Related papers: Kohn-Sham equations as regularizer: building prior…

Despite impressive performance on numerous visual tasks, Convolutional Neural Networks (CNNs) --- unlike brains --- are often highly sensitive to small perturbations of their input, e.g. adversarial noise leading to erroneous decisions. We…

In the last years, the design of image reconstruction methods in the field of quantitative Magnetic Resonance Imaging (qMRI) has experienced a paradigm shift. Often, when dealing with (quantitative) MR image reconstruction problems, one is…

A myriad of phenomena in materials science and chemistry rely on quantum-level simulations of the electronic structure in matter. While moving to larger length and time scales has been a pressing issue for decades, such large-scale…

We present a multigrid algorithm for self consistent solution of the Kohn-Sham equations in real space. The entire problem is discretized on a real space mesh with a high order finite difference representation. The resulting self consistent…

Prior domain knowledge can greatly help to learn generative models. However, it is often too costly to hard-code prior knowledge as a specific model architecture, so we often have to use general-purpose models. In this paper, we propose a…

We show that deep neural networks can be integrated into, or fully replace, the Kohn-Sham density functional theory scheme for multi-electron systems in simple harmonic oscillator and random external potentials with no feature engineering.…

The successful training of deep neural networks requires addressing challenges such as overfitting, numerical instabilities leading to divergence, and increasing variance in the residual stream. A common solution is to apply regularization…

Closure problems are omnipresent when simulating multiscale systems, where some quantities and processes cannot be fully prescribed despite their effects on the simulation's accuracy. Recently, scientific machine learning approaches have…

Statistical (machine learning) tools for equation discovery require large amounts of data that are typically computer generated rather than experimentally observed. Multiscale modeling and stochastic simulations are two areas where learning…

A recently developed formalism in which Kohn-Sham calculations are combined with an ``average pair density functional theory'' is reviewed, and some new properties of the effective electron-electron interaction entering in this formalism…

One of the potential applications of a quantum computer is solving quantum chemical systems. It is known that one of the fastest ways to obtain somewhat accurate solutions classically is to use approximations of density functional theory.…

Regularization is crucial to the success of many practical deep learning models, in particular in a more often than not scenario where there are only a few to a moderate number of accessible training samples. In addition to weight decay,…

Operator inference learns low-dimensional dynamical-system models with polynomial nonlinear terms from trajectories of high-dimensional physical systems (non-intrusive model reduction). This work focuses on the large class of physical…

Underpinning the success of deep learning is effective regularizations that allow a variety of priors in data to be modeled. For example, robustness to adversarial perturbations, and correlations between multiple modalities. However, most…

Deep neural networks have become very popular in modeling complex nonlinear processes due to their extraordinary ability to fit arbitrary nonlinear functions from data with minimal expert intervention. However, they are almost always…

Efficiently harvesting thermodynamic resources requires a precise understanding of their structure. This becomes explicit through the lens of information engines -- thermodynamic engines that use information as fuel. Maximizing the work…

A trained neural network can be interpreted as a structural causal model (SCM) that provides the effect of changing input variables on the model's output. However, if training data contains both causal and correlational relationships, a…

Proper regularization is critical for speeding up training, improving generalization performance, and learning compact models that are cost efficient. We propose and analyze regularized gradient descent algorithms for learning shallow…

Continual learning of deep neural networks is a key requirement for scaling them up to more complex applicative scenarios and for achieving real lifelong learning of these architectures. Previous approaches to the problem have considered…

Deep Neural Networks reached state-of-the-art performance across numerous domains, but this progress has come at the cost of increasingly large and over-parameterized models, posing serious challenges for deployment on resource-constrained…