PolymerGPT: Multi-property Optimization with a Decoder-Based GPT Model for Generative Polymer Design

Polymer property prediction and inverse generative design targeting desired properties are two crucial tasks in machine learning-assisted polymer design. While the former has received considerable attention, there have been limited methods developed for the latter. Existing methods focus on single-property optimization in the generative process, whereas accurate prediction of macroscopic material behavior requires simultaneous control of multiple physical properties. In this paper, we provide a transformative framework for direct optimization of a large collection of polymer properties. We propose PolymerGPT, a decoder-based GPT model that incorporates up to 37 commonly used polymer properties into the generative process via learned conditioning prefixes. It also supports a scaffold condition that specifies a desired scaffold for predicted structures. Our experimental results demonstrate that PolymerGPT achieves exceptional performance for unconditional and conditional generation while maintaining high validity, uniqueness, and novelty. Conditioning on five key properties yields generated structures whose predicted values closely match all target properties simultaneously.

Branched Signature Kernel Solvers for ODEs with rough Single-Trajectory signals

We develop a branched signature kernel solver for linear and nonlinear ordinary differential equations driven by a \emph{single observed trajectory} of a possibly rough forcing signal -- a setting that arises naturally in earthquake engineering, finance, biology, and structural health monitoring, where the forcing is observed exactly once and the solver must respect the underlying physical law without recourse to an ensemble of realizations. Two ingredients are new. First, a \emph{count-sampling} construction turns the single observation into a hierarchical family of $N+1$ nested training paths on which the branched signature kernel can be evaluated; this allows the signature kernel machinery, originally designed for multi-realization regression problems, to operate on a single-trajectory observation. Second, a kernel-collocation framework places the ansatz either on the highest-order derivative of the solution (with lower derivatives recovered by integrating the kernel) or on the solution itself (after $m$-fold integration of the ODE). We prove a universal approximation theorem for the branched signature kernel, leveraging the Hairer--Kelly morphism to express branched signature evaluations through geometric signatures of time-extended paths. The offline solver is extended to a streaming Test/Train/Retrain protocol with closed-form online updates in the linear case and scalar Newton steps in the nonlinear case. Numerical experiments on six benchmarks (El-Centro earthquake displacement, the Solow capital-stock model, an fBM-driven second-order ODE, a forced Duffing oscillator, a path-dependent Arias-intensity-degraded oscillator with variable coefficients, and a noisy Kuramoto phase-oscillator system) show that the branched signature-kernel solver delivers accurate, stable predictions across all regimes.