The Open Knowledgebase of Interatomic Models (OpenKIM) is a framework intended to facilitate access to standardized implementations of interatomic models for molecular simulations along with computational protocols to evaluate them. These protocols include tests to compute material properties predicted by models and verification checks to assess their coding integrity.

We show that the predicted probability distributions for any N-parameter statistical model taking the form of an exponential family can be explicitly and analytically embedded isometrically in a N+N-dimensional Minkowski space. That is, the model predictions can be visualized as control parameters are varied, preserving the natural distance between probability distributions. All pairwise distances between model instances are given by the symmetrized Kullback-Leibler divergence.

The nonequilibrium random-field Ising model is well studied, yet there are outstanding questions. In two dimensions, power-law scaling approaches fail and the critical disorder is difficult to pin down. Additionally, the presence of faceting on the square lattice creates avalanches that are lattice dependent at small scales. We propose two methods which we find solve these issues. First, we perform large-scale simulations on a Voronoi lattice to mitigate the effects of faceting.

The transition from elastic to plastic deformation in crystalline metals shares history dependence and scale-invariant avalanche signature with other nonequilibrium systems under external loading such as colloidal suspensions.

Unsupervised learning makes manifest the underlying structure of data without curated training and specific problem definitions. However, the inference of relationships between data points is frustrated by the “curse of dimensionality†in high dimensions. Inspired by replica theory from statistical mechanics, we consider replicas of the system to tune the dimensionality and take the limit as the number of replicas goes to zero. The result is intensive embedding, which not only is isometric (preserving local distances) but also allows global structure to be more transparently visualized.

Particle storage rings are a rich application domain for online optimization algorithms. The Cornell Electron Storage Ring (CESR) has hundreds of independently powered magnets, making it a high-dimensional test-problem for algorithmic tuning. We investigate algorithms that restrict the search space to a small number of linear combinations of parameters ("knobs") which contain most of the effect on our chosen objective (the vertical emittance), thus enabling efficient tuning.

The results of the renormalization group are commonly advertised as the existence of power-law singularities near critical points. The classic predictions are often violated and logarithmic and exponential corrections are treated on a case-by-case basis. We use the mathematics of normal form theory to systematically group these into universality families of seemingly unrelated systems united by common scaling variables. We recover and explain the existing literature and predict the nonlinear generalization for the universal homogeneous scaling functions.

Complex nonlinear models are typically ill conditioned or sloppy; their predictions are significantly affected by only a small subset of parameter combinations, and parameters are difficult to reconstruct from model behavior. Despite forming an important universality class and arising frequently in practice when performing a nonlinear fit to data, formal and systematic explanations of sloppiness are lacking. By unifying geometric interpretations of sloppiness with Chebyshev approximation theory, we rigorously explain sloppiness as a consequence of model smoothness.

A replica-symmetry-breaking phase transition is predicted in a host of disordered media. The criticality of the transition has, however, long been questioned below its upper critical dimension, six, due to the absence of a critical fixed point in the renormalization-group flows at one-loop order. A recent two-loop analysis revealed a possible strong-coupling fixed point, but given the uncontrolled nature of perturbative analysis in the strong-coupling regime, debate persists.

We introduce a natural way to extend celebrated spin-cluster Monte Carlo algorithms for fast thermal lattice simulations at criticality, such as the Wolff algorithm, to systems in arbitrary fields, be they linear magnetic vector fields or nonlinear anisotropic ones. By generalizing the "ghost spin" representation to one with a "ghost transformation," global invariance to spin symmetry transformations is restored at the cost of an extra degree of freedom which lives in the space of symmetry transformations. The ordinary cluster-building process can then be run on the representation.