Unisoma: A Unified Transformer-based Solver for Multi-Solid Systems

Shilong Tao, Zhe Feng, Haonan Sun, Zhanxing Zhu, Yunhuai Liu
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:59132-59153, 2025.

Abstract

Multi-solid systems are foundational to a wide range of real-world applications, yet modeling their complex interactions remains challenging. Existing deep learning methods predominantly rely on implicit modeling, where the factors influencing solid deformation are not explicitly represented but are instead indirectly learned. However, as the number of solids increases, these methods struggle to accurately capture intricate physical interactions. In this paper, we introduce a novel explicit modeling paradigm that incorporates factors influencing solid deformation through structured modules. Specifically, we present Unisoma, a unified and flexible Transformer-based model capable of handling variable numbers of solids. Unisoma directly captures physical interactions using contact modules and adaptive interaction allocation mechanism, and learns the deformation through a triplet relationship. Compared to implicit modeling techniques, explicit modeling is more well-suited for multi-solid systems with diverse coupling patterns, as it enables detailed treatment of each solid while preventing information blending and confusion. Experimentally, Unisoma achieves consistent state-of-the-art performance across seven well-established datasets and two complex multi-solid tasks. Code is avaiable at https://github.com/therontau0054/Unisoma.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-tao25b, title = {Unisoma: A Unified Transformer-based Solver for Multi-Solid Systems}, author = {Tao, Shilong and Feng, Zhe and Sun, Haonan and Zhu, Zhanxing and Liu, Yunhuai}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {59132--59153}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/tao25b/tao25b.pdf}, url = {https://proceedings.mlr.press/v267/tao25b.html}, abstract = {Multi-solid systems are foundational to a wide range of real-world applications, yet modeling their complex interactions remains challenging. Existing deep learning methods predominantly rely on implicit modeling, where the factors influencing solid deformation are not explicitly represented but are instead indirectly learned. However, as the number of solids increases, these methods struggle to accurately capture intricate physical interactions. In this paper, we introduce a novel explicit modeling paradigm that incorporates factors influencing solid deformation through structured modules. Specifically, we present Unisoma, a unified and flexible Transformer-based model capable of handling variable numbers of solids. Unisoma directly captures physical interactions using contact modules and adaptive interaction allocation mechanism, and learns the deformation through a triplet relationship. Compared to implicit modeling techniques, explicit modeling is more well-suited for multi-solid systems with diverse coupling patterns, as it enables detailed treatment of each solid while preventing information blending and confusion. Experimentally, Unisoma achieves consistent state-of-the-art performance across seven well-established datasets and two complex multi-solid tasks. Code is avaiable at https://github.com/therontau0054/Unisoma.} }
Endnote
%0 Conference Paper %T Unisoma: A Unified Transformer-based Solver for Multi-Solid Systems %A Shilong Tao %A Zhe Feng %A Haonan Sun %A Zhanxing Zhu %A Yunhuai Liu %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-tao25b %I PMLR %P 59132--59153 %U https://proceedings.mlr.press/v267/tao25b.html %V 267 %X Multi-solid systems are foundational to a wide range of real-world applications, yet modeling their complex interactions remains challenging. Existing deep learning methods predominantly rely on implicit modeling, where the factors influencing solid deformation are not explicitly represented but are instead indirectly learned. However, as the number of solids increases, these methods struggle to accurately capture intricate physical interactions. In this paper, we introduce a novel explicit modeling paradigm that incorporates factors influencing solid deformation through structured modules. Specifically, we present Unisoma, a unified and flexible Transformer-based model capable of handling variable numbers of solids. Unisoma directly captures physical interactions using contact modules and adaptive interaction allocation mechanism, and learns the deformation through a triplet relationship. Compared to implicit modeling techniques, explicit modeling is more well-suited for multi-solid systems with diverse coupling patterns, as it enables detailed treatment of each solid while preventing information blending and confusion. Experimentally, Unisoma achieves consistent state-of-the-art performance across seven well-established datasets and two complex multi-solid tasks. Code is avaiable at https://github.com/therontau0054/Unisoma.
APA
Tao, S., Feng, Z., Sun, H., Zhu, Z. & Liu, Y.. (2025). Unisoma: A Unified Transformer-based Solver for Multi-Solid Systems. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:59132-59153 Available from https://proceedings.mlr.press/v267/tao25b.html.

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