Materials Genomics
Unit 5: Graph-Based Crystal Representations

Prof. Dr. Philipp Pelz

FAU Erlangen-Nürnberg

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01. Title: Graph-Based Crystal Representations

  • Frame the unit in the end-to-end materials discovery workflow and state the decision problems it addresses.
  • Applied anchor: build graph from CIF.
  • Book anchor: [Sandfeld 2.2].

02. Learning objectives and expected outputs

  • State measurable outcomes (what students can explain, implement, and critique by the end of the unit).
  • Applied anchor: compare two cutoff radii.
  • Book anchor: [Neuer 4.5.1–4.5.4].

03. Recap from previous unit and dependency map

  • Reconnect prerequisite concepts from earlier units and make dependency assumptions explicit.
  • Applied anchor: descriptor MLP vs CGCNN.
  • Book anchor: [McClarren Ch8].

04. Why this unit matters for materials discovery

  • Motivate with a realistic failure/success scenario from materials discovery practice.
  • Applied anchor: readout pooling ablation.
  • Book anchor: [Bishop Ch5].

05. Reading map and chapter anchors

  • Map slide blocks to the key book chapters so students can pre-read and post-review effectively.
  • Applied anchor: prototype-wise generalization split.
  • Book anchor: [Murphy representation basics].

06. Why crystals map naturally to graph objects

  • Explain why crystals map naturally to graph objects using one concrete materials example and one common failure mode.
  • Applied anchor: build graph from CIF.
  • Book anchor: [Sandfeld 2.2].

07. Node, edge, and global attributes in crystal graphs

  • Compare node, edge, and global attributes in crystal graphs using one concrete materials example and one common failure mode.
  • Applied anchor: compare two cutoff radii.
  • Book anchor: [Neuer 4.5.1–4.5.4].

08. Periodic boundary conditions in graph construction

  • Diagnose periodic boundary conditions in graph construction using one concrete materials example and one common failure mode.
  • Applied anchor: descriptor MLP vs CGCNN.
  • Book anchor: [McClarren Ch8].

09. Neighbor cutoff choices and physics implications

  • Apply neighbor cutoff choices and physics implications using one concrete materials example and one common failure mode.
  • Applied anchor: readout pooling ablation.
  • Book anchor: [Bishop Ch5].

10. Distance/angle encoding for bonding environments

  • Define distance/angle encoding for bonding environments using one concrete materials example and one common failure mode.
  • Applied anchor: prototype-wise generalization split.
  • Book anchor: [Murphy representation basics].

11. Invariance and equivariance requirements

  • Explain invariance and equivariance requirements using one concrete materials example and one common failure mode.
  • Applied anchor: build graph from CIF.
  • Book anchor: [Sandfeld 2.2].

12. Message passing intuition for materials graphs

  • Compare message passing intuition for materials graphs using one concrete materials example and one common failure mode.
  • Applied anchor: compare two cutoff radii.
  • Book anchor: [Neuer 4.5.1–4.5.4].

13. How CGCNN represents local interactions

  • Diagnose how cgcnn represents local interactions using one concrete materials example and one common failure mode.
  • Applied anchor: descriptor MLP vs CGCNN.
  • Book anchor: [McClarren Ch8].

14. How MEGNet adds global state variables

  • Apply how megnet adds global state variables using one concrete materials example and one common failure mode.
  • Applied anchor: readout pooling ablation.
  • Book anchor: [Bishop Ch5].

15. SchNet-like continuous-filter intuition

  • Define schnet-like continuous-filter intuition using one concrete materials example and one common failure mode.
  • Applied anchor: prototype-wise generalization split.
  • Book anchor: [Murphy representation basics].

16. Pooling/readout choices for property prediction

  • Explain pooling/readout choices for property prediction using one concrete materials example and one common failure mode.
  • Applied anchor: build graph from CIF.
  • Book anchor: [Sandfeld 2.2].

17. Graph depth vs over-smoothing tradeoff

  • Compare graph depth vs over-smoothing tradeoff using one concrete materials example and one common failure mode.
  • Applied anchor: compare two cutoff radii.
  • Book anchor: [Neuer 4.5.1–4.5.4].

