Materials Genomics
Unit 12: Uncertainty-Aware Discovery and Gaussian Processes

Prof. Dr. Philipp Pelz

FAU Erlangen-Nürnberg

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01. Title: Uncertainty-Aware Discovery and Gaussian Processes

  • Frame the unit in the end-to-end materials discovery workflow and state the decision problems it addresses.
  • Applied anchor: GP posterior with confidence bands.
  • Book anchor: [Neuer 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: acquisition simulation loop.
  • Book anchor: [Neuer 6.4].

03. Recap from previous unit and dependency map

  • Reconnect prerequisite concepts from earlier units and make dependency assumptions explicit.
  • Applied anchor: ensemble uncertainty map.
  • Book anchor: [McClarren Ch3].

04. Why this unit matters for materials discovery

  • Motivate with a realistic failure/success scenario from materials discovery practice.
  • Applied anchor: calibration plot.
  • Book anchor: [Murphy Ch15].

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: uncertainty-ranked shortlist.
  • Book anchor: [Bishop Bayesian view].

06. Aleatoric vs epistemic uncertainty in materials workflows

  • Explain aleatoric vs epistemic uncertainty in materials workflows using one concrete materials example and one common failure mode.
  • Applied anchor: GP posterior with confidence bands.
  • Book anchor: [Neuer 2.2].

07. Why point predictions are insufficient for discovery

  • Compare why point predictions are insufficient for discovery using one concrete materials example and one common failure mode.
  • Applied anchor: acquisition simulation loop.
  • Book anchor: [Neuer 6.4].

08. Uncertainty decomposition in practical pipelines

  • Diagnose uncertainty decomposition in practical pipelines using one concrete materials example and one common failure mode.
  • Applied anchor: ensemble uncertainty map.
  • Book anchor: [McClarren Ch3].

09. Calibration and reliability for regression outputs

  • Apply calibration and reliability for regression outputs using one concrete materials example and one common failure mode.
  • Applied anchor: calibration plot.
  • Book anchor: [Murphy Ch15].

10. Gaussian Process intuition: prior over functions

  • Define gaussian process intuition: prior over functions using one concrete materials example and one common failure mode.
  • Applied anchor: uncertainty-ranked shortlist.
  • Book anchor: [Bishop Bayesian view].

11. Kernel choice and materials similarity assumptions

  • Explain kernel choice and materials similarity assumptions using one concrete materials example and one common failure mode.
  • Applied anchor: GP posterior with confidence bands.
  • Book anchor: [Neuer 2.2].

12. Posterior mean and variance interpretation

  • Compare posterior mean and variance interpretation using one concrete materials example and one common failure mode.
  • Applied anchor: acquisition simulation loop.
  • Book anchor: [Neuer 6.4].

13. Computational scaling limits of exact GPs

  • Diagnose computational scaling limits of exact gps using one concrete materials example and one common failure mode.
  • Applied anchor: ensemble uncertainty map.
  • Book anchor: [McClarren Ch3].

14. Sparse/approximate GP strategies (conceptual)

  • Apply sparse/approximate gp strategies (conceptual) using one concrete materials example and one common failure mode.
  • Applied anchor: calibration plot.
  • Book anchor: [Murphy Ch15].

15. GP regression for small-to-medium materials datasets

  • Define gp regression for small-to-medium materials datasets using one concrete materials example and one common failure mode.
  • Applied anchor: uncertainty-ranked shortlist.
  • Book anchor: [Bishop Bayesian view].

16. NN ensembles and MC-dropout as uncertainty proxies

  • Explain nn ensembles and mc-dropout as uncertainty proxies using one concrete materials example and one common failure mode.
  • Applied anchor: GP posterior with confidence bands.
  • Book anchor: [Neuer 2.2].

17. Comparing GP uncertainty to ensemble uncertainty

  • Compare comparing gp uncertainty to ensemble uncertainty using one concrete materials example and one common failure mode.
  • Applied anchor: acquisition simulation loop.
  • Book anchor: [Neuer 6.4].

18. Exploration vs exploitation tradeoff in screening

  • Diagnose exploration vs exploitation tradeoff in screening using one concrete materials example and one common failure mode.
  • Applied anchor: ensemble uncertainty map.
  • Book anchor: [McClarren Ch3].

