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Recently, several algorithms for symbolic regression (SR) emerged which employ a form of multiple linear regression (LR) to produce generalized linear models. The use of LR allows the algorithms to create models with relatively small error…

The success of first principles electronic structure calculation for predictive modeling in chemistry, solid state physics, and materials science is constrained by the limitations on simulated length and time scales due to computational…

Probabilistic graphical models (PGMs) are widely used to discover latent structure in data, but their success hinges on selecting an appropriate model design. In practice, model specification is difficult and often requires iterative…

Machine learning in atomistic materials science has grown to become a powerful tool, with most approaches focusing on atomic arrangements, typically decomposed into local atomic environments. This approach, while well-suited for…

We briefly summarize the kernel regression approach, as used recently in materials modelling, to fitting functions, particularly potential energy surfaces, and highlight how the linear algebra framework can be used to both predict and train…

Symbolic regression (SR) models complex systems by discovering mathematical expressions that capture underlying relationships in observed data. However, most SR methods prioritize minimizing prediction error over identifying the governing…

We investigate the ability of decoder-only transformer models to perform abstract symbolic reasoning; specifically solving propositional logic reasoning problems given in-context. Previous work demonstrated that models fail to generalize to…

Symbolic regression refers to the task of finding a closed-form mathematical expression to fit a set of data points. Genetic programming based techniques are the most common algorithms used to tackle this problem, but recently,…

Predicting molecular properties (e.g., atomization energy) is an essential issue in quantum chemistry, which could speed up much research progress, such as drug designing and substance discovery. Traditional studies based on density…

Recent equivariant models have shown significant progress in not just chemical property prediction, but as surrogates for dynamical simulations of molecules and materials. Many of the top performing models in this category are built within…

This chapter discusses the importance of incorporating three-dimensional symmetries in the context of statistical learning models geared towards the interpolation of the tensorial properties of atomic-scale structures. We focus on Gaussian…

The mathematical formula is the human language to describe nature and is the essence of scientific research. Finding mathematical formulas from observational data is a major demand of scientific research and a major challenge of artificial…

We developed new modified embedded-atom method (MEAM) interatomic potentials for the Mg-Al alloy system using a first-principles method based on density functional theory (DFT). The materials parameters, such as the cohesive energy,…

Training machine learning interatomic potentials that are both computationally and data-efficient is a key challenge for enabling their routine use in atomistic simulations. To this effect, we introduce franken, a scalable and lightweight…

Humans have the ability to rapidly understand rich combinatorial concepts from limited data. Here we investigate this ability in the context of auditory signals, which have been evolved in a cultural transmission experiment to study the…

Machine learning interatomic potentials (MLIPs) have become increasingly effective at approximating quantum mechanical calculations at a fraction of the computational cost. However, lower errors on held out test sets do not always translate…

Soft, porous mechanical metamaterials exhibit pattern transformations that may have important applications in soft robotics, sound reduction and biomedicine. To design these innovative materials, it is important to be able to simulate them…

Probabilistic embeddings have proven useful for capturing polysemous word meanings, as well as ambiguity in image matching. In this paper, we study the advantages of probabilistic embeddings in a cross-modal setting (i.e., text and images),…

Molecule property prediction is a fundamental problem for computer-aided drug discovery and materials science. Quantum-chemical simulations such as density functional theory (DFT) have been widely used for calculating the molecule…

Flow matching models generate high-fidelity molecular geometries but incur significant computational costs during inference, requiring hundreds of network evaluations. This inference overhead becomes the primary bottleneck when such models…