IPINN — Physics-Informed Inverse Design for Crashworthiness Optimization

Forward prediction and inverse design of hexagonal composite ring structures under quasi-static crushing, using three physics-informed neural-network architectures compared on the same data + protocol, with multi-start GP-BO inverse design, ill-posedness characterization, and multi-objective Pareto sweep.

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Headline results

Forward-prediction accuracy on the unseen-angle protocol (θ*=60° held out; M=20 bootstrap ensemble; conformal-calibrated):

Approach	Load R²	Energy R²	Load RMSE (kN)	Load MAE (kN)	M_eff/M_total
DDNS	0.7175	0.9803	0.082	0.060	18/20
Soft-PINN	0.7875	0.9911	0.071	0.050	20/20
Hard-PINN	0.8217	0.9888	0.065	0.046	20/20

Full results in paper/tables/Table1_forward_results.csv. All 43 figures (main text + supplementary) rendered at 600 DPI in paper/figures/; see paper/figures/README.md for the main-vs-SI split.

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Repository layout

IPINN/
├── composite_design.py        # Main pipeline (forward + inverse + analysis)
├── data/                       # Experimental dataset (LC1.xlsx, LC2.xlsx)
├── hpo/                        # Optuna HPO + per-member parallel training
├── slurm/                      # HPC submission scripts
├── scripts/                    # Utility scripts (bundle assembly, etc.)
├── tests/                      # 124 unit + integration tests
├── docs/                       # ARCHITECTURE.md (file/line map for reviewers)
├── paper/                      # Publication artifacts
│   ├── figures/                # 43 figures: main text + SI (PNG, 600 DPI)
│   └── tables/                 # Numerical tables (CSV) backing the manuscript
└── CHANGELOG.md

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Reproducing the paper from scratch

git clone https://github.com/kprodigi/IPINN.git
cd IPINN
git checkout v1.0-paper-final

# Environment
conda env create -f environment.yml
conda activate ipinn

# Full pipeline (forward + inverse + figures + tables)
python composite_design.py --mode all \
    --data_dir ./data \
    --output_dir ./results_paper \
    --strict_paper

# Or on HPC, parallel SLURM submission (see slurm/README.md)
bash slurm/submit_pipeline.sh

End-to-end wall time on a 15-GPU SLURM allocation is approximately 14–18 hours (Hard-PINN forward training dominates).

Reproducing the figures without retraining

If you have a previously trained set of model bundles staged at ./results_paper/:

python composite_design.py --mode replot \
    --output_dir ./results_paper \
    --replot_from ./results_paper \
    --force_cpu

Runs in approximately 5 minutes on a single CPU.

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Hyperparameter optimisation

The hyperparameters reported in the paper are tuned per approach by an Optuna TPE study with a MedianPruner across trials. Re-run on your own hardware:

APPROACH=ddns N_TRIALS=150 N_WORKERS=6  bash slurm/submit_hpo.sh
APPROACH=soft N_TRIALS=150 N_WORKERS=6  bash slurm/submit_hpo.sh
APPROACH=hard N_TRIALS=150 N_WORKERS=15 bash slurm/submit_hpo.sh

See hpo/README.md for the full workflow, including warm-start configuration and the resume-from-preemption protocol.

