Use AI, data, optimization, digital twins, and simulation responsibly inside engineering workflows.
Course outline only for now. Full chapter-level lessons are still in progress. Use this page for readiness, concepts, worked-example format, practice, review, and portfolio direction. Complete course contents are live today for Math, Physics, and Statics.
01
Readiness check
Before starting, confirm the prerequisite habits.
Understand training versus validation data.
Know basic simulation inputs and outputs.
Read error metrics critically.
Recognize when physics checks override model confidence.
0 or 1 weak itemContinue, but slow down at the worked example.
2 weak itemsReview the foundation page linked in the roadmap before solving practice problems.
3 or more weak itemsStep back to prerequisites; this module depends on them.
02
The core idea
Use AI to accelerate modeling and review while keeping physics, validation, and accountability with the engineer.
AI in engineering is a fast approximator wrapped around physics you still own: a surrogate or ML model is only trustworthy inside its training range and after you validate it against the governing equations.
validate before use
Works when: the model is validated on held-out data and used only inside the range it was trained on.
Breaks down when: you extrapolate a surrogate beyond its training data, or accept a prediction with no physics check.
Figure 1. Concept model for AI and Digital Engineering. The figure names inputs, computed variables, geometry, and result.
Figure 2. Worked problem setup: A surrogate predicts bracket mass within 2 percent on training data but 11 percent on validation data. Decide whether it is ready Figure 3. Calculation model. The result follows from the model, units, and reasonableness check.
A surrogate predicts bracket mass within 2 percent on training data but 11 percent on validation data. Decide whether it is ready for design screening.
Problem A surrogate predicts bracket mass within 2 percent on training data but 11 percent on validation data. Decide whether it is ready for design screening.
Given and find Training error 2 percent, validation error 11 percent, target validation error below 5 percent. Find: Use decision and next action.
Assumptions Idealized model, consistent units, and no hidden effects outside the stated scope.
Step Compare against validation error, not training error.
Step 11 percent is above the 5 percent target.
Step Add data where prediction error is large and retrain.
Step Keep the physics model as authority until validation passes.
Conclusion not ready. Carry this result into the design decision, not just into the answer box.
05
Misconceptions and diagnostics
Mistake
Symptom
Diagnostic question
Correction
Extrapolation
Trusts the model outside its data
Is this input inside the training range?
Use the surrogate only within its validated domain.
Train vs. validate gap
2 percent error on train, 11 percent on new data
Did you check held-out performance?
Report validation error, not training error.
No physics check
Accepts a non-physical prediction
Does this obey conservation laws?
Sanity-check ML output against governing physics.
06
Practice ladder
Level 1: direct skill
Redo the worked example with one changed input. Predict the trend before calculating.
Check yourself
The trend must match the governing relation: validate before use.
Level 2: mixed concept
Draw the model from memory, label knowns and unknowns, then write the first equation without looking.
Check yourself
Your first equation should connect the model to design decision.
Level 3: independent problem
Create a similar problem from a real object near you. State assumptions, solve it, and include a reasonableness check.
Check yourself
A valid solution has a sketch, given/find list, governing relation, units, and a conclusion.
Level 4: transfer task
Turn the result into a design decision: what would you change if the output missed its target by 25 percent?
Check yourself
Name the design variable with the strongest influence and justify it from the equation.
07
Working with AI, and proving it yourself
Useful AI role
Ask for a critique of assumptions, units, diagram labels, and missing checks after you have attempted the solution.
Do not outsource
Do not paste the problem and accept a final answer. Your evidence is the model, the checks, and the explanation.
08
Retrieval and spaced review
Closed-notes prompts: state what the model predicts, name its training range, write the validation error, and give one physics check the prediction must pass.
TodayRedo the worked example from a blank page.
+1 daySolve Level 1 without notes.
+3 daysSolve Level 2 with changed numbers.
+7 daysConnect this module to another course.
+30 daysAdd a portfolio artifact.
09
Mapping and portfolio task
Course mapping
AI and digital engineering accelerate the other courses rather than replace them: a surrogate is only as good as the FEM, CFD, or test data it learned from and the physics you check it against.
First-pass focus: definitions, model setup, units, and worked examples. Save edge cases for the second pass.
Portfolio task
Create a one-page surrogate-model note stating the training range and a physics check: sketch, assumptions, equations, result, reasonableness check, limitation, and recommendation.