# Periodic Topological Deep Learning for Polymer Design and Discovery

arXiv: https://arxiv.org/abs/2605.26833 · HTML: https://mlsanity.com/paper/2605.26833/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 110 references that are in the map.
- First posted on arXiv 26 May 2026.

## Builds on (most cited first, 30 of 34)

- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [How transferable are features in deep neural networks?](https://mlsanity.com/paper/1411.1792/) (2014)
- [DeeperGCN: All You Need to Train Deeper GCNs](https://mlsanity.com/paper/2006.07739/) (2020)
- [Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks](https://mlsanity.com/paper/2103.03212/) (2021)
- [Weisfeiler and Lehman Go Cellular: CW Networks](https://mlsanity.com/paper/2106.12575/) (2021)
- [Motif-based Graph Self-Supervised Learning for Molecular Property Prediction](https://mlsanity.com/paper/2110.00987/) (2021)
- [A roadmap for the computation of persistent homology](https://mlsanity.com/paper/1506.08903/) (2015)
- [Topological Deep Learning: Going Beyond Graph Data](https://mlsanity.com/paper/2206.00606/) (2022)
- [What are higher-order networks?](https://mlsanity.com/paper/2104.11329/) (2021)
- [Position: Topological Deep Learning is the New Frontier for Relational Learning](https://mlsanity.com/paper/2402.08871/) (2024)
- [polyBERT: A chemical language model to enable fully machine-driven ultrafast polymer informatics](https://mlsanity.com/paper/2209.14803/) (2022)
- [TransPolymer: a Transformer-based language model for polymer property predictions](https://mlsanity.com/paper/2209.01307/) (2022)
- [Simplicial Attention Networks](https://mlsanity.com/paper/2204.09455/) (2022)
- [Simplicial Convolutional Neural Networks](https://mlsanity.com/paper/2110.02585/) (2021)
- [Cell Attention Networks](https://mlsanity.com/paper/2209.08179/) (2022)
- [Message-passing neural networks for high-throughput polymer screening](https://mlsanity.com/paper/1807.10363/) (2018)
- [Polymer Informatics with Multi-Task Learning](https://mlsanity.com/paper/2010.15166/) (2020)
- [Polymer Informatics: Current Status and Critical Next Steps](https://mlsanity.com/paper/2011.00508/) (2020)
- [Evaluating Self-Supervised Learning for Molecular Graph Embeddings](https://mlsanity.com/paper/2206.08005/) (2022)
- [Characterizing Complex Networks with Forman-Ricci Curvature and Associated Geometric Flows](https://mlsanity.com/paper/1607.08654/) (2016)
- [Hierarchical Message-Passing Graph Neural Networks](https://mlsanity.com/paper/2009.03717/) (2020)
- [A graph representation of molecular ensembles for polymer property prediction](https://mlsanity.com/paper/2205.08619/) (2022)
- [Combinatorial Complexes: Bridging the Gap Between Cell Complexes and Hypergraphs](https://mlsanity.com/paper/2312.09504/) (2023)
- [ResMem: Learn what you can and memorize the rest](https://mlsanity.com/paper/2302.01576/) (2023)
- [Molecular geometric deep learning](https://mlsanity.com/paper/2306.15065/) (2023)
- [Effective Structural Encodings via Local Curvature Profiles](https://mlsanity.com/paper/2311.14864/) (2023)
- [Signal processing on simplicial complexes](https://mlsanity.com/paper/2106.07471/) (2021)
- [Graph neural networks for the prediction of molecular structure-property relationships](https://mlsanity.com/paper/2208.04852/) (2022)
- [MMPolymer: A Multimodal Multitask Pretraining Framework for Polymer Property Prediction](https://mlsanity.com/paper/2406.04727/) (2024)
- [Bioplastic Design using Multitask Deep Neural Networks](https://mlsanity.com/paper/2203.12033/) (2022)

## Abstract (arXiv)

Polymers underpin applications across energy, healthcare, and materials science, yet their vast chemical space makes systematic discovery challenging. Most machine learning approaches represent polymers as molecular graphs of a single repeating unit, thereby missing both the periodicity of polymer chains and many-body interactions beyond pairwise bonds. We introduce Periodic-TDL, a deep learning framework built on periodic Vietoris-Rips complexes that capture many-body interactions across multiple spatial scales, followed by a hierarchical simplicial message-passing (HSMP) encoder that propagates information from long-range interactions to covalent bonds, yielding representations enriched by higher-order topological features. Periodic-TDL outperforms all state-of-the-art models across polymer property prediction tasks spanning electronic, optical, physical, and thermal targets. Furthermore, we quantitatively validate how ester-to-amide substitution and α-methylation enhance thermal stability. Using a computationally synthesized dataset of 48,208 structures-generated via systematic substitution of acrylate and acrylamide polymers-we observed a mean Tg increase of ~ 55^circC for ester-to-amide substitutions and ~ 14^circC for backbone α-methylation across matched polymer pairs. To verify these predicted trends, we use our Periodic-TDL model to analyze six novel polymer pairs from independent experimental measurements, including three newly synthesized polymers previously unreported in the literature. The experimental data successfully confirmed the model's predictions. Ultimately, these findings demonstrate that Periodic-TDL captures the underlying physical effects of specific functional group modifications, rather than merely optimizing predictive performance on benchmark datasets.