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@article{hillerCrystallographyCohomologyGroups1986,
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}

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  year = 1971,
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}

@book{bourbakiLieGroupsLie2002,
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}

@incollection{pleskenApplicationsRepresentationTheory1991,
  title = {Some Applications of Representation Theory},
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  editor = {Michler, G. O. and Ringel, C. M.},
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  pages = {477--496},
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  title = {International tables for crystallography volume A: Space-group symmetry},
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  volume = {A},
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}

@book{shmueliInternationalTablesCrystallography2010,
  title = {International {{Tables}} for {{Crystallography}}: {{Reciprocal}} Space},
  editor = {Shmueli, U.},
  year = 2010,
  edition = {2},
  volume = {B},
  publisher = {International Union of Crystallography}
}

@book{guilleminDifferentialTopology1974,
  title = {Differential Topology},
  author = {Guillemin, Victor and Pollack, Alan},
  year = 1974,
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@book{artinAlgebra2011,
  title = {Algebra},
  author = {Artin, Michael},
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  publisher = {Pearson Education},
  keywords = {Algebra}
}

@book{brunsCohenMacaulayRings1998,
  title = {Cohen-{{Macaulay}} Rings},
  author = {Bruns, Winfried and Herzog, J{\"u}rgen},
  year = 1998,
  series = {Cambridge Studies in Advanced Mathematics},
  edition = {Rev. ed.},
  number = {39},
  publisher = {Cambridge Univ. Press}
}

@article{stanleyInvariantsFiniteGroups1979,
  title = {Invariants of Finite Groups and Their Applications to Combinatorics},
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  year = 1979,
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@book{mumfordRedBookVarieties2004,
  title = {The Red Book of Varieties and Schemes},
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  year = 2004,
  series = {Lecture Notes in Mathematics},
  edition = {2., expanded ed},
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  publisher = {Springer}
}

@article{farkasReflectionGroupsMultiplicative1986,
  title = {Reflection {{Groups}} and {{Multiplicative Invariants}}},
  author = {Farkas, Daniel R.},
  year = 1986,
  journal = {The Rocky Mountain Journal of Mathematics},
  volume = {16},
  number = {2},
  eprint = {44236989},
  eprinttype = {jstor},
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  publisher = {Rocky Mountain Mathematics Consortium}
}

@book{atiyahIntroductionCommutativeAlgebra1994,
  title = {Introduction {{To Commutative Algebra}}},
  author = {Atiyah, Michael and Macdonald, Ian G.},
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}

@book{derksenComputationalInvariantTheory2002,
  title = {Computational Invariant Theory},
  author = {Derksen, Harm and Kemper, Gregor},
  year = 2002,
  series = {Encyclopaedia of {{Mathematical Sciences}}},
  number = {Volume 130},
  publisher = {Springer}
}


@inproceedings{
poole2023dreamfusion,
title={DreamFusion: Text-to-3D using 2D Diffusion},
author={Ben Poole and Ajay Jain and Jonathan T. Barron and Ben Mildenhall},
booktitle={The Eleventh International Conference on Learning Representations },
year={2023}
}

@inproceedings{rombach2022high,
  title={High-resolution image synthesis with latent diffusion models},
  author={Rombach, Robin and Blattmann, Andreas and Lorenz, Dominik and Esser, Patrick and Ommer, Bj{\"o}rn},
  booktitle={Proceedings of the IEEE/CVF conference on computer vision and pattern recognition},
  pages={10684--10695},
  year={2022}
}

@article{podellsdxl,
  title={Sdxl: Improving latent diffusion models for high-resolution image synthesis},
  author={Podell, Dustin and English, Zion and Lacey, Kyle and Blattmann, Andreas and Dockhorn, Tim and M{\"u}ller, Jonas and Penna, Joe and Rombach, Robin},
  journal={arXiv preprint arXiv:2307.01952},
  year={2023}
}

@article{hu2022lora,
  title={LoRA: Low-Rank Adaptation of Large Language Models},
  author={Hu, Edward J and Shen, Yelong and Wallis, Phillip and Allen-Zhu, Zeyuan and Li, Yuanzhi and Wang, Shean and Wang, Lu and Chen, Weizhu and others},
  journal={ICLR},
  volume={1},
  number={2},
  pages={3},
  year={2022}
}

