation Basics (Beginner to Intermediate)

• DFT and Classical Potentials:
  Learn the difference between DFT and classical MD. Understand why MLPs are needed.
  Goal: Be able to explain the need for ML potentials.
  Resources: DFT tutorials, “DFT 101”, “Understanding Molecular Simulation”.

• Potential Energy Surfaces and Forces:
  Understand energy landscapes and how forces relate to gradients.
  Goal: Explain how forces are computed and used in MD.

• Running Simple MD Simulations:
  Run MD with LAMMPS, ASE, or other tools using classical potentials.
  Goal: Run a basic MD simulation and understand output.

Stage 3: Atomic Descriptors and Representations (Intermediate)

• Symmetry Functions (ACSF) and SOAP:
  Learn how local atomic environments are described.
  Goal: Compute descriptors for a small system (e.g., using DScribe).

• Graph Neural Networks (Optional Advanced Path):
  Learn how GNNs model atomic systems via message passing.
  Goal: Understand how graphs represent molecules and materials.

• Feature Quality:
  Understand what features capture relevant physics (distances, angles, etc.).
  Goal: Choose and justify a descriptor method for your own project.

Stage 4: Energy and Force Prediction with ML Models (Intermediate)

• Atomic Energy Decomposition:
  Learn how total energy = sum of atomic energies in MLPs.
  Goal: Implement a per-atom NN model to predict total energy.

• Differentiation for Forces:
  Use autograd to compute forces from energy predictions.
  Goal: Implement a force calculation using automatic differentiation.

• Combined Loss Functions:
  Train models using both energy and force loss.
  Goal: Define a custom loss and train a model with weighted energy and force terms.

• Physical Constraints and Regularization:
  Apply regularization, unit conversions, and physical sanity checks.

Stage 5: Data Generation and Preprocessing (Intermediate)

• Generating DFT Reference Data:
  Use DFT or ab initio MD to generate diverse atomic structures and outputs.
  Goal: Build a training dataset of structures, energies, and forces.

• Neighbor Lists and Cutoffs:
  Implement cutoff-based neighbor list generation.
  Goal: For each atom, find neighbors within a fixed radius.

• Feature Scaling and Formatting:
  Normalize descriptors and subtract per-atom reference energies.
  Goal: Prepare dataset for training.

• Tools:
  Use ASE, DScribe, and other utilities to automate preprocessing.
  Goal: Have a clean training dataset ready for ML input.

Stage 6: Training and Evaluating MLPs (Advanced)

• Training Setup:
  Choose network architecture, optimizer, and loss terms.
  Goal: Successfully train a model on your dataset.

• Hyperparameter Tuning:
  Experiment with network size, learning rate, loss weights.
  Goal: Minimize test error and avoid overfitting.

• Error Evaluation:
  Use RMSE on energies and forces. Check predictions vs. DFT.
  Goal: Achieve meV-level errors if possible.

• Physical Validation:
  Run short MD or structure relaxations using your model.
  Goal: Confirm conservation of energy, correct equilibrium structures, etc.

• Active Learning (Optional):
  Expand dataset based on failure regions.
  Goal: Iteratively improve performance.

Stage 7: Integration into Simulation Frameworks (Advanced)

• ASE Integration:
  Write an ASE Calculator that calls your model.
  Goal: Use your MLP in ASE for optimization or MD.

• LAMMPS Integration:
  Options include custom pair styles, Python callbacks, or external libraries.
  Goal: Run LAMMPS using your model (start with small test systems).

• OpenMM or Other Engines (Optional):
  Use with other tools like OpenMM for biomolecular systems.
  Goal: Connect MLP to any tool that supports custom force fields.

• Final Tests:
  Validate energy/force agreement between standalone and simulation engine.
  Goal: Use your model in real MD runs with confidence.

End Goal: Be able to train your own machine learning potential on DFT data, validate its accuracy, and run real simulations (structure optimization or MD) using it in ASE or LAMMPS.