19. Acquisition functions: UCB, EI, PI (conceptual)

  • Apply acquisition functions: ucb, ei, pi (conceptual) using one concrete materials example and one common failure mode.
  • Applied anchor: calibration plot.
  • Book anchor: [Murphy Ch15].

20. Batch acquisition under limited experimental budget

  • Define batch acquisition under limited experimental budget using one concrete materials example and one common failure mode.
  • Applied anchor: uncertainty-ranked shortlist.
  • Book anchor: [Bishop Bayesian view].

21. Constraint-aware candidate selection

  • Explain constraint-aware candidate selection using one concrete materials example and one common failure mode.
  • Applied anchor: GP posterior with confidence bands.
  • Book anchor: [Neuer 2.2].

22. Uncertainty under dataset shift and OOD inputs

  • Compare uncertainty under dataset shift and ood inputs using one concrete materials example and one common failure mode.
  • Applied anchor: acquisition simulation loop.
  • Book anchor: [Neuer 6.4].

23. Failure mode: overconfident wrong predictions

  • Diagnose failure mode: overconfident wrong predictions using one concrete materials example and one common failure mode.
  • Applied anchor: ensemble uncertainty map.
  • Book anchor: [McClarren Ch3].

24. Failure mode: uncertainty miscalibration under shift

  • Apply failure mode: uncertainty miscalibration under shift using one concrete materials example and one common failure mode.
  • Applied anchor: calibration plot.
  • Book anchor: [Murphy Ch15].

25. Failure mode: acquisition over-exploits known chemistry

  • Define failure mode: acquisition over-exploits known chemistry using one concrete materials example and one common failure mode.
  • Applied anchor: uncertainty-ranked shortlist.
  • Book anchor: [Bishop Bayesian view].

26. Case: GP-driven candidate ranking for bandgap

  • Explain case: gp-driven candidate ranking for bandgap using one concrete materials example and one common failure mode.
  • Applied anchor: GP posterior with confidence bands.
  • Book anchor: [Neuer 2.2].

27. Case: uncertainty-guided stability screening

  • Compare case: uncertainty-guided stability screening using one concrete materials example and one common failure mode.
  • Applied anchor: acquisition simulation loop.
  • Book anchor: [Neuer 6.4].

28. Case: NN ensemble vs GP on same benchmark

  • Diagnose case: nn ensemble vs gp on same benchmark using one concrete materials example and one common failure mode.
  • Applied anchor: ensemble uncertainty map.
  • Book anchor: [McClarren Ch3].

29. Decision thresholds with uncertainty and cost

  • Apply decision thresholds with uncertainty and cost using one concrete materials example and one common failure mode.
  • Applied anchor: calibration plot.
  • Book anchor: [Murphy Ch15].

30. Human review loop for high-uncertainty recommendations

  • Define human review loop for high-uncertainty recommendations using one concrete materials example and one common failure mode.
  • Applied anchor: uncertainty-ranked shortlist.
  • Book anchor: [Bishop Bayesian view].

31. Reporting uncertainty in scientific claims

  • Explain reporting uncertainty in scientific claims using one concrete materials example and one common failure mode.
  • Applied anchor: GP posterior with confidence bands.
  • Book anchor: [Neuer 2.2].

32. Connection to physics constraints in Unit 13

  • Compare connection to physics constraints in unit 13 using one concrete materials example and one common failure mode.
  • Applied anchor: acquisition simulation loop.
  • Book anchor: [Neuer 6.4].

33. Connection to end-to-end discovery governance

  • Diagnose connection to end-to-end discovery governance using one concrete materials example and one common failure mode.
  • Applied anchor: ensemble uncertainty map.
  • Book anchor: [McClarren Ch3].

34. Exercise: GP baseline and uncertainty plots

  • Apply exercise: gp baseline and uncertainty plots using one concrete materials example and one common failure mode.
  • Applied anchor: calibration plot.
  • Book anchor: [Murphy Ch15].

35. Exercise: acquisition simulation over iterations

  • Define exercise: acquisition simulation over iterations using one concrete materials example and one common failure mode.
  • Applied anchor: uncertainty-ranked shortlist.
  • Book anchor: [Bishop Bayesian view].