@misc{von-platen-etal-2022-diffusers,
  author = {Patrick von Platen and Suraj Patil and Anton Lozhkov and Pedro Cuenca and Nathan Lambert and Kashif Rasul and Mishig Davaadorj and Dhruv Nair and Sayak Paul and William Berman and Yiyi Xu and Steven Liu and Thomas Wolf},
  title = {Diffusers: State-of-the-art diffusion models},
  year = {2022},
  publisher = {GitHub},
  journal = {GitHub repository},
  howpublished = {\url{https://github.com/huggingface/diffusers}}
}

@book{shubnikovSymmetryScienceArt1974,
  title = {{Symmetry in science and art}},
  author = {Shubnikov, A. V. and Koptsik, V. A.},
  year = 1974,
  publisher = {Plenum Press},
  keywords = {Symmetry (Art)}
}

@article{zhongTopologyOptimizationTextguided2023,
  title = {Topology Optimization with Text-Guided Stylization},
  author = {Zhong, Shengze and Punpongsanon, Parinya and Iwai, Daisuke and Sato, Kosuke},
  year = 2023,
  journal = {Structural and Multidisciplinary Optimization},
  volume = {66},
  number = {12},
  pages = {256}
}

@inproceedings{wangHarmonyCutSupportingCreative2025,
  title = {{{HarmonyCut}}: {{Supporting Creative Chinese Paper-cutting Design}} with {{Form}} and {{Connotation Harmony}}},
  booktitle = {Proceedings of the 2025 {{CHI Conference}} on {{Human Factors}} in {{Computing Systems}}},
  author = {Wang, Huanchen and Qiu, Tianrun and Li, Jiaping and Lu, Zhicong and Ma, Yuxin},
  year = 2025,
  series = {{{CHI}} '25},
  pages = {1--22},
  publisher = {Association for Computing Machinery}
}

@article{schuhmann2022laion,
  title={Laion-5b: An open large-scale dataset for training next generation image-text models},
  author={Schuhmann, Christoph and Beaumont, Romain and Vencu, Richard and Gordon, Cade and Wightman, Ross and Cherti, Mehdi and Coombes, Theo and Katta, Aarush and Mullis, Clayton and Wortsman, Mitchell and others},
  journal={Advances in neural information processing systems},
  volume={35},
  pages={25278--25294},
  year={2022}
}

@inproceedings{wang2025harmonycut,
  title={HarmonyCut: Supporting creative Chinese paper-cutting design with form and connotation harmony},
  author={Wang, Huanchen and Qiu, Tianrun and Li, Jiaping and Lu, Zhicong and Ma, Yuxin},
  booktitle={Proceedings of the 2025 CHI Conference on Human Factors in Computing Systems},
  pages={1--22},
  year={2025}
}

@misc{googledeepmind2025gemini,
  author = {{Google DeepMind}},
  title  = {{Gemini}},
  year   = {2025},
  url    = {https://deepmind.google/models/gemini/}
}

@article{mildenhallNeRFRepresentingScenes2021,
  title = {{{NeRF}}: Representing Scenes as Neural Radiance Fields for View Synthesis},
  author = {Mildenhall, Ben and Srinivasan, Pratul P. and Tancik, Matthew and Barron, Jonathan T. and Ramamoorthi, Ravi and Ng, Ren},
  year = 2021,
  journal = {Commun. ACM},
  volume = {65},
  number = {1},
  pages = {99--106}
}

@article{mullerInstantNeuralGraphics2022,
  title = {Instant Neural Graphics Primitives with a Multiresolution Hash Encoding},
  author = {M{\"u}ller, Thomas and Evans, Alex and Schied, Christoph and Keller, Alexander},
  year = 2022,
  journal = {ACM Transactions on Graphics (TOG)},
  publisher = {ACMPUB27New York, NY, USA}
}

@article{liStructuralTopologyOptimization2016,
  title = {Structural Topology Optimization Considering Connectivity Constraint},
  author = {Li, Quhao and Chen, Wenjiong and Liu, Shutian and Tong, Liyong},
  year = 2016,
  journal = {Structural and Multidisciplinary Optimization},
  volume = {54},
  number = {4},
  pages = {971--984},
  keywords = {Connectivity constraint,Manufacturing constraints,Topology optimization,Virtual scalar field method}
}

