Related papers: Data-driven discovery of Green's functions with hu…

We show that density models describing multiple observables with (i) hard boundaries and (ii) dependence on external parameters may be created using an auto-regressive Gaussian mixture model. The model is designed to capture how observable…

Partial differential equations (PDEs) that fit scientific data can represent physical laws with explainable mechanisms for various mathematically-oriented subjects, such as physics and finance. The data-driven discovery of PDEs from…

In this work, we present a mesh-independent, data-driven library, chebgreen, to mathematically model one-dimensional systems, possessing an associated control parameter, and whose governing partial differential equation is unknown. The…

In this paper we design and use two Deep Learning models to generate the ground and excited wavefunctions of different Hamiltonians suitable for the study the vibrations of molecular systems. The generated neural networks are trained with…

Experimental data is often comprised of variables measured independently, at different sampling rates (non-uniform ${\Delta}$t between successive measurements); and at a specific time point only a subset of all variables may be sampled.…

Distilling data into compact and interpretable analytic equations is one of the goals of science. Instead, contemporary supervised machine learning methods mostly produce unstructured and dense maps from input to output. Particularly in…

Physics-driven discovery in an autonomous experiment has emerged as a dream application of machine learning in physical sciences. Here we develop and experimentally implement a deep kernel learning workflow combining the correlative…

Before we attempt to learn a function between two (sets of) observables of a physical process, we must first decide what the inputs and what the outputs of the desired function are going to be. Here we demonstrate two distinct, data-driven…

Near-term prediction of the structured spatio-temporal processes driving our climate is of profound importance to the safety and well-being of millions, but the prounced nonlinear convection of these processes make a complete mechanistic…

Identifying underlying governing equations and physical relevant information from high-dimensional observable data has always been a challenge in physical sciences. With the recent advances in sensing technology and available datasets,…

Despite tremendous progress over the past decade, deep learning methods generally fall short of human-level systematic generalization. It has been argued that explicitly capturing the underlying structure of data should allow connectionist…

Learning the Green's function using deep learning models enables to solve different classes of partial differential equations. A practical limitation of using deep learning for the Green's function is the repeated computationally expensive…

This work leverages recent advances in probabilistic machine learning to discover conservation laws expressed by parametric linear equations. Such equations involve, but are not limited to, ordinary and partial differential,…

Causal learning has garnered significant attention in recent years because it reveals the essential relationships that underpin phenomena and delineates the mechanisms by which the world evolves. Nevertheless, traditional causal learning…

Modeling of conservative systems with neural networks is an area of active research. A popular approach is to use Hamiltonian neural networks (HNNs) which rely on the assumptions that a conservative system is described with Hamilton's…

The data-driven models allow one to define the model structure in cases when a priori information is not sufficient to build other types of models. The possible way to obtain physical interpretation is the data-driven differential equation…

Discovery of the molecular candidates for applications in drug targets, biomolecular systems, catalysts, photovoltaics, organic electronics, and batteries, necessitates development of machine learning algorithms capable of rapid exploration…

With several advantages and as an alternative to predict physics field, machine learning methods can be classified into two distinct types: data-driven relying on training data and physics-driven using physics law. Choosing heat conduction…

We present a method of discovering governing differential equations from data without the need to specify a priori the terms to appear in the equation. The input to our method is a dataset (or ensemble of datasets) corresponding to a…

For more than two centuries, solutions of differential equations have been obtained either analytically or numerically based on typically well-behaved forcing and boundary conditions for well-posed problems. We are changing this paradigm in…