PolyFun · Polymer mechanics via Function spaces

Polymers are three-dimensional, flexible materials composed of macromolecular chains interconnected by crosslinks, which are indispensable in everyday products. Accurate computation of these materials is crucial to avoid trial-and-error synthesis, thereby extending polymer lifetimes and minimizing production waste. To date, continuum mechanics is the only discipline capable of achieving large-scale multi-physics computation of polymers. However, complex mechanical behaviors of polymers present significant challenges, necessitating the development of unconventional continuum theories and advanced machine learning techniques. While the former facilitates the capture of both local and nonlocal behaviors of polymers, the latter ensures model reliability by utilizing rich information from large datasets. Unfortunately, current machine learning approaches, when coupled with immature continuum theories, suffer from limited interpretability and an ad hoc nature. This underscores the need for a theoretically grounded machine learning approach to drive genuine advance in human knowledge.PolyFun aims to enable machine learning not only to recognize pattern, but also to develop a deeper understanding of data through the principles of continuum mechanics and polymer physics. This will be achieved by representing polymers as reproducing kernel Hilbert spaces and defining their structural and topological properties via these physical insights. PolyFun consists of two stages. Stage 1 focuses on learning from polymeric data and the domain knowledge of continuum and polymer mechanics. Stage 2 extrapolates understanding gained in Stage 1 to learn from real-world data and further enhance the computational scalability of the methodology. PolyFun’s unique perspective serves as a unified scientific language that bridges various disciplines (polymer physics, continuum mechanics and machine learning), fundamentally transforming the way we study and research in continuum interdisciplinary mechanics.