@inproceedings{bergmannLearningTextureManifolds2017a,
  title = {Learning {{Texture Manifolds}} with the {{Periodic Spatial GAN}}},
  booktitle = {Proceedings of the 34th {{International Conference}} on {{Machine Learning}}},
  author = {Bergmann, Urs and Jetchev, Nikolay and Vollgraf, Roland},
  year = 2017,
  pages = {469--477},
  publisher = {PMLR}
}

@article{xia2015design,
  title={Design of materials using topology optimization and energy-based homogenization approach in Matlab},
  author={Xia, Liang and Breitkopf, Piotr},
  journal={Structural and multidisciplinary optimization},
  volume={52},
  number={6},
  pages={1229--1241},
  year={2015},
  publisher={Springer}
}

@inproceedings{chung2023diffusion,
  title={Diffusion posterior sampling for general noisy inverse problems},
  author={Chung, Hyungjin and Kim, Jeongsol and McCann, Michael T and Klasky, Marc L and Ye, Jong Chul},
  booktitle={11th International Conference on Learning Representations, ICLR 2023},
  year={2023}
}

@inproceedings{domingo2025adjoint,
  title={Adjoint matching: Fine-tuning flow and diffusion generative models with memoryless stochastic optimal control},
  author={Domingo-Enrich, Carles and Drozdzal, Michal and Karrer, Brian and Chen, Ricky TQ},
  booktitle={International Conference on Learning Representations},
  volume={2025},
  pages={53791--53846},
  year={2025}
}

@article{ye2024tfg,
  title={Tfg: Unified training-free guidance for diffusion models},
  author={Ye, Haotian and Lin, Haowei and Han, Jiaqi and Xu, Minkai and Liu, Sheng and Liang, Yitao and Ma, Jianzhu and Zou, James and Ermon, Stefano},
  journal={Advances in Neural Information Processing Systems},
  volume={37},
  pages={22370--22417},
  year={2024}
}

@article{vatani2025tripoptimizer,
  title={TripOptimizer: Generative three-dimensional shape optimization and drag prediction using triplane variational autoencoder networks},
  author={Vatani, Parsa and Elrefaie, Mohamed and Nazarpour, Farhad and Ahmed, Faez},
  journal={Physics of Fluids},
  volume={37},
  number={12},
  year={2025},
  publisher={AIP Publishing}
}

@article{wu2026dao,
   	title = {Siamese foundation models for crystal structure prediction},
   	issn = {2041-1723},
   	doi = {10.1038/s41467-026-72362-3},
   	journal = {Nature Communications},
   	author = {Wu, Liming and Huang, Wenbing and Jiao, Rui and Huang, Jianxing and Liu, Liwei and Zhou, Yipeng and Sun, Hao and Liu, Yang and Sun, Fuchun and Ren, Yuxiang and Wen, Ji-Rong},
   	year = {2026},
}

@inproceedings{
li2026unipath,
title={One Path to Model Them All: Learnable-Time Flow Matching for Crystal Structure and Energy Prediction},
author={Songyou Li and Mingze Li and Qianpu Liu and Jiacheng Cen and Liming Wu and Tingyang Xu and Yu Rong and Deli Zhao and Wenbing Huang},
booktitle={32nd SIGKDD Conference on Knowledge Discovery and Data Mining - AI for Sciences Track},
year={2026},
}

@inproceedings{
wu2026dmflow,
title={DMFlow: Disordered Materials Generation by Flow Matching},
author={Liming Wu and Rui Jiao and Qi Li and Mingze Li and Songyou Li and Shifeng Jin and Wenbing Huang},
booktitle={32nd SIGKDD Conference on Knowledge Discovery and Data Mining - AI for Sciences Track},
year={2026}
}

@article{chen2026optimization,
  title={Optimization and Generation in Aerodynamics Inverse Design},
  author={Chen, Huaguan and Lin, Ning and Chen, Luxi and Zhang, Rui and Huang, Wenbing and Li, Chongxuan and Sun, Hao},
  journal={arXiv preprint arXiv:2602.03582},
  year={2026}
}

@inproceedings{zhang2023adding,
  title={Adding conditional control to text-to-image diffusion models},
  author={Zhang, Lvmin and Rao, Anyi and Agrawala, Maneesh},
  booktitle={Proceedings of the IEEE/CVF international conference on computer vision},
  pages={3836--3847},
  year={2023}
}