36. Exercise: calibration diagnostics and correction

  • Explain exercise: calibration diagnostics and correction using one concrete materials example and one common failure mode.
  • Applied anchor: GP posterior with confidence bands.
  • Book anchor: [Neuer 2.2].

37. Exam checklist: uncertainty-aware decision argument

  • Compare exam checklist: uncertainty-aware decision argument using one concrete materials example and one common failure mode.
  • Applied anchor: acquisition simulation loop.
  • Book anchor: [Neuer 6.4].

38. Advanced note: Uncertainty-Aware Discovery and Gaussian Processes concept extension 33

  • Diagnose advanced note: uncertainty-aware discovery and gaussian processes concept extension 33 using one concrete materials example and one common failure mode.
  • Applied anchor: ensemble uncertainty map.
  • Book anchor: [McClarren Ch3].

39. Advanced note: Uncertainty-Aware Discovery and Gaussian Processes concept extension 34

  • Apply advanced note: uncertainty-aware discovery and gaussian processes concept extension 34 using one concrete materials example and one common failure mode.
  • Applied anchor: calibration plot.
  • Book anchor: [Murphy Ch15].

40. Advanced note: Uncertainty-Aware Discovery and Gaussian Processes concept extension 35

  • Define advanced note: uncertainty-aware discovery and gaussian processes concept extension 35 using one concrete materials example and one common failure mode.
  • Applied anchor: uncertainty-ranked shortlist.
  • Book anchor: [Bishop Bayesian view].

41. Advanced note: Uncertainty-Aware Discovery and Gaussian Processes concept extension 36

  • Explain advanced note: uncertainty-aware discovery and gaussian processes concept extension 36 using one concrete materials example and one common failure mode.
  • Applied anchor: GP posterior with confidence bands.
  • Book anchor: [Neuer 2.2].

42. Advanced note: Uncertainty-Aware Discovery and Gaussian Processes concept extension 37

  • Compare advanced note: uncertainty-aware discovery and gaussian processes concept extension 37 using one concrete materials example and one common failure mode.
  • Applied anchor: acquisition simulation loop.
  • Book anchor: [Neuer 6.4].

43. Advanced note: Uncertainty-Aware Discovery and Gaussian Processes concept extension 38

  • Diagnose advanced note: uncertainty-aware discovery and gaussian processes concept extension 38 using one concrete materials example and one common failure mode.
  • Applied anchor: ensemble uncertainty map.
  • Book anchor: [McClarren Ch3].

44. Advanced note: Uncertainty-Aware Discovery and Gaussian Processes concept extension 39

  • Apply advanced note: uncertainty-aware discovery and gaussian processes concept extension 39 using one concrete materials example and one common failure mode.
  • Applied anchor: calibration plot.
  • Book anchor: [Murphy Ch15].

45. Exercise setup and dataset definition

  • Define dataset, split protocol, and expected deliverables before any coding begins.
  • Applied anchor: uncertainty-ranked shortlist.
  • Book anchor: [Bishop Bayesian view].

46. Exercise task 1 (pipeline core)

  • Implement the core pipeline component with reproducible settings and documented assumptions.
  • Applied anchor: GP posterior with confidence bands.
  • Book anchor: [Neuer 2.2].

47. Exercise task 2 (comparison/ablation)

  • Run an ablation/comparison under identical validation protocol and interpret differences.
  • Applied anchor: acquisition simulation loop.
  • Book anchor: [Neuer 6.4].

48. Exercise task 3 (failure analysis)

  • Perform structured failure analysis and propose one evidence-backed mitigation.
  • Applied anchor: ensemble uncertainty map.
  • Book anchor: [McClarren Ch3].

49. Exam-oriented key statements

  • Summarize high-yield statements in concise written-exam style with definitions and caveats.
  • Applied anchor: calibration plot.
  • Book anchor: [Murphy Ch15].

50. Summary, next-unit bridge, and references

  • Consolidate the unit into a checklist: concepts, pitfalls, and decisions for next-unit transfer.
  • Applied anchor: uncertainty-ranked shortlist.
  • Book anchor: [Bishop Bayesian view].