Learning

Predict mechanical properties of low-alloy steels

Screen four mechanical properties from alloy composition and temperature

This multi-output neural network estimates proof stress, tensile strength, elongation and reduction in area for recorded low-alloy steel families. It can support candidate screening and test prioritization, while physical coupon testing and materials engineering remain responsible for qualification.

915material-temperature records

4mechanical properties predicted together

183testing records

0.850average testing R²

Review the deployment workflow Download the data

Industrial challenge
Data set
Model
Training
Model selection
Testing
Deployment
Limitations

1. Industrial challenge

Low-alloy steel development must balance strength and ductility across composition and temperature. Because every candidate still requires standards-based mechanical testing, a validated surrogate model can help engineers rank familiar alloy families, identify weak margins and focus laboratory effort on the most informative candidates.

Screen candidate conditions

Estimate four linked properties before scheduling a complete coupon-test campaign.

Expose strength–ductility trade-offs

Review proof stress and tensile strength together with elongation and area reduction.

Prioritize verification

Direct laboratory attention to candidates near a specification boundary or outside familiar data coverage.

Materials engineeringMetallurgy & heat treatmentQuality & testingProduct R&DMaterials data teams

Scope of this example. This is a static, data-driven multi-output surrogate for the alloy families and temperatures represented in the dataset. It is not a microstructure model, a material certificate or a replacement for tensile testing.

2. Data set

The local steel_properties.csv contains 915 rows and 20 source columns: one categorical alloy identifier, 15 numeric composition or temperature inputs, and four continuous targets. The categorical alloy_code has 95 known values and expands the 16 source inputs into 110 model features.

Composition variables are reported as percentages, temperature in degrees Celsius, proof and tensile stress in MPa, and elongation and reduction in area as percentages. niobinium_tantalum is retained as the dataset’s technical column name and described here as niobium + tantalum.

Target	Available rows	Minimum	Maximum	Mean	Unit
0.2% proof stress `proof_stress`	914	114	690	328.5	MPa
Tensile strength `tensile_strength`	914	199	830	490.0	MPa
Elongation `elongation`	915	10	78	26.8	%
Reduction in area `reduction_in_area`	915	18	94	70.2	%

0.2% proof stress distribution in the low-alloy steel dataset — 0.2% proof stress distribution (MPa).

Tensile strength distribution in the low-alloy steel dataset — Tensile strength distribution (MPa).

Elongation distribution in the low-alloy steel dataset — Elongation distribution (%).

Reduction in area distribution in the low-alloy steel dataset — Reduction in area distribution (%).

Input–target relationships

To keep a four-target article readable, the regenerated correlation charts are summarized below rather than repeated as four additional full-size figures. These are marginal relationships reported by Neural Designer and do not establish causality.

Property	Strongest reported relationships	Engineering reading
0.2% proof stress	Vanadium +0.639; manganese +0.480; temperature −0.439	Strength varies with both chemistry and test temperature.
Tensile strength	Temperature −0.622; vanadium +0.449; nickel +0.282	Temperature is the dominant marginal relationship in this dataset.
Elongation	Vanadium −0.596; molybdenum −0.485; temperature +0.408	The apparent strength–ductility trade-off motivates multi-output modelling.
Reduction in area	Temperature +0.565; carbon −0.296; carbon equivalent +0.234	Ductility indicators should be reviewed jointly, not inferred from one variable.

Saved split. Two rows with missing target values are marked unused. The remaining 913 rows are divided into 548 training, 182 selection and 183 testing records. This is an interpolation test: every one of the 85 alloy codes in the testing subset also occurs in training. A production study should additionally hold out complete alloy codes or development campaigns.

3. Model

The baseline network applies minimum–maximum encoding to the 95 alloy-code categories and mean–standard-deviation scaling to the 15 numeric inputs. The resulting 110 features feed three tanh hidden neurons and four linear outputs, followed by output unscaling and data-range bounds.

The four outputs are trained jointly so the model can share information across related strength and ductility responses. The baseline has 349 trainable weights and biases.

Baseline Neural Designer architecture with 16 source inputs, 3 hidden neurons and 4 mechanical-property outputs

4. Training strategy

The baseline uses normalized squared error with L2 regularization (weight 0.01) and the Levenberg–Marquardt algorithm. This optimizer is appropriate for the sum-of-squares loss and the moderate network size.

After 122 epochs, the training error is 0.1611 NSE and the selection error is 0.2348 NSE.

Levenberg-Marquardt training and selection error history

5. Model selection

Growing-neuron selection evaluates hidden-layer sizes from 1 to 10. The lowest reported selection error occurs at the upper limit, 10 neurons: training error 0.0922 NSE and selection error 0.1703 NSE. The final 110–10–4 network has 1,154 trainable weights and biases.

Boundary result. Because 10 neurons is the largest tested model, this is the best candidate inside the search range, not proof of a global optimum. A wider search should be assessed only with grouped validation by alloy family.

Growing-neuron selection errors from one to ten hidden neurons — Selection error decreases through the tested upper limit.

Final Neural Designer architecture with ten hidden neurons and four outputs — Final 110–10–4 multi-output architecture.

6. Testing analysis

The final model is evaluated on 183 held-out rows. The table reports Neural Designer’s squared-correlation determination coefficient together with independently calculated MAE, RMSE and 95th-percentile absolute error from the exported testing pairs. Percentage targets use percentage points (pp).

