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Unisoma: A Unified Transformer-based Solver for Multi-Solid Systems
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Proposes Unisoma, a Transformer solver for multi-solid systems that explicitly models contact modules, load/contact allocation, and per-solid deformation triplets on slice-based tokens, outperforming implicit neural operator and GNN baselines on seven datasets.
Problem
Predicting deformation of multi-solid systems (rigid and deformable solids with contacts and loads) is hard because existing deep learning methods model solid interactions implicitly, which degrades as the number of solids grows.
Approach
Explicitly model the factors driving solid deformation: per-pair contact modules, adaptive allocation of equivalent loads and contact constraints to each deformable solid, and a per-solid deformation module operating on a (solid, load, contact) triplet, with kNN edge-augmented slice tokens per object.
Key results
- On long-time prediction, Unisoma achieves Relative L2 of 0.0892 geometry on Deforming Plate and 0.0253 on Tissue Manipulation, best among compared methods.
- On autoregressive simulation, Unisoma reaches RMSE-all 9.50e-3 on Cavity Grasping versus 12.43e-3 for HOOD, and 11.98e-2 on Cavity Extruding versus 53.98e-2 for HOOD.
- Unisoma uses 0.93 GiB on bilateral stamping and 1.10 GiB on unilateral stamping, far less memory than Transolver (6.35 and 16.33 GiB).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Unisoma instead of the strongest listed baseline | long-time prediction · Deforming Plate, Geometry | Relative L2: 0.0931 -> 0.0892 | Helped |
| Use Unisoma instead of the strongest listed baseline | long-time prediction · Deforming Plate, Stress | Relative L2: 0.4968 -> 0.4713 | Helped |
| Use Unisoma instead of the strongest listed baseline | long-time prediction · Cavity Grasping and Tissue Manipulation | Relative L2: 0.1073 -> 0.0984; 0.0316 -> 0.0253 | Helped |
| Use Unisoma instead of the strongest listed baseline | long-time prediction · Bilateral Stamping | Relative L2: 0.0083 -> 0.0057; 0.0081 -> 0.0052; 0.0346 -> 0.0278; 0.1378 -> 0.1039; 0.3592 -> 0.2817; 0.3276 -> 0.2265 | Helped |
| Use Unisoma instead of the strongest listed baseline | long-time prediction · Unilateral Stamping | Relative L2: 0.0079 -> 0.0071; 0.0075 -> 0.0063; 0.0839 -> 0.0807; 0.0862 -> 0.0773; 0.2938 -> 0.2591; 0.2675 -> 0.2114 | Helped |
| Use Unisoma instead of the strongest listed baseline | autoregressive simulation · Cavity Grasping | RMSE-all: 12.43 ± 0.34 -> 9.50 ± 0.54 | Helped |
| Use Unisoma instead of the strongest listed baseline | autoregressive simulation · Tissue Manipulation | RMSE-all: 9.56 ± 0.29 -> 7.51 ± 0.28 | Helped |
| Use Unisoma instead of the strongest listed baseline | autoregressive simulation · Rice Grip | RMSE-all: 18.36 ± 0.47 -> 17.68 ± 0.36 | Helped |
| Use Unisoma instead of the strongest listed baseline | autoregressive simulation · Cavity Extruding | RMSE-all: 53.98 ± 1.84 -> 11.98 ± 0.27 | Helped |
Surprising findings
- Transolver, a point-slice implicit model, is the strongest baseline on most stamping targets, suggesting slice-based tokens help even without explicit interaction modeling.
- On the simple Deforming Plate dataset with one contact pair, the advantage of explicit modeling is small and baselines perform similarly.
Limitations
- Explicit modeling requires predefining which solid pairs may contact, so contact modules must be arranged in advance.
- Baselines were adapted to Lagrangian data via padding or grid mapping, which may disadvantage them.
- Only few hyperparameter settings (2 processors, 128 channels, 32 slices) are reported; sensitivity is not studied.
Experimental setup
Datasets: Deforming Plate Cavity Grasping Tissue Manipulation Rice Grip Bilateral Stamping Unilateral Stamping Cavity Extruding
Benchmarks: Deforming Plate Cavity Grasping Tissue Manipulation Bilateral Stamping Unilateral Stamping Cavity Extruding Rice Grip
Metrics: Relative L2 RMSE GPU memory training time
Baselines: GNO Geo-FNO GINO LSM Galerkin Transformer FactFormer OFormer ONO Transolver GraphSAGE GraphUNet MGN
Builds on: Transolver MeshGraphNets Geo-FNO
Closest papers by meaning
- Unisolver: PDE-Conditional Transformers Towards Universal Neural PDE Solvers (ICML 2025 · similarity 0.83)
- Diffusion-Based Hierarchical Graph Neural Networks for Simulating Nonlinear Solid Mechanics (NeurIPS 2025 · similarity 0.83)
- UniPhy: Learning a Unified Constitutive Model for Inverse Physics Simulation (CVPR 2025 · similarity 0.83)
- CODA: Rewriting Transformer Blocks as GEMM-Epilogue Programs (NeurIPS 2026 · similarity 0.82)
- Dense Structural Compression of Transformers via Gauge-Correct Channel Removal (NeurIPS 2026 · similarity 0.82)
- LEIA: Learned Environment for Interactive Architected Materials (NeurIPS 2026 · similarity 0.82)
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