Advances in robotic control and sensing have propelled the rise of automated scientific laboratories capable of high-throughput experiments. However, automated scientific laboratories are currently limited by human intuition in their ability to efficiently design and interpret experiments in high-dimensional spaces, throttling scientific discovery. We present AutoSciLab, a machine learning framework for driving autonomous scientific experiments, forming a surrogate researcher purposed for scientific discovery in high-dimensional spaces. AutoSciLab autonomously follows the scientific method in four steps: (i) generating high-dimensional experiments ($x ∈ R^D$) using a variational autoencoder (ii) selecting optimal experiments by forming hypotheses using active learning (iii) distilling the experimental results to discover relevant low-dimensional latent variables ($z ∈ R^d$, with $d ≪ D$) with a ‘directional autoencoder’ and (iv) learning a human interpretable equation connecting the discovered latent variables with a quantity of interest ($y = f (z)$), using a neural network equation learner. We validate the generalizability of AutoSciLab by rediscovering a) the principles of projectile motion and b) the phase-transitions within the spin-states of the Ising model (NP-hard problem). Applying our framework to an open-ended nanophotonics problem, AutoSciLab discovers a new way to steer incoherent light emission beyond current state-of-the-art, defining a new structure(material)-property(light-emission) relationship governing the physical process using closed-loop noisy experimental feedback.