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In typical machine learning tasks and applications, it is necessary to obtain or create large labeled datasets in order to to achieve high performance. Unfortunately, large labeled datasets are not always available and can be expensive to…

Exact numerical simulations of dynamics of open quantum systems often require immense computational resources. We demonstrate that a deep artificial neural network comprised of convolutional layers is a powerful tool for predicting…

Physics perception very often faces the problem that only limited data or partial measurements on the scene are available. In this work, we propose a strategy to learn the full state of sloshing liquids from measurements of the free…

The data-driven learning of solutions of partial differential equations can be based on a divide-and-conquer strategy. First, the high dimensional data is compressed to a latent space with an autoencoder; and, second, the temporal dynamics…

Online learning has become crucial to many problems in machine learning. As more data is collected sequentially, quickly adapting to changes in the data distribution can offer several competitive advantages such as avoiding loss of prior…

Direct numerical simulation of hierarchical materials via homogenization-based concurrent multiscale models poses critical challenges for 3D large scale engineering applications, as the computation of highly nonlinear and path-dependent…

A long-standing problem at the interface of artificial intelligence and applied mathematics is to devise an algorithm capable of achieving human level or even superhuman proficiency in transforming observed data into predictive mathematical…

Autoencoders are neural network formulations where the input and output of the network are identical and the goal is to identify the hidden representation in the provided datasets. Generally, autoencoders project the data nonlinearly onto a…

Parameterized mathematical models play a central role in understanding and design of complex information systems. However, they often cannot take into account the intricate interactions innate to such systems. On the contrary, purely…

This work presents a novel means for understanding learning dynamics and scaling relations in neural networks. We show that certain measures on the spectrum of the empirical neural tangent kernel, specifically entropy and trace, yield…

We propose a thermodynamics-based learning strategy for non-equilibrium evolution equations based on Onsager's variational principle, which allows to write such PDEs in terms of two potentials: the free energy and the dissipation potential.…

Complex chaotic dynamics, seen in natural and industrial systems like turbulent flows and weather patterns, often span vast spatial domains with interactions across scales. Accurately capturing these features requires a high-dimensional…

A common strategy for the dimensionality reduction of nonlinear partial differential equations relies on the use of the proper orthogonal decomposition (POD) to identify a reduced subspace and the Galerkin projection for evolving dynamics…

Learning reduced descriptions of chaotic many-body dynamics is fundamentally challenging: although microscopic equations are Markovian, collective observables exhibit strong memory and exponential sensitivity to initial conditions and…

The one-body reduced density matrix (1-RDM) of a many-body system at zero temperature gives direct access to many observables, such as the charge density, kinetic energy and occupation numbers. It would be desirable to express it as a…

We introduce DeepMoD, a Deep learning based Model Discovery algorithm. DeepMoD discovers the partial differential equation underlying a spatio-temporal data set using sparse regression on a library of possible functions and their…

Noting the importance of the latent variables in inference and learning, we propose a novel framework for autoencoders based on the homeomorphic transformation of latent variables, which could reduce the distance between vectors in the…

In Compressed Sensing, a real-valued sparse vector has to be estimated from an underdetermined system of linear equations. In many applications, however, the elements of the sparse vector are drawn from a finite set. For the estimation of…

This work studies the problem of modeling visual processes by leveraging deep generative architectures for learning linear, Gaussian representations from observed sequences. We propose a joint learning framework, combining a vector…

Deep neural networks offer an alternative paradigm for modeling weather conditions. The ability of neural models to make a prediction in less than a second once the data is available and to do so with very high temporal and spatial…