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Methodology highlights

• Hard-PINN architecture: single-output energy network with force recovered exactly by autograd as F = ∂E/∂d — the derivative consistency F = dE/dd holds by construction. Boundary conditions E(0)=0 and F(0)=0 are not architecturally enforced in production; they are shaped through three auxiliary soft regularisers (monotonicity, angle smoothness, energy curvature).
• Soft-PINN architecture: two-headed (F, E) network with the work-energy identity penalised by a soft residual loss and a paired E(0)/F(0) BC penalty.
• DDNS baseline: data-driven only — same two-headed network, no physics terms.
• Honest-reporting note: in the experimental data the energy channel is the trapezoidal integral of the load channel (verified to machine precision), so F = dE/dd holds in the data by construction. The PINN physics terms act as an inductive bias / structural regulariser — they are not validation against an independently measured physical channel.
• M=20 bootstrap ensemble with Tukey-fence convergence filter on training-set R²; survivor-only and all-member statistics are both reported (Mean_Member_Load_R2 vs Mean_Member_Load_R2_all) so the filter's effect is visible.
• Split-conformal calibration (curve-level): ±1σ/±2σ inflation factors are fit on a calibration half of the validation curves and coverage is reported on the held-out half — corrected coverage is a measurement, not a tautology. In-sample factors are retained under *_insample keys for reference.
• Design-level validation: predicted vs experimental EA@80mm / IPF at every measured design (Table_forward_design_errors.csv, overlay stars in Fig_design_space), a no-model interpolation baseline (Table_null_baseline_design_level.csv), a deployment-time physics audit (Table_physical_plausibility_audit.csv), and inverse-design ground-truth recovery (Δθ / LC-match columns in Table 3, off-grid + infeasibility verification targets in Table_inverse_verification.csv).

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Explainability & interpretability

All artifacts below are faithful model readouts (exact decompositions of the trained surrogate), not post-hoc approximations:

• Physics-structural transparency: the Hard-PINN's force is defined as F = ∂E/∂d, so the model's internal mechanical quantities are directly readable and verifiable (Fig_physics_verification).
• Global attribution — which design factor controls what: Table_design_variance_decomposition.csv gives the exact Sobol/ANOVA variance split of EA and IPF into θ main effect, LC main effect, and their interaction, computed on the balanced dense sweep grid (no sampling error).
• Local sensitivity: Fig_forward_map_jacobian (∂EA/∂θ, ∂IPF/∂θ per LC, with bifurcation detection).
• Self-explanatory architecture (opt-in): the separable Hard-PINN variant E(d, θ, LC) = Σₖ φₖ(θ, LC)·Bₖ(d) restricts the θ-dependence to a printed, first-order-Fourier coefficient map; Fig_separable_interpretability plots the learned crush-mode basis Bₖ(d) and design coefficients φₖ(θ) — the figure is the model.
• Inverse decision audit: Table_inverse_design_explanation.csv decomposes each recovered design's objective at the optimum (EA-fit vs IPF-fit vs LC-plausibility penalty, with p_LC and the dominant term) — why the optimizer selected each design; plus the solution landscape, multiplicity index, and approximate posterior for well-posedness.
• Multi-start GP-BO inverse design: 5 restarts × 20 calls/restart, joint kernel over continuous θ and the categorical loading case, with a calibrated VotingClassifier penalty enforcing LC plausibility.
• Ill-posedness diagnostics: solution-landscape mapping, multiplicity index, forward-map Jacobian with bifurcation detection, and an approximate inverse posterior with 95% credible interval.
• Pareto sweep: weighted-sum and Chebyshev scalarisations with 2-D dominance filtering on a dense surrogate landscape.

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CLI reference

Flag	Effect
--data_dir DIR	Input data location (default: ./data)
--output_dir DIR	Output directory (default: ./results_paper)
--mode {all,forward,inverse,replot}	Pipeline stage
--seed N	Global seed base (default: 2026)
--n_ensemble M	Bootstrap ensemble size (default: 20)
--strict_paper	Require optional deps (skopt) — abort if missing
--force_cpu	Use CPU even when CUDA is available
--no_robustness	Skip baselines + sensitivity + ablation
--use_pretrained_inverse PATH	Reuse a pre-trained inverse ensemble bundle
--dry_run	CI/smoke: tiny budgets, M ≤ 2, no GP-BO

Run python composite_design.py --help for the full list.

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Testing

pytest tests/ -q

124 unit + integration tests covering network forward passes, physics losses, training schedules, ensemble aggregation, conformal calibration, classifier behaviour, and inverse-design diagnostics.

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License

MIT