Related papers: Kohn-Sham equations as regularizer: building prior…
A long-standing puzzle in density-functional theory is the issue of the long-range behavior of the Kohn-Sham exchange-correlation potential at metal surfaces. As an important step towards its solution, it is proved here, through a rigurouos…
In this paper, we study finite dimensional approximations of Kohn-Sham models, which are widely used in electronic structure calculations. We prove the convergence of the finite dimensional approximations and derive the a priori error…
Differential equations are used to model and predict the behaviour of complex systems in a wide range of fields, and the ability to solve them is an important asset for understanding and predicting the behaviour of these systems.…
Predictivity of the Kohn-Sham approach to dynamical problems, when regarded as an initial value problem in a time-dependent density functional framework, is analysed for a class of models for which the argument devised in the work of Maitra…
The electron density of a molecule or material has recently received major attention as a target quantity of machine-learning models. A natural choice to construct a model that yields transferable and linear-scaling predictions is to…
Variational segmentation algorithms require a prior imposed in the form of a regularisation term to enforce smoothness of the solution. Recently, it was shown in the Deep Image Prior work that the explicit regularisation in a model can be…
Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for…
We introduce a novel stochastic regularization technique for deep neural networks, which decomposes a layer into multiple branches with different parameters and merges stochastically sampled combinations of the outputs from the branches…
Learning complex physical dynamics purely from data is challenging due to the intrinsic properties of systems to be satisfied. Incorporating physics-informed priors, such as in Hamiltonian Neural Networks (HNNs), achieves high-precision…
Regularization techniques are widely employed in optimization-based approaches for solving ill-posed inverse problems in data analysis and scientific computing. These methods are based on augmenting the objective with a penalty function,…
The knowledge that humans hold about a problem often extends far beyond a set of training data and output labels. While the success of deep learning mostly relies on supervised training, important properties cannot be inferred efficiently…
There exist many forms of deep latent variable models, such as the variational autoencoder and adversarial autoencoder. Regardless of the specific class of model, there exists an implicit consensus that the latent distribution should be…
We use density-matrix renormalization group, applied to a one-dimensional model of continuum Hamiltonians, to accurately solve chains of hydrogen atoms of various separations and numbers of atoms. We train and test a machine-learned…
Neural scaling laws are driving the machine learning community toward training ever-larger foundation models across domains, assuring high accuracy and transferable representations for extrapolative tasks. We test this promise in quantum…
Much as replacing hand-designed features with learned functions has revolutionized how we solve perceptual tasks, we believe learned algorithms will transform how we train models. In this work we focus on general-purpose learned optimizers…
There is growing body of learning problems for which it is natural to organize the parameters into matrix, so as to appropriately regularize the parameters under some matrix norm (in order to impose some more sophisticated prior knowledge).…
We develop methods to learn the correlation potential for a time-dependent Kohn-Sham (TDKS) system in one spatial dimension. We start from a low-dimensional two-electron system for which we can numerically solve the time-dependent…
Traditionally, quantization is designed to minimize the reconstruction error of a data source. When considering downstream classification tasks, other measures of distortion can be of interest; such as the 0-1 classification loss.…
Recurrent neural networks are a widely used class of neural architectures. They have, however, two shortcomings. First, it is difficult to understand what exactly they learn. Second, they tend to work poorly on sequences requiring long-term…
Neural networks have emerged as effective tools for solving ill-posed inverse problems. In many scientific applications, however, observational training data are insufficient, and learned inverse operators must instead be trained on…