It's All Connected: Topology-Aware Structural Graph Encoding Improves Performance on Polymer Prediction

Polymer property prediction lacks open, standardized benchmarks that enable rigorous comparison of machine-learning methods, with existing resources covering only a narrow fraction of polymer architectures, such as homopolymers. We introduce Polymer Benchmark 2026 (PolyBench26), an open dataset comprising nearly 250,000 polymer-property datapoints across eight physical properties, including data from experimental measurements, density functional theory, and molecular dynamics. The benchmark supports four evaluation tasks across homopolymers and alternating, random, and block copolymers: in-distribution property prediction, dataset-size scaling, repeat-unit complexity, and transfer to held-out polymer architectures. We compare language model, graph-based, and descriptor-based approaches and find graph-based models provide the lowest errors in property prediction, retain their advantage across the evaluated training-set sizes, and remain robust to increasing repeat-unit complexity. PolyBench26 provides a reproducible foundation for developing models for the increasingly complex polymer design space. The PolyBench26 benchmark is available open-source at https://github.com/rlearsch/PolymerBenchmark2026.

Message-passing graph neural networks are bounded by the 1-WL test and can miss topological structure that distinguishes non-isomorphic graphs. Positional and structural encodings (PSE) inject such topology-derived signals, and learned PSE encoders such as GPSE pretrain a single encoder to produce these signals from random node probes, which can then be frozen and reused as inputs across downstream graph models. We present CondPSE, a learned PSE encoder that applies a learnable polynomial graph filter bank to standard Gaussian node probes and refines the resulting structural-response branches through FiLM-style modulation conditioned on cross-filter, local message-passing, and graph-level signals. CondPSE is pretrained to reconstruct node-level positional/structural targets and graph-level invariants, and is then frozen for use as a downstream input encoding. On synthetic structural-discrimination benchmarks, CondPSE separates graph structures that 1-WL-bounded message passing cannot: it raises CSL accuracy from 42.9% to 97.3% and EXP accuracy from 68.3% to 99.9% relative to GPSE, and ablations show that the polynomial filter bank accounts for most of this gain. On real molecular property prediction, the picture is more limited. With a hybrid local-message-passing/global-attention backbone, CondPSE performs comparably to GPSE without surpassing it, and a ZINC backbone sweep shows no consistent ordering between the two encoders. We report these results and discuss why strong synthetic structural discrimination does not, on its own, yield a downstream advantage for frozen learned PSE encoders, including the role of downstream integration and possible mismatch between structural pretraining targets and molecular property labels.

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 $T_g$ increase of $\sim 55^\circ$C for ester-to-amide substitutions and $\sim 14^\circ$C 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.