Lattice Beam Optimization using Deep Learning

A deep learning pipeline for predicting and minimizing peak von Mises stress in lattice cantilever beam structures using neural network surrogates and gradient-based optimization.

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Overview

The structure is a 2D cantilever beam made of centered rectangular lattice unit cells, with thickness values assigned at 226 nodes. The goal is to train neural networks on 5,000 FEA-simulated configurations to predict peak von Mises stress and then use those networks as differentiable surrogates to minimize it through gradient-based optimization, without running any additional FEA solves.

The dataset is not committed to this repository due to size. See data/README.md for the expected directory structure.

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Notebooks

stress_prediction_mlp.ipynb MLP Baseline

A standard fully connected network mapping the 226-node thickness vector to scalar peak stress.

Test R²	Test MAPE
0.73	10.18%

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gradient_computation.ipynb Sensitivity via Backpropagation

Uses GradientTape on the trained MLP to compute how peak stress changes with each nodal thickness identifying which design variables matter most.

Test R²	Test MAPE
0.69	12.1%

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topology_optimization_adam.ipynb Optimization with Adam

Treats nodal thicknesses as differentiable variables and minimizes surrogate-predicted stress using Adam, with a smoothness regularizer and volume-fraction constraint.

Test R²	Test MAPE	Initial Stress	Optimized Stress
0.62	13.27%	15,567,858 Pa	4,418,916 Pa

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topology_optimization_sgd.ipynb Optimization with SGD

Same setup as above using SGD. Direct comparison in convergence speed and final stress reduction.

Test R²	Test MAPE	Stress Reduction
0.67	11.80%	47.11%

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stress_prediction_cnn.ipynb CNN Surrogate

The thickness vector is reshaped into an 11×21 spatial grid and fed into a CNN, allowing the network to pick up on spatial correlations between neighboring nodes.

Test R²	Test MAPE
0.7639	14.01%

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stress_field_unet.ipynb U-Net for Full-Field Prediction

A U-Net encoder-decoder predicts von Mises stress at all 3,304 nodes. Peak stress is extracted as the field maximum. Harder than scalar regression the network must get every node right, not just the overall maximum.

	Full Field	Max Stress
Train R²	0.68	0.71
Test R²	0.59	0.66
Test MAPE		12.75%

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Results Summary

Method	Task	Test R²	Test MAPE
MLP	Peak stress	0.73	10.18%
CNN	Peak stress	0.76	14.01%
U-Net	Full field + peak extraction	0.66	12.75%
Adam optimization	Stress minimization	0.62	13.27%
SGD optimization	Stress minimization	0.67	11.80%

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Repository Structure

stress-surrogate-optimization/
│
├── notebooks/
│   ├── stress_prediction_mlp.ipynb
│   ├── gradient_computation.ipynb
│   ├── topology_optimization_adam.ipynb
│   ├── topology_optimization_sgd.ipynb
│   ├── stress_prediction_cnn.ipynb
│   └── stress_field_unet.ipynb
│
├── results/
├── data/
│   └── README.md
├── requirements.txt
└── README.md

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Dependencies

pip install -r requirements.txt

tensorflow, keras, keras-tuner, numpy, pandas, scikit-learn, matplotlib, scipy, openpyxl

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Context

Developed as part of ME-504: Deep Learning in Physical Systems at IIT Ropar.