WORRKFLOWS workflow_2.ipynb

• generates the synthetic dataset, validates the physics, puts the data into the PINN
• please see notes, variable, equation, function lists, and citations here: [https://docs.google.com/document/d/1CRuVP2ta7WAxRMIw37ggpHAKsiX_LRi3ehZopM3fYvU/edit?usp=sharing]
• PINN
  • Input: max defect
  • Output: fatigue life
  • Results Summary
    • synthetic data is validated by physics, shiozawa collapse
    • PINN works: predicted data follows PINN exactly as expected since synthetic data and PINN are both built from paris law

pinn_zhou_ti.ipynb

• Zhou Ti-6Al-4V dataset
• 30 samples
• Data: stress_max, sqrt_A_um, defect_position_um, Nf
• PINN
  • Input: log(max defect), log(stress_max), Y
    • adding Y as input or not makes no difference to the output
  • Output: fatigue life
  • Results Summary
    • overfitting
    • physics loss is constant and high as data loss decreases
    • the data likely does not fit the paris law well
    • train and test predictions overlap and follow the trend, but are compressed (regressing toward the mean)

pinn_zhou_slm.ipynb

• Zhou SLM 316l dataset
• 44 samples
• Data: stress_max, deltaK, sqrt_A_um, L/L_eff, Nf
• PINN
  • Input: log(max defect), log(stress_max), Y
    • adding Y as input or not makes no difference to the output
  • Output: fatigue life
  • Results Summary
    • overfitting
    • physics loss is constant and extremely high as data loss decreases
    • the data likely does not fit the paris law well
    • train and test predictions overlap and follow the trend, but are compressed (regressing toward the mean)

pinn_database_ti.ipynb

• Zhang fatigue database, filtered for L-PBF Ti-6Al-4V
• Data is filtered for R = 0.1, fatigue temperature = 25 C, fatigue environment = "air", build direction = 90.0 degrees
• 10,886 samples
• Data: 'Nf', 'stress_amp', 'strain_amp', 'deltaK', 'dadN', 'fatigue_data_type', 'am_process', 'power_w', 'scan_speed', 'hatch_spacing', 'layer_thickness', 'preheat_temp', 'scan_pattern', 'scan_rotation', 'frequency_hz', 'load_control', 'specimen_description', 'spec_cross_area_mm', 'Kt', 'E_gpa', 'yield_strength', 'uts', 'elongation'
• C and m are treated as updatable parameters
• PINN
  • valid samples for input: 169
  • input: log(max defect), log(stress_amp), Y, log(VED_op), log(delta_sigma), log(frequency)
  • output: fatigue life, C, m
  • Results Summary
    • very mild overfitting
    • physics loss drops rapidly before plateauing at a low value
    • data loss decreases steadily, indicating improvement with the experimental data
    • train and test predictions overlap and follow the trend with improved generalization
    • learned C appears to be in a few different clusters
    • learned m is centered around 2.7
  • Sensitivity Study: Data Availability
    • Error decreases with the first between 5-20% of the data (8-33 samples)
    • Beyond 20%, additional data provides diminishing improvements in performance.

pinn_database_slm.ipynb

• Zhang fatigue database, filtered for L-PBF 316L
• Data is filtered for R = 0.1, fatigue temperature = 25 C, fatigue environment = "air", build direction = 90.0 degrees
• 1,912 samples
• Data: 'Nf', 'stress_amp', 'strain_amp', 'deltaK', 'dadN', 'fatigue_data_type', 'am_process', 'power_w', 'scan_speed', 'hatch_spacing', 'layer_thickness', 'preheat_temp', 'scan_pattern', 'scan_rotation', 'frequency_hz', 'load_control', 'specimen_description', 'spec_cross_area_mm', 'Kt', 'E_gpa', 'yield_strength', 'uts', 'elongation'
• C and m are updatable parameters
• PINN
  • valid samples for input: 73
  • Input: log(max defect), log(stress_amp), Y, log(VED_op), log(delta_sigma), log(frequency)
  • Output: fatigue life, C, m
  • Results Summary
    • Train RMSE and Validation RMSE are nearly identical, decrease sharply, then steadily with no widening gap, no divergence, no overfitting.
    • Both losses decrease then level off, the data loss more rapidly at first.
    • The network is trying to satisfy a Paris law with much larger m, which is a stiffer constraint.
    • The test points follow the train scatter reasonably well.
    • The scatter plot closely follows the perfect prediction, with no obvious signs of memorization or overfitting.
    • The highest-life (>10^8) specimens are only mildly underpredicted as expected, since there are few of them.
    • learned C:
      • The network learns roughly 2.5×10^−14 to 1.4×10^−13 centered near (0.9−1.0)×10^−13, which is only about a factor of five variation.
      • The distribution appears multimodal, instead of one universal Paris coefficient.
    • learned m:
      • The learned value is 5.4 to 7.6, centered around 6.4 to 6.4, which is close to the literature value of m=5.86.
      • So, the PINN is making moderate corrections rather than inventing new physics.
  • Sensitivity Study: Data Availability
    • significant improvement in error with 10% of data (7 specimens) then a plateau

DATA

• fatigue database
  • FatigueData-AM2022.xlsx
    • raw fatigue database for additive manufacturing materials (2022)
  • data_fatigue2022.ipynb
    • data cleaning and exploration of fatigue database
  • 316l_fatiguedata_clean.csv
    • cleaned fatigue data for 316L stainless steel
  • fatigue_database_clean.csv
    • cleaned full fatigue database
  • other_fatiguedata_clean.csv
    • cleaned fatigue data for other materials
  • ti64_fatiguedata_clean.csv
    • cleaned fatigue data for Ti-6Al-4V
• zhou
  • data_zhou.xlsx
    • datasets from Zhou, S. et al. (2025). A general physics-informed neural network framework for fatigue life prediction of metallic materials. Engineering Fracture Mechanics, 322, 111136.
  • data_zhou_cleaned.xlsx
    • cleaned version of Zhou dataset
  • data_zhou_metadata.json
    • metadata for Zhou dataset
  • data_zhou.ipynb
    • data cleaning and exploration of Zhou

OTHERS

• practice_paris
  • workflow.ipynb
    • a first draft of the workflow
    • contains:
      • generated inputs
      • volume, defect density, PDF
      • max defects
  • inputs.py
    • inputs manipulation
    • same as workflow.ipynb
    • easier to reference later in other notebooks
  • density.py
    • volume, defect density, PDF
    • same as workflow.ipynb
    • easier to reference later in other notebooks
• practice_basquin
  • deterministic.ipynb
    • deterministic model
    • predicts a single fatigue life for a given defect and stress using Basquin's law
    • S-N, Shozawa curves
  • probabilistic.ipynb
    • probabilistic model
    • predicts a distribution of fatigue lives using Basquin's law
    • PDFs, GEV, S-N, Shiozawa, reliability curves under fixed and varying stress levels
  • probabilistic_ved.ipynb
    • probabilistic model using the defect density and VED as a process input that controls defect statistics
    • predicts a distribution of fatigue lives using Basquin's law
    • PDFs, GEV, S-N, Shiozawa, reliability curves under fixed and varying stress levels
• practice
  • shiozawa.ipynb
    • the first deterministic/probabilistic model
  • practice.ipynb
    • neural network basics
  • practice_parislaw.ipynb
    • neural network basics with the Paris law