18. Data efficiency compared with descriptor MLP baselines

  • Diagnose data efficiency compared with descriptor mlp baselines using one concrete materials example and one common failure mode.
  • Applied anchor: descriptor MLP vs CGCNN.
  • Book anchor: [McClarren Ch8].

19. Handling variable-size crystal inputs

  • Apply handling variable-size crystal inputs using one concrete materials example and one common failure mode.
  • Applied anchor: readout pooling ablation.
  • Book anchor: [Bishop Ch5].

20. Graph construction reproducibility and determinism

  • Define graph construction reproducibility and determinism using one concrete materials example and one common failure mode.
  • Applied anchor: prototype-wise generalization split.
  • Book anchor: [Murphy representation basics].

21. Edge feature engineering beyond distances

  • Explain edge feature engineering beyond distances using one concrete materials example and one common failure mode.
  • Applied anchor: build graph from CIF.
  • Book anchor: [Sandfeld 2.2].

22. Incorporating composition priors into graph models

  • Compare incorporating composition priors into graph models using one concrete materials example and one common failure mode.
  • Applied anchor: compare two cutoff radii.
  • Book anchor: [Neuer 4.5.1–4.5.4].

23. Training stability and batch construction issues

  • Diagnose training stability and batch construction issues using one concrete materials example and one common failure mode.
  • Applied anchor: descriptor MLP vs CGCNN.
  • Book anchor: [McClarren Ch8].

24. Computational cost on large datasets

  • Apply computational cost on large datasets using one concrete materials example and one common failure mode.
  • Applied anchor: readout pooling ablation.
  • Book anchor: [Bishop Ch5].

25. Interpretability in graph models (attention/sensitivity)

  • Define interpretability in graph models (attention/sensitivity) using one concrete materials example and one common failure mode.
  • Applied anchor: prototype-wise generalization split.
  • Book anchor: [Murphy representation basics].

26. Failure mode: shortcut learning from cell-size proxies

  • Explain failure mode: shortcut learning from cell-size proxies using one concrete materials example and one common failure mode.
  • Applied anchor: build graph from CIF.
  • Book anchor: [Sandfeld 2.2].

27. Failure mode: cutoff choice causing nonphysical neighbors

  • Compare failure mode: cutoff choice causing nonphysical neighbors using one concrete materials example and one common failure mode.
  • Applied anchor: compare two cutoff radii.
  • Book anchor: [Neuer 4.5.1–4.5.4].

28. Transferability across chemistry families

  • Diagnose transferability across chemistry families using one concrete materials example and one common failure mode.
  • Applied anchor: descriptor MLP vs CGCNN.
  • Book anchor: [McClarren Ch8].

29. OOD behavior for unseen prototypes

  • Apply ood behavior for unseen prototypes using one concrete materials example and one common failure mode.
  • Applied anchor: readout pooling ablation.
  • Book anchor: [Bishop Ch5].

30. Baseline comparison protocol: descriptor vs graph

  • Define baseline comparison protocol: descriptor vs graph using one concrete materials example and one common failure mode.
  • Applied anchor: prototype-wise generalization split.
  • Book anchor: [Murphy representation basics].

31. Evaluation metrics for regression and ranking

  • Explain evaluation metrics for regression and ranking using one concrete materials example and one common failure mode.
  • Applied anchor: build graph from CIF.
  • Book anchor: [Sandfeld 2.2].

32. Uncertainty with graph ensembles (preview)

  • Compare uncertainty with graph ensembles (preview) using one concrete materials example and one common failure mode.
  • Applied anchor: compare two cutoff radii.
  • Book anchor: [Neuer 4.5.1–4.5.4].

33. Case: bandgap from crystal graph

  • Diagnose case: bandgap from crystal graph using one concrete materials example and one common failure mode.
  • Applied anchor: descriptor MLP vs CGCNN.
  • Book anchor: [McClarren Ch8].

34. Case: formation energy from graph representation

  • Apply case: formation energy from graph representation using one concrete materials example and one common failure mode.
  • Applied anchor: readout pooling ablation.
  • Book anchor: [Bishop Ch5].

