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UniPhy: Learning a Unified Constitutive Model for Inverse Physics Simulation
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Proposes UniPhy, a single latent-conditioned neural constitutive model trained on simulated MPM trajectories across elastic, plasticine, sand, and fluid materials, enabling material inference via latent optimization through differentiable simulation.
Problem
Inverse simulation: inferring material properties from observed 3D particle motion without user-specified constitutive model type, and with robust, accurate re-simulation under new conditions.
Approach
A shared latent-conditioned deformation gradient projection network and constitutive law network trained jointly across many materials and trajectories (each trajectory gets its own latent), so that at inference only the latent is optimized through a frozen, differentiable MPM simulator instead of training a separate network per scene.
Key results
- UniPhy achieves lower reconstruction error than NCLaw on elastic (5.2e-6 vs 2.4e-4), sand (1.5e-5 vs 2.6e-5), plasticine (3.9e-5 vs 6.5e-5), and Newtonian (1.1e-6 vs 2.0e-5) materials.
- Without teacher forcing, UniPhy (w/o TF) still outperforms NCLaw (w/o TF) on all four materials (e.g., elastic 1.1e-4 vs 3.6e-3).
- Latent-size ablation finds 32 dimensions gives the best reconstruction among 4, 32, and 256.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a shared latent-conditioned constitutive model instead of NCLaw | UniPhy · Elastic | reconstruction error: 2.4e-4 -> 5.2e-6 | Helped |
| Use a shared latent-conditioned constitutive model instead of NCLaw | UniPhy · Sand | reconstruction error: 2.6e-5 -> 1.5e-5 | Helped |
| Use a shared latent-conditioned constitutive model instead of NCLaw | UniPhy · Plasticine | reconstruction error: 6.5e-5 -> 3.9e-5 | Helped |
| Use a shared latent-conditioned constitutive model instead of NCLaw | UniPhy · Newtonian | reconstruction error: 2.0e-5 -> 1.1e-6 | Helped |
| Use latent size 4 instead of 32 (ablation) | UniPhy · Elastic | reconstruction error: 1.1e-4 -> 7.8e-4 | Hurt |
| Use latent size 256 instead of 32 (ablation) | UniPhy · Elastic | reconstruction error: 1.1e-4 -> 1.5e-4 | Hurt |
| Use latent size 4 instead of 32 (ablation) | UniPhy · Sand | reconstruction error: 2.4e-4 -> 3.4e-4 | Hurt |
| Use latent size 256 instead of 32 (ablation) | UniPhy · Sand | reconstruction error: 2.4e-4 -> 2.7e-4 | Hurt |
| Use latent size 4 instead of 32 (ablation) | UniPhy · Plasticine | reconstruction error: 6.2e-5 -> 1.7e-4 | Hurt |
| Use latent size 256 instead of 32 (ablation) | UniPhy · Plasticine | reconstruction error: 6.2e-5 -> 7.1e-5 | Hurt |
| Use latent size 4 instead of 32 (ablation) | UniPhy · Newtonian | reconstruction error: 8.9e-6 -> 2.9e-5 | Hurt |
| Use latent size 256 instead of 32 (ablation) | UniPhy · Newtonian | reconstruction error: 8.9e-6 -> 9.4e-6 | No clear effect |
Surprising findings
- Optimized latents clearly outperform random latents from other trajectories, but the paper reports that ground-truth constitutive law or projection function substitution yields similar errors, suggesting both networks are accurately learned.
Limitations
- Cannot handle non-homogeneous scenes or inference of multiple latents/materials in one scene.
- Requires known initial geometry and 3D (or 2D) motion observations.
- Evaluated only on simulated data with MPM-generated trajectories.
Experimental setup
Datasets: MPM-simulated trajectories (200 per material, five materials)
Benchmarks: NCLaw trajectories reconstruction generalization to extended time, unseen velocity, and different geometry
Metrics: reconstruction error (L2 particle position)
Baselines: NCLaw spline neural constitutive law GNN simulator NCLaw (w/o teacher forcing)
Builds on: NCLaw Material Point Method APIC PAC-NeRF
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