Related papers: Weakly-supervised learning on Schrodinger equation

We build upon recent work on using Machine Learning models to estimate Hamiltonian parameters using continuous weak measurement of qubits as input. We consider two settings for the training of our model: (1) supervised learning where the…

We present a method for learning generalized Hamiltonian decompositions of ordinary differential equations given a set of noisy time series measurements. Our method simultaneously learns a continuous time model and a scalar energy function…

This report discusses two new ideas for using perturbation methods to solve the time-independent Schr\"odinger equation. The first concept begins with rewriting the perturbation equations in a form that is closely related to matrix…

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…

Curation of large fully supervised datasets has become one of the major roadblocks for machine learning. Weak supervision provides an alternative to supervised learning by training with cheap, noisy, and possibly correlated labeling…

The reduction of Hamiltonian systems aims to build smaller reduced models, valid over a certain range of time and parameters, in order to reduce computing time. By maintaining the Hamiltonian structure in the reduced model, certain…

Time-dependent wave equations represent an important class of partial differential equations (PDE) for describing wave propagation phenomena, which are often formulated over unbounded domains. Given a compactly supported initial condition,…

The wave equation is an important physical partial differential equation, and in recent years, deep learning has shown promise in accelerating or replacing traditional numerical methods for solving it. However, existing deep learning…

As machine learning algorithms become increasingly sophisticated to exploit subtle features of the data, they often become more dependent on simulations. This paper presents a new approach called weakly supervised classification in which…

In unsupervised learning, the training data for deep learning does not come with any labels, thus forcing the algorithm to discover hidden patterns in the data for discerning useful information. This, in principle, could be a powerful tool…

There has been a wave of interest in applying machine learning to study dynamical systems. We present a Hamiltonian neural network that solves the differential equations that govern dynamical systems. This is an equation-driven machine…

Transcranial ultrasound therapy is increasingly used for the non-invasive treatment of brain disorders. However, conventional numerical wave solvers are currently too computationally expensive to be used online during treatments to predict…

In many applications, training machine learning models involves using large amounts of human-annotated data. Obtaining precise labels for the data is expensive. Instead, training with weak supervision provides a low-cost alternative. We…

It is common practice to approximate a weakly nonlinear wave equation through a kinetic transport equation, thus raising the issue of controlling the validity of the kinetic limit for a suitable choice of the random initial data. While for…

The use of Variational Autoencoders in different Machine Learning tasks has drastically increased in the last years. They have been developed as denoising, clustering and generative tools, highlighting a large potential in a wide range of…

Recently, researches related to unsupervised disentanglement learning with deep generative models have gained substantial popularity. However, without introducing supervision, there is no guarantee that the factors of interest can be…

In recent years, deep learning for modeling physical phenomena which can be described by partial differential equations (PDEs) have received significant attention. For example, for learning Hamiltonian mechanics, methods based on deep…

In the process of the deep learning, we integrate more integrable information of nonlinear wave models, such as the conservation law obtained from the integrable theory, into the neural network structure, and propose a conservation-law…

Machine learning techniques have been shown to be effective to recognize different phases of matter and produce phase diagrams in the parameter space interested, while they usually require prior labeled data to perform well. Here, we…

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…