@article{lu2025dpm,
  title={Dpm-solver++: Fast solver for guided sampling of diffusion probabilistic models},
  author={Lu, Cheng and Zhou, Yuhao and Bao, Fan and Chen, Jianfei and Li, Chongxuan and Zhu, Jun},
  journal={Machine Intelligence Research},
  volume={22},
  number={4},
  pages={730--751},
  year={2025},
  publisher={Springer}
}

@article{mildenhall2021nerf,
  title={Nerf: Representing scenes as neural radiance fields for view synthesis},
  author={Mildenhall, Ben and Srinivasan, Pratul P and Tancik, Matthew and Barron, Jonathan T and Ramamoorthi, Ravi and Ng, Ren},
  journal={Communications of the ACM},
  volume={65},
  number={1},
  pages={99--106},
  year={2021},
  publisher={ACM New York, NY, USA}
}

@misc{openai2024sora,
  author = {{OpenAI}},
  title  = {{Video Generation Models as World Simulators}},
  year   = {2024},
  month  = feb,
  url    = {https://openai.com/index/video-generation-models-as-world-simulators/}
}

@misc{openai2025gpt52,
  author = {{OpenAI}},
  title  = {{Introducing GPT-5.2}},
  year   = {2025},
  url    = {https://openai.com/index/introducing-gpt-5-2/}
}

@article{guan2025taming,
  title={Taming Text-to-Sounding Video Generation via Advanced Modality Condition and Interaction},
  author={Guan, Kaisi and Wang, Xihua and Lai, Zhengfeng and Cheng, Xin and Zhang, Peng and Liu, XiaoJiang and Song, Ruihua and Cao, Meng},
  journal={arXiv preprint arXiv:2510.03117},
  year={2025}
}

@article{chen2025microdreamer,
  title={MicroDreamer: Efficient 3D Generation in ~20 Seconds by Score-based Iterative Reconstruction},
  author={Chen, Luxi and Wang, Zhengyi and Zhou, Zihan and Gao, Tingting and Su, Hang and Zhu, Jun and Li, Chongxuan},
  journal={IEEE Transactions on Pattern Analysis and Machine Intelligence},
  year={2025},
  publisher={IEEE}
}

@article{jiao2023crystal,
     title={Crystal structure prediction by joint equivariant diffusion},
     author={Jiao, Rui and Huang, Wenbing and Lin, Peijia and Han, Jiaqi and Chen, Pin and Lu, Yutong and Liu, Yang},
     journal={Advances in Neural Information Processing Systems},
     volume={36},
     pages={17464--17497},
     year={2023}
   }

@book{bendsoe2013topology,
  title={Topology optimization: theory, methods, and applications},
  author={Bendsoe, Martin Philip and Sigmund, Ole},
  year={2013},
  publisher={Springer Science \& Business Media}
}

@article{andreassen2011efficient,
  title={Efficient topology optimization in MATLAB using 88 lines of code},
  author={Andreassen, Erik and Clausen, Anders and Schevenels, Mattias and Lazarov, Boyan S and Sigmund, Ole},
  journal={Structural and Multidisciplinary Optimization},
  volume={43},
  number={1},
  pages={1--16},
  year={2011},
  publisher={Springer}
}

@article{martinez2015structure,
  title={Structure and appearance optimization for controllable shape design},
  author={Mart{\'\i}nez, Jon{\`a}s and Dumas, J{\'e}r{\'e}mie and Lefebvre, Sylvain and Wei, Li-Yi},
  journal={ACM Transactions on Graphics (TOG)},
  volume={34},
  number={6},
  pages={1--11},
  year={2015},
  publisher={ACM New York, NY, USA}
}

@article{chen2023vlp,
  title={Vlp: A survey on vision-language pre-training},
  author={Chen, Fei-Long and Zhang, Du-Zhen and Han, Ming-Lun and Chen, Xiu-Yi and Shi, Jing and Xu, Shuang and Xu, Bo},
  journal={Machine Intelligence Research},
  volume={20},
  number={1},
  pages={38--56},
  year={2023},
  publisher={Springer}
}

@inproceedings{radford2021learning,
  title={Learning transferable visual models from natural language supervision},
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  year={2021},
  organization={PmLR}
}

@article{levy2025symmcd,
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  year={2025}
}

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  year={2024}
}

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}

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  booktitle={The Eleventh International Conference on Learning Representations},
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}

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