Related papers: chebgreen: Learning and Interpolating Continuous E…

Machine learning is a powerful tool to design accurate, highly non-local, exchange-correlation functionals for density functional theory. So far, most of those machine learned functionals are trained for systems with an integer number of…

The output of a machine learning algorithm can usually be represented by one or more multivariate functions of its input variables. Knowing the global properties of such functions can help in understanding the system that produced the data…

There is a wide gap between symbolic reasoning and deep learning. In this research, we explore the possibility of using deep learning to improve symbolic reasoning. Briefly, in a reasoning system, a deep feedforward neural network is used…

Discrete Green's functions are the inverses or pseudo-inverses of combinatorial Laplacians. We present compact formulas for discrete Green's functions, in terms of the eigensystems of corresponding Laplacians, for products of regular graphs…

In recent years, understanding the implicit regularization of neural networks (NNs) has become a central task in deep learning theory. However, implicit regularization is itself not completely defined and well understood. In this work, we…

The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…

Intelligent real-world systems critically depend on expressive information about their system state and changing operation conditions, e.g., due to variation in temperature, location, wear, or aging. To provide this information, online…

There have been attempts in reinforcement learning to exploit a priori knowledge about the structure of the system. This paper proposes a hybrid reinforcement learning controller which dynamically interpolates a model-based linear…

Direct load control of a heterogeneous cluster of residential demand flexibility sources is a high-dimensional control problem with partial observability. This work proposes a novel approach that uses a convolutional neural network to…

We investigate the applicability of machine learning techniques in studying the finite-size effects associated with many-body physics. These techniques have an emerging presence in many-body theory as they have been used for interpolations,…

The nonequilibrium Green's function formalism provides a versatile and powerful framework for numerical studies of nonequilibrium phenomena in correlated many-body systems. For calculations starting from an equilibrium initial state, a…

Numerous control and learning problems face the situation where sequences of high-dimensional highly dependent data are available but no or little feedback is provided to the learner, which makes any inference rather challenging. To address…

We tackle the problem of building explainable recommendation systems that are based on a per-user decision tree, with decision rules that are based on single attribute values. We build the trees by applying learned regression functions to…

One of the challenges in diagrammatic simulations of nonequilibrium phenomena in lattice models is the large memory demand for storing momentum-dependent two-time correlation functions. This problem can be overcome with the recently…

Causal reasoning can be considered a cornerstone of intelligent systems. Having access to an underlying causal graph comes with the promise of cause-effect estimation and the identification of efficient and safe interventions. However,…

At the boundary between the known and the unknown, an agent inevitably confronts the dilemma of whether to explore or to exploit. Epistemic uncertainty reflects such boundaries, representing systematic uncertainty due to limited knowledge.…

Learning internal representations from data using no or few labels is useful for machine learning research, as it allows using massive amounts of unlabeled data. In this work, we use the Bayesian Confidence Propagation Neural Network…

A explicit formula on semiclassical Green functions in mixed position and momentum spaces is given, which is based on Maslov's multi-dimensional semiclassical theory. The general formula includes both coordinate and momentum representations…

This article investigates the use of random feature neural networks for learning Kolmogorov partial (integro-)differential equations associated to Black-Scholes and more general exponential L\'evy models. Random feature neural networks are…

A major challenge in modern reinforcement learning (RL) is efficient control of dynamical systems from high-dimensional sensory observations. Learning controllable embedding (LCE) is a promising approach that addresses this challenge by…