# Mixing Vector Model for Copolymer Inference via Mixed Integer Linear Programming

arXiv: https://arxiv.org/abs/2605.29329 · HTML: https://mlsanity.com/paper/2605.29329/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 70 references that are in the map.
- First posted on arXiv 28 May 2026.

## Builds on (most cited first, 10 of 10)

- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [FP-GNN: a versatile deep learning architecture for enhanced molecular property prediction](https://mlsanity.com/paper/2205.03834/) (2022)
- [A Universal Framework for Accurate and Efficient Geometric Deep Learning of Molecular Systems](https://mlsanity.com/paper/2311.11228/) (2023)
- [A Novel Method for Inference of Acyclic Chemical Compounds with Bounded Branch-height Based on Artificial Neural Networks and Integer Programming](https://mlsanity.com/paper/2009.09646/) (2020)
- [Inverse Design of Copolymers Including Stoichiometry and Chain Architecture](https://mlsanity.com/paper/2410.02824/) (2024)
- [Molecular Design Based on Artificial Neural Networks, Integer Programming and Grid Neighbor Search](https://mlsanity.com/paper/2108.10266/) (2021)
- [A Method for Inferring Polymers Based on Linear Regression and Integer Programming](https://mlsanity.com/paper/2109.02628/) (2021)
- [An Inverse QSAR Method Based on Linear Regression and Integer Programming](https://mlsanity.com/paper/2107.02381/) (2021)
- [A Physics-Enforced Neural Network to Predict Polymer Melt Viscosity](https://mlsanity.com/paper/2409.05240/) (2024)
- [Combining Graph Neural Networks and Mixed Integer Linear Programming for Molecular Inference under the Two-Layered Model](https://mlsanity.com/paper/2507.03920/) (2025)

## Abstract (arXiv)

A novel two-phase molecule inference framework, mol-infer, has recently been developed to infer chemical graphs with prescribed abstract structures and desired property values through mixed integer linear programming (MILP) under the two-layered model, with guaranteed optimality and exactness relative to the given learned prediction function and structural constraints. In this study, we extend this framework to copolymers by introducing a simple feature representation, called the mixing vector (MV) model. In the proposed model, a copolymer feature vector is represented as a convex combination of MILP-tractable monomer descriptors weighted by the mixing ratio of the constituent monomers. This representation does not require explicit sequence-class information and is therefore naturally compatible with MILP-based inverse design. Under this model, we construct prediction functions for several copolymer property datasets using artificial neural networks, reduced quadratic multiple linear regression, and random forests. The proposed representation achieves practically useful predictive performance across multiple physicochemical property datasets; in particular, the best test R^2 score exceeds 0.7 for nine of the ten datasets and exceeds 0.9 for six datasets. We also formulate a multi-monomer inverse-design problem under the MV representation with a prescribed mixing ratio and show that the resulting MILP instances remain tractable, even for three-monomer settings. Finally, we perform an external consistency check by re-evaluating the inferred candidates and comparing the re-computed property values with those predicted by the learned model. Overall, the proposed framework gives a tractable first step toward model-level exact inverse design of copolymers under the two-layered model.