Unveil the unseen: exploit information hidden in noise

Noise and uncertainty are usually the enemy of machine learning, noise in the training data leads to uncertainty and inaccuracy in the predictions. However, Wilson's Renormalization Group Theory tells us that noise within a physical system can determine its macroscopic state. This idea inspired us to develop a machine learning architecture that extracts crucial information out of the noise. The phenomenology computes and then utilizes uncertainty in one target variable to predict a second target variable. We first apply this formalism to crystalline PbZr_0.7Sn_0.3O₃, using the uncertainty in dielectric constant to extrapolate heat capacity, correctly predicting a phase transition that would otherwise be missed. We then apply the methodology to specify a concrete mix that has high resistance to carbonation, and another concrete mix that has low environmental impact. Both mixes also fulfil targets on the strength, density, and cost. The specified mixes are experimentally validated against their predictions. Our generic formalism enables the exploitation of uncertainty in machine learning, which has a broad range of applications in the physical sciences and beyond.