Skip to content

UniPhy: Learning a Unified Constitutive Model for Inverse Physics Simulation

Conference: CVPR 2025
arXiv: 2505.16971
Code: https://himangim.github.io/UniPhy
Area: Others / Physics Simulation
Keywords: Inverse physics simulation, constitutive model, latent variable optimization, MPM simulation, material parameter estimation

TL;DR

This work proposes UniPhy, the first unified latent-conditioned constitutive model that encodes diverse material properties (such as elastomers, sand, plastics, Newtonian, and non-Newtonian fluids) within a shared latent space. During inference, the latent variables are optimized through a differentiable Material Point Method (MPM) simulator to match observed particle trajectories, reducing reconstruction errors by 1 to 2 orders of magnitude compared to NCLaw.

Background & Motivation

Background: Inverse physics simulation infers material properties (e.g., elastic modulus, viscosity) from observational data. Existing methods either design specialized models for each material type (such as Neo-Hookean for elasticity, Navier-Stokes for fluids) or utilize learning-based methods like NCLaw which require pre-specifying the material type.

Limitations of Prior Work: In real-world scenarios, the material type is often unknown; for instance, a soft-looking object could be either an elastomer or a plastic. Existing approaches require classifying the material before inferring its properties, making both steps prone to errors.

Key Challenge: The physical behaviors of different materials vary drastically (e.g., elastomeric bouncing vs. sand collapsing vs. fluid flowing), making a unified representation with a single model seemingly impractical.

Key Insight: Material properties are encoded into a continuous latent vector \(z\), where different materials correspond to distinct regions in the latent space while sharing the same neural network architecture. During inference, optimizing the latent vector automatically "discovers" the material type.

Core Idea: Latent-conditioned deformation projection \(g_\phi(F,z)\) + constitutive law \(f_\theta(F_{proj},z)\) = a unified multi-material physics model.

Method

Key Designs

  1. Latent-Conditioned Dual-Network Architecture:

    • Function: Uniformly encodes the physical behavior of various materials
    • Mechanism: Two neural networks are employed: a deformation gradient projection function \(g_\phi(F,z)\) that projects the deformation gradient onto a material-dependent subspace (e.g., projecting elastomers onto a volume-preserving manifold), and a constitutive law function \(f_\theta(F_{proj},z)\) that computes stress from the projected deformation. The latent vector \(z\) encodes material properties.
    • Design Motivation: To decouple "how deformation is decomposed" from "how stress is computed." Different materials decompose and project deformation differently (e.g., volume-preservation for elasticity vs. yield surfaces for sand), but the network structure for stress computation can be shared.

  2. Latent Variable Optimization via Differentiable MPM:

    • Function: Infers material properties from observed particle trajectories
    • Mechanism: The pre-trained \(g_\phi\) and \(f_\theta\) are embedded into a differentiable Material Point Method (MPM) simulator. While holding the network parameters fixed, the latent vector \(z\) is optimized so that the simulated trajectories match the observations, using L2 distance as the loss.
    • Design Motivation: By backpropagating through the simulator's gradient stream to the latent space, end-to-end "observation to material" inference is achieved.

Loss & Training

Training: \(L = \sum_n \sum_t \sum_p (L(F_{proj}, \hat{F}_{proj}) + L(S, \hat{S}) + \frac{1}{\sigma^2}\|z_n\|^2)\), which includes deformation projection error + stress error + latent variable regularization. Inference: L2 particle position error. A 32-dimensional latent space is optimal.

Key Experimental Results

Main Results

Reconstruction Error (\(\times 10^{-5}\)):

Material UniPhy NCLaw
Elastomer 0.052 2.40
Sand 1.50 2.60
Plastic 3.90 6.50
Newtonian Fluid 0.011 2.00

Ablation Study

Configuration Elastomer Error
UniPhy (w/ teacher forcing) 0.052
UniPhy (w/o TF) 1.10
NCLaw (w/o TF) 36.0
4D Latent Space 7.80
32D Latent Space 1.10
256D Latent Space 1.50

Key Findings

  • UniPhy reduces error by 1-2 orders of magnitude compared to NCLaw—showing that a unified model is not only feasible but actually outperforms dedicated models.
  • A 32-dimensional latent space represents the optimal balance—too small cannot distinguish between materials, while too large leads to overfitting.
  • The optimized latent variables accurately reflect material types—different materials cluster into distinct regions.

Highlights & Insights

  • Counter-intuitive Result of Unified > Dedicated: Handling all materials with a single model outperforms designing specialized models for each, likely due to shared knowledge across materials (e.g., the general structure of continuum mechanics).
  • Latent Vector as Material Fingerprint: No prior classification of material types is required; the optimized latent vector automatically encodes the material properties.

Limitations & Future Work

  • Only homogeneous materials are supported (no multi-material mixtures).
  • Requires known initial geometry and 3D motion observations.
  • Trained only on simulated data; generalization to the real world remains unverified.

Rating

  • Novelty: ⭐⭐⭐⭐⭐ First unified multi-material constitutive model.
  • Experimental Thoroughness: ⭐⭐⭐⭐ Diverse material types and thorough generalization testing.
  • Writing Quality: ⭐⭐⭐⭐ Clear theoretical derivations.
  • Value: ⭐⭐⭐⭐ Provides a new paradigm for inverse physics simulation.