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Raw data and supplementary data organized as referenced in the main text, figure legends, methods and appendix.

As computational power grows, materials simulation becomes an increasingly valuable scientific tool. Simulations are used to calculate properties that are difficult to obtain experimentally, perform high-throughput design and discovery, and investigate material behavior and theory. Ultimately we want to push the time and length scales of simulation and connect atomic scale with continuum scale properties. There is a trade-off between accuracy and computational cost. One approach is to use machine learned (ML) potentials as fast, accurate approximations to quantum chemical methods. ML potentials are systematically improvable, and can be as accurate as density functional theory at much lower computational cost. Potential challenges are that ML potentials extrapolate, and it is nonobvious when extrapolation occurs and how to efficiently build the training dataset. In addition we would like to have uncertainty measurements of ML models and physically simulated properties. In this dissertation, we investigate the relationship between atomic scale and continuum properties in liquid Al-Si using molecular dynamics (MD). We study the local order using Voronoi polyhedrons and agglomerative clustering, which allowed us to analyze the large amount of data generated from MD trajectories in an efficient manner. We found that clusters have minimal effect on diffusion while increasing viscosity, which is a likely origin of the Stokes-Einstein deviation for liquid Al-Si at low temperatures near the melting point. This study demonstrates the value of MD simulation and using ML clustering and large datasets analysis to find new phenomena. In the next part, we build a neural network (NN) potential for a complex Ni-Al-W liquid alloy. We conducted hyperparameter studies on NN architecture and Behler-Parrinello fingerprints. The ML potential was iteratively tested in MD simulation and retrained with diverse dataset. The final potential achieved comparable results with ab initio simulation. We found that the NN potential extrapolated on inputs that were dissimilar from its training data, which motivates uncertainty quantification. We implement the multiparameter delta method for NN potentials (and generally for other nonlinear models) with parameters trained by least squares regression. The uncertainty measure requires the gradient of the model prediction and the Hessian of the loss function, both with respect to model parameters. We obtain the derivatives from ML software with automatic differentiation. We show that the uncertainty measure is larger for input space regions that are not part of the training data. Therefore this method can be used to identify extrapolation, aid in selecting training data, and assess model reliability. In the final part, we compare uncertainties of physical properties from delta method, Bayesian nonlinear regression, and Gaussian process (GP). Many physical properties of interest require derivatives, therefore we derived GP with joint distribution over a function and its first and second derivatives. We show that delta method and Bayesian nonlinear regression give model specific uncertainty while GP variance includes uncertainty with respect to model selection.