35. Case: elasticity prediction under limited data

  • Define case: elasticity prediction under limited data using one concrete materials example and one common failure mode.
  • Applied anchor: prototype-wise generalization split.
  • Book anchor: [Murphy representation basics].

36. How graph embeddings feed Unit 9 representation learning

  • Explain how graph embeddings feed unit 9 representation learning using one concrete materials example and one common failure mode.
  • Applied anchor: build graph from CIF.
  • Book anchor: [Sandfeld 2.2].

37. How this unit connects to local environments in Unit 6

  • Compare how this unit connects to local environments in unit 6 using one concrete materials example and one common failure mode.
  • Applied anchor: compare two cutoff radii.
  • Book anchor: [Neuer 4.5.1–4.5.4].

38. Advanced note: Graph-Based Crystal Representations concept extension 33

  • Diagnose advanced note: graph-based crystal representations concept extension 33 using one concrete materials example and one common failure mode.
  • Applied anchor: descriptor MLP vs CGCNN.
  • Book anchor: [McClarren Ch8].

39. Advanced note: Graph-Based Crystal Representations concept extension 34

  • Apply advanced note: graph-based crystal representations concept extension 34 using one concrete materials example and one common failure mode.
  • Applied anchor: readout pooling ablation.
  • Book anchor: [Bishop Ch5].

40. Advanced note: Graph-Based Crystal Representations concept extension 35

  • Define advanced note: graph-based crystal representations concept extension 35 using one concrete materials example and one common failure mode.
  • Applied anchor: prototype-wise generalization split.
  • Book anchor: [Murphy representation basics].

41. Advanced note: Graph-Based Crystal Representations concept extension 36

  • Explain advanced note: graph-based crystal representations concept extension 36 using one concrete materials example and one common failure mode.
  • Applied anchor: build graph from CIF.
  • Book anchor: [Sandfeld 2.2].

42. Advanced note: Graph-Based Crystal Representations concept extension 37

  • Compare advanced note: graph-based crystal representations concept extension 37 using one concrete materials example and one common failure mode.
  • Applied anchor: compare two cutoff radii.
  • Book anchor: [Neuer 4.5.1–4.5.4].

43. Advanced note: Graph-Based Crystal Representations concept extension 38

  • Diagnose advanced note: graph-based crystal representations concept extension 38 using one concrete materials example and one common failure mode.
  • Applied anchor: descriptor MLP vs CGCNN.
  • Book anchor: [McClarren Ch8].

44. Advanced note: Graph-Based Crystal Representations concept extension 39

  • Apply advanced note: graph-based crystal representations concept extension 39 using one concrete materials example and one common failure mode.
  • Applied anchor: readout pooling ablation.
  • Book anchor: [Bishop Ch5].

45. Exercise setup and dataset definition

  • Define dataset, split protocol, and expected deliverables before any coding begins.
  • Applied anchor: prototype-wise generalization split.
  • Book anchor: [Murphy representation basics].

46. Exercise task 1 (pipeline core)

  • Implement the core pipeline component with reproducible settings and documented assumptions.
  • Applied anchor: build graph from CIF.
  • Book anchor: [Sandfeld 2.2].

47. Exercise task 2 (comparison/ablation)

  • Run an ablation/comparison under identical validation protocol and interpret differences.
  • Applied anchor: compare two cutoff radii.
  • Book anchor: [Neuer 4.5.1–4.5.4].

48. Exercise task 3 (failure analysis)

  • Perform structured failure analysis and propose one evidence-backed mitigation.
  • Applied anchor: descriptor MLP vs CGCNN.
  • Book anchor: [McClarren Ch8].

49. Exam-oriented key statements

  • Summarize high-yield statements in concise written-exam style with definitions and caveats.
  • Applied anchor: readout pooling ablation.
  • Book anchor: [Bishop Ch5].

50. Summary, next-unit bridge, and references

  • Consolidate the unit into a checklist: concepts, pitfalls, and decisions for next-unit transfer.
  • Applied anchor: prototype-wise generalization split.
  • Book anchor: [Murphy representation basics].