DPC-GNN

A unified physics-constrained Graph Neural Network that simulates biological tissues spanning four orders of magnitude in stiffness, from brain parenchyma (~1 kPa) to trabecular bone (~10 MPa), plus a companion SPH-GNN for non-Newtonian blood flow.

The network encodes continuum-mechanical invariants as architectural and constitutive properties rather than additive loss terms:

• Antisymmetric Message Passing (AMP) enforces Newton's third law as an algebraic identity at every forward pass: a shared edge network is evaluated forward and reverse and combined by subtraction, so m_ij = -m_ji by construction.
• Modified Neo-Hookean energy with a compact-support barrier at J → 0+ prevents Jacobian inversion.
• Global Dilatation Regularization (GDR) replaces element-local F-bar with a single mesh-level mean-dilatation projection, removing volumetric locking at near-incompressibility.
• Stiffness-aware decoder rescaling uses the analytic Euler–Bernoulli tip displacement to keep training signals at unit scale across four stiffness decades.
• Velocity Verlet integration preserves the symplectic structure of conservative dynamics.

Training is unsupervised: the model minimises Neo-Hookean strain energy plus gravitational potential directly, without paired FEM displacement labels.

multi_tissue/src/         FEM-GNN training (solid tissues) + SPH-GNN (blood)
                          + reference FEM solvers (scipy.sparse)
phase_d/                  small reusable modules (material_features.py,
                          material_scaling.py) with their own tests
experiments/              cached experimental results (JSON + log) for the
                          published 20-seed sweeps; backs the headline numbers
scripts/                  utility scripts

# Single tissue, single seed
python3 multi_tissue/src/solid_tissue_train.py --tissue bone --epochs 1000 --seed 42

# High-resolution variant used in the published 20-seed sweeps
python3 multi_tissue/src/solid_tissue_train_hires.py --tissue brain --seed 42 --epochs 3000

# Full 6-tissue × 20-seed sweep (uses /root paths; edit before running locally)
bash multi_tissue/src/run_20seed.sh

# Steady-state Poiseuille blood flow
python3 multi_tissue/src/poiseuille_v2.py --epochs 500 --dp 0.001 --delta-p 0.5

# Pulsatile Womersley (smoke test)
python3 multi_tissue/src/womersley_test.py --epochs 50 --quick

Tissue identifiers recognised by the trainer: brain, kidney, myocardium, cartilage, vessel, bone.

Twenty seeds are used for every solid-tissue table entry: 42, 123, 456, 789, 2026, 1337, 999, 31415, 271828, 1000, 2024, 3407, 7777, 8888, 12345, 54321, 99999, 11111, 66666, 100.

Aggregated experimental results (per-tissue, per-seed) live under experiments/ as JSON.

Any new message-passing layer in this codebase must preserve m_ij = -m_ji. Breaking that identity invalidates the physics claim of the underlying method.

Training was developed for an NVIDIA RTX 5090 (PyTorch 2.12 / CUDA 12.8). The runner scripts hardcode /root/... paths used on the training box; edit those before running on a different machine.

Apache License, Version 2.0 — see LICENSE.