Property	Test rows	R²	MAE	RMSE	95th-percentile absolute error	Mean-baseline RMSE
0.2% proof stress	183	0.903	25.50 MPa	38.78 MPa	57.75 MPa	124.33 MPa
Tensile strength	183	0.933	24.34 MPa	30.94 MPa	60.60 MPa	119.60 MPa
Elongation	183	0.751	3.15 pp	4.15 pp	8.58 pp	8.28 pp
Reduction in area	183	0.812	3.74 pp	5.41 pp	9.46 pp	12.40 pp

Neural Designer goodness-of-fit chart for 0.2% proof stress — 0.2% proof stress: predicted versus observed testing values.

Neural Designer goodness-of-fit chart for Tensile strength — Tensile strength: predicted versus observed testing values.

Neural Designer goodness-of-fit chart for Elongation — Elongation: predicted versus observed testing values.

Neural Designer goodness-of-fit chart for Reduction in area — Reduction in area: predicted versus observed testing values.

7. Model deployment

For engineering use, the model should operate as a screening layer between a materials database and the physical test programme. It returns all four properties for the same candidate; no property should be optimized in isolation.

Alloy family and composition

Temperature and range checks

Four-output surrogate model

Specification-margin review

Coupon-test prioritization

Candidate comparison

Rank familiar alloy-temperature combinations by their complete strength and ductility vector.

Margin-based review

Flag predictions close to a product-specific acceptance threshold for early laboratory confirmation.

Traceable hand-off

Store model version, input ranges, predicted properties and subsequent measured results together.

Case study: thermal derating of alloy VaC

To illustrate this workflow, the composition of alloy VaC is fixed and only temperature is varied. The grey point in each chart is the reference condition at 27 °C. This isolates the temperature response learned by the four-output model without changing the alloy chemistry.

Input	Value	Input	Value
Carbon	0.29%	Silicon	0.20%
Manganese	0.75%	Phosphorus	0.010%
Sulfur	0.009%	Nickel	0.34%
Chromium	1.00%	Molybdenum	1.25%
Copper	0.14%	Vanadium	0.26%
Aluminium	0.002%	Nitrogen	0.0075%
Carbon equivalent	0	Niobium + tantalum	0

Predicted proof stress of alloy VaC as temperature increases — Proof stress decreases as temperature rises.

Predicted tensile strength of alloy VaC as temperature increases — Tensile strength shows the same high-temperature derating.

Predicted elongation of alloy VaC as temperature increases — Elongation increases at higher temperatures.

Predicted reduction in area of alloy VaC as temperature increases — Reduction in area also rises as the material becomes more ductile.

The four curves expose the expected engineering trade-off: the model predicts a progressive loss of strength and greater ductility as temperature increases. This can help identify temperatures where specification margins become small and physical testing should be prioritized.

Valid interpretation range. The chart axes are rounded to 0–700 °C by the export, but this example should only be interpreted between 27 and 650 °C, the temperature interval represented for VaC in the dataset. These are model responses, not material qualification results.

Recommended deployment contract

Stage	Required control
Input validation	Known alloy code; numeric values inside observed ranges; joint composition checks; temperature in the supported test domain.
Model output	Proof stress, tensile strength, elongation and reduction in area returned together, with model and dataset version.
Decision rule	Compare every property with application-specific limits and flag low margins or unfamiliar coverage for review.
Verification	Use standards-based physical testing for material qualification and feed measured residuals back into monitoring.

Why the former optimization is not presented as a recommendation. Minimizing elongation while leaving most variables and the other three properties unconstrained drives the search toward a bound, but it does not represent a credible steel-design objective. A useful optimization must vary only controllable inputs and impose strength, ductility, chemistry and processing constraints together.

Download steel_properties.csv Download Neural Designer project + CSV (ZIP)Reproduce with Neural Designer

8. Scope and limitations

The dataset contains 915 records from 95 named alloy codes, not the complete low-alloy-steel design space.
All 85 alloy codes represented in testing also occur in training. Reported testing metrics therefore measure interpolation for known alloy families, not performance on a new alloy family.
alloy_code expands to 95 one-hot features. An unseen code cannot be used without an explicit unknown-category policy and retraining.
Two rows with missing strength targets are excluded from the saved split. Missing-value handling must be documented if the source data is rebuilt.
Composition, alloy identity and temperature do not fully describe processing route, heat treatment, microstructure, specimen geometry, test standard or laboratory effects.
The model bounds outputs to observed target ranges. A bounded prediction does not prove that an out-of-domain input is safe or physically plausible.
The four one-variable correlation screens are descriptive and non-causal; alloy chemistry is multivariate and constrained.
One proof-stress testing record has an absolute error of approximately 333 MPa. It should be investigated as a possible data, coverage or regime-change issue before operational use.
Production use requires grouped or campaign-based validation, uncertainty and applicability-domain checks, drift monitoring, version control and periodic recalibration.
Predictions support screening only. Qualified materials personnel and standards-based physical tests remain responsible for specification and acceptance.

References

Kaggle: MatNavi Mechanical properties of low-alloy steels.
Neural Designer testing analysis: goodness-of-fit and regression evidence.
Neural Designer model selection: growing-neuron selection.
Neural Designer model deployment: model export, directional outputs and constrained optimization.