Related papers: Learning and extrapolating scale-invariant process…

A well-known drawback of state-of-the-art machine-learning interatomic potentials is their poor ability to extrapolate beyond the training domain. For small-scale problems with tens to hundreds of atoms this can be solved by using active…

The computational complexity of kernel methods has often been a major barrier for applying them to large-scale learning problems. We argue that this barrier can be effectively overcome. In particular, we develop methods to scale up kernel…

In this paper, we present a simple model of scale-free networks that incorporates both preferential & random attachment and anti-preferential & random deletion at each time step. We derive the degree distribution analytically and show that…

Machine Learning is becoming more prevalent in science and engineering, but many approaches do not provide meaningful uncertainty estimates and predictions may also violate known physical knowledge. We propose a Bayesian framework to embed…

Extreme value theory provides rigorous theory and statistical tools for extrapolation in machine learning, particularly in settings where traditional methods struggle due to data scarcity in the tails. A broad range of tasks benefit from…

The problem of classifying turbulent environments from partial observation is key for some theoretical and applied fields, from engineering to earth observation and astrophysics, e.g. to precondition searching of optimal control policies in…

Machine learning, deep learning, has been accelerating computational physics, which has been used to simulate systems on a lattice. Equivariance is essential to simulate a physical system because it imposes a strong induction bias for the…

Training a high-quality deep neural network requires choosing suitable hyperparameters, which is a non-trivial and expensive process. Current works try to automatically optimize or design principles of hyperparameters, such that they can…

Deep neural networks have shown great potential in image reconstruction problems in Euclidean space. However, many reconstruction problems involve imaging physics that are dependent on the underlying non-Euclidean geometry. In this paper,…

We show that the error of iteratively magnitude-pruned networks empirically follows a scaling law with interpretable coefficients that depend on the architecture and task. We functionally approximate the error of the pruned networks,…

When data is plentiful, the loss achieved by well-trained neural networks scales as a power-law $L \propto N^{-\alpha}$ in the number of network parameters $N$. This empirical scaling law holds for a wide variety of data modalities, and may…

Machine learning has emerged as an invaluable tool in many research areas. In the present work, we harness this power to predict highly accurate molecular infrared spectra with unprecedented computational efficiency. To account for…

Classical graph algorithms work well for combinatorial problems that can be thoroughly formalized and abstracted. Once the algorithm is derived, it generalizes to instances of any size. However, developing an algorithm that handles complex…

Scale-free networks play a fundamental role in the study of complex networks and various applied fields due to their ability to model a wide range of real-world systems. A key characteristic of these networks is their degree distribution,…

The immense computational cost of traditional numerical weather and climate models has sparked the development of machine learning (ML) based emulators. Because ML methods benefit from long records of training data, it is common to use…

Most successful applications of deep learning involve similar training and test conditions. However, tasks such as biological sequence design involve searching for sequences that improve desirable properties beyond previously known values,…

The requirement of generating predictions that exactly fulfill the fundamental symmetry of the corresponding physical quantities has profoundly shaped the development of machine-learning models for physical simulations. In many cases,…

This survey investigates wall modeling in large eddy simulations (LES) using data-driven machine learning (ML) techniques. To this end, we implement three ML wall models in an open-source code and compare their performances with the…

Recent advancements in machine learning have showcased its potential to significantly accelerate the discovery of new materials. Central to this progress is the development of rapidly computable property predictors, enabling the…

Machine learning has revolutionized materials property prediction, yet fails catastrophically when extrapolating beyond training distributions-precisely the capability required for discovering unprecedented materials. Graph neural networks…