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Humans gain an implicit understanding of physical laws through observing and interacting with the world. Endowing an autonomous agent with an understanding of physical laws through experience and observation is seldom practical: we should…
The evolution of linear initial conditions present in the early universe into extended halos of dark matter at late times can be computed using cosmological simulations. However, a theoretical understanding of this complex process remains…
On a variety of tasks, the performance of neural networks predictably improves with training time, dataset size and model size across many orders of magnitude. This phenomenon is known as a neural scaling law. Of fundamental importance is…
Deep learning sometimes appears to work in unexpected ways. In pursuit of a deeper understanding of its surprising behaviors, we investigate the utility of a simple yet accurate model of a trained neural network consisting of a sequence of…
The large-scale structure in cosmology is highly non-Gaussian at late times and small length scales, making it difficult to describe analytically. Parameter inference, data reconstruction, and data generation tasks in cosmology are greatly…
While a real-world research program in mathematics may be guided by a motivating question, the process of mathematical discovery is typically open-ended. Ideally, exploration needed to answer the original question will reveal new…
A longstanding goal in deep learning research has been to precisely characterize training and generalization. However, the often complex loss landscapes of neural networks have made a theory of learning dynamics elusive. In this work, we…
Despite deep-learning being state-of-the-art for data-driven model predictions, it has not yet found frequent application in ecology. Given the low sample size typical in many environmental research fields, the default choice for the…
Deep Learning has revolutionized the fields of computer vision, natural language understanding, speech recognition, information retrieval and more. Many techniques have evolved over the past decade that made models lighter, faster, and…
Understanding and predicting microstructure evolution is fundamental to materials science, as it governs the resulting properties and performance of materials. Traditional simulation methods, such as phase-field models, offer high-fidelity…
While the basic laws of Newtonian mechanics are well understood, explaining a physical scenario still requires manually modeling the problem with suitable equations and estimating the associated parameters. In order to be able to leverage…
Near-future cosmological observations targeted at investigations of dark energy pose stringent requirements on the accuracy of theoretical predictions for the clustering of matter. Currently, N-body simulations comprise the only viable…
We demonstrate the capability of a convolutional deep neural network in predicting the nearest-neighbor energy of the 4x4 Ising model. Using its success at this task, we motivate the study of the larger 8x8 Ising model, showing that the…
Measuring the sum of the three active neutrino masses, $M_\nu$, is one of the most important challenges in modern cosmology. Massive neutrinos imprint characteristic signatures on several cosmological observables in particular on the…
Reproducibility of a deep-learning fully convolutional neural network is evaluated by training several times the same network on identical conditions (database, hyperparameters, hardware) with non-deterministic Graphics Processings Unit…
Discrete-time modeling of acoustic, mechanical and electrical systems is a prominent topic in the musical signal processing literature. Such models are mostly derived by discretizing a mathematical model, given in terms of ordinary or…
The evaluation of Deep Learning models has traditionally focused on criteria such as accuracy, F1 score, and related measures. The increasing availability of high computational power environments allows the creation of deeper and more…
It is believed that one of the first useful applications for a quantum computer will be the preparation of groundstates of molecular Hamiltonians. A crucial task involving state preparation and readout is obtaining physical observables of…
Using transformers over large generated datasets, we train models to learn mathematical properties of differential systems, such as local stability, behavior at infinity and controllability. We achieve near perfect prediction of qualitative…
Simulations of purely self-gravitating N-body systems are often used in astrophysics and cosmology to study the collisionless limit of such systems. Their results for macroscopic quantities should then converge well for sufficiently large…