Machine learning for and from physics

This thesis explores the application of machine learning to complex systems, focusing on knotted polymer rings, protein secondary structures, and physics-inspired clustering. We demonstrate that artificial neural networks are capable of precisely classifying knot types within confined rings, effectively generalizing their knowledge across various chain lengths and accurately identifying topological families, even when the specific knot type has not been previously encountered. Although raw geometric features offer superior performance, their deficiency in rotational invariance underscores the importance of developing symmetry-aware features. Variational Autoencoders with a classifier reveal that the latent space captures topological structure, clustering knots by family and chirality, and correlating with measures such as unknotting number and braid index. This demonstrates that neural networks can encode complex topological concepts from raw 3D configurations. Restricted Boltzmann machines applied to amino acid sequences uncover known and novel patterns in α-helices and β-sheets, providing interpretable insights into hydrophobicity, amphiphilicity, and residue correlations. Finally, a spin-glass-inspired loss function enhances clustering performance by capturing complex sample interactions, offering a physics-based approach to interpretable learning. Overall, this work demonstrates that machine learning, guided by physical and biological principles, can effectively capture non-local structures while providing both predictive power and interpretability.