UniPhy: Learning a Unified Constitutive Model for Inverse Physics Simulation

TL;DR

UniPhy presents a unified, latent-conditioned neural constitutive model that learns a shared representation across diverse materials and enables inverse physics via differentiable simulation. By training two networks—the deformation gradient projection and the constitutive law network—conditioned on a trajectory latent, the approach captures material behavior across elastic, plasticine, sand, and fluid regimes within a single model. Inference uses latent optimization in a differentiable MPM simulator to reconstruct material properties from observed trajectories, enabling accurate replay and re-simulation under novel conditions and geometries. The method demonstrates improved reconstruction accuracy and generalization over baselines, highlighting the potential for cross-material physical inference without requiring explicit material labels.

Abstract

We propose UniPhy, a common latent-conditioned neural constitutive model that can encode the physical properties of diverse materials. At inference UniPhy allows `inverse simulation' i.e. inferring material properties by optimizing the scene-specific latent to match the available observations via differentiable simulation. In contrast to existing methods that treat such inference as system identification, UniPhy does not rely on user-specified material type information. Compared to prior neural constitutive modeling approaches which learn instance specific networks, the shared training across materials improves both, robustness and accuracy of the estimates. We train UniPhy using simulated trajectories across diverse geometries and materials -- elastic, plasticine, sand, and fluids (Newtonian & non-Newtonian). At inference, given an object with unknown material properties, UniPhy can infer the material properties via latent optimization to match the motion observations, and can then allow re-simulating the object under diverse scenarios. We compare UniPhy against prior inverse simulation methods, and show that the inference from UniPhy enables more accurate replay and re-simulation under novel conditions.

Figures (4)

• Figure 1: Overview (a) We use the Material Point Method simulator to generate a dataset with various geometries, motions, and material parameters (e.g. Young's modulus) as represented in the parameter grid. The dataset comprises of the particle to node deformation gradient matrix, projected deformation gradient matrix, and stress matrix. The visualizations show some example trajectories of different materials. (b) Next, we use the dataset to train the latent-conditioned deformation gradient projection network ($g_\phi$) in orange with the particle-to-node deformation gradient matrix and the latent as input and the latent-conditioned constitutive law network ($f_\theta$) in green block with the projected deformation gradient matrix and the latent as the input. Each trajectory in the dataset is initialized with its unique random latent. Note that the same trajectory latent is given to both the networks. We use the $\mathcal{L}2$ objective function between the predicted and ground truth deformation gradient matrix, and the predicted and ground truth stress matrix to optimize both the neural networks and the latent.
• Figure 2: We show the inference setup in the figure where given an object trajectory along with a random latent, we do not have the material properties beforehand. After training the deformation gradient projection function network ($g_\phi$) and constitutive law network ($f_\theta$), we embed the networks (weights frozen) in the differentiable Material Point Method (MPM) simulator and optimize the latent ($z$) using the $\mathcal{L}2$ loss between the predicted trajectory and ground truth trajectory. The latent after optimization is able to capture the material properties of the given object.
• Figure 3: We show our results (w/ and w/o teacher forcing (TF)) in columns four and three respectively compared with NCLaw (w/ and w/o teacher forcing (TF)) in columns two and one respectively, on reconstruction and generalization settings of extended time, unseen velocity, and different geometry. We show these differences in yellow dotted circles. We can see that in elastic our method is able to reconstruct the edge better. In newtonian, the separation between the fluid particles is ellipsoidal in ours and ground truth whereas the separation is circular in other visualizations. For sand, the fold of our method is more defined/sharper like GT as compared to the other visuals where the fold is smoother/softer. Finally, in plasticine, the spread and fold of the particles on the ground of ours and GT is similar.
• Figure 4: Qualitative Results on non-Newtonian and Elastic materials. The difference in the shape of the optimized latent (ours) versus latent from other random trajectory shows that our method is able to learn the material properties of non-Newtonian materials (as well as other materials) when compared with optimized versus other trajectory latent.