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This paper investigates the use of artificial neural networks (ANNs) to solve differential equations (DEs) and the construction of the loss function which meets both differential equation and its initial/boundary condition of a certain DE.…
Artificial neural networks (ANNs) have recently also been applied to solve partial differential equations (PDEs). In this work, the classical problem of pricing European and American financial options, based on the corresponding PDE…
Purpose: To use a deep neural network (DNN) for solving the optimization problem of water/fat separation and to compare supervised and unsupervised training. Methods: The current T2*-IDEAL algorithm for solving fat/water separation is…
Many binary systems of interest for gravitational-wave astronomy are orbited by a third distant body, which can considerably alter their relativistic dynamics. Precision computations are needed to understand the interplay between…
In this paper, we report on the construction of a deep Artificial Neural Network (ANN) to localize simulated gravitational wave signals in the sky with high accuracy. We have modelled the sky as a sphere and have considered cases where the…
We present an efficient variational integrator for multibody systems. Variational integrators reformulate the equations of motion for multibody systems as discrete Euler-Lagrange (DEL) equations, transforming forward integration into a…
Recently, there has been significant progress in solving quantum many-particle problem via machine learning based on the restricted Boltzmann machine. However, it is still highly challenging to solve frustrated models via machine learning,…
The paper presents the electronic design and motion planning of a robot based on decision making regarding its straight motion and precise turn using Artificial Neural Network (ANN). The ANN helps in learning of robot so that it performs…
Quantum many-body physics simulation has important impacts on understanding fundamental science and has applications to quantum materials design and quantum technology. However, due to the exponentially growing size of the Hilbert space…
Artificial neural network (ANN) is a very useful tool in solving learning problems. Boosting the performances of ANN can be mainly concluded from two aspects: optimizing the architecture of ANN and normalizing the raw data for ANN. In this…
Solving nonlinear algebraic equations is a fundamental but challenging problem in scientific computations and also has many applications in system engineering. Though traditional iterative methods and modern optimization algorithms have…
Ternary Neural Networks (TNNs) have received much attention due to being potentially orders of magnitude faster in inference, as well as more power efficient, than full-precision counterparts. However, 2 bits are required to encode the…
An implementation and an application of the combination of the genetic algorithm and Newton's method for solving a system of nonlinear equations is presented. The method first uses the advantage of the robustness of the genetic algorithm…
An ab-initio description of atomic nuclei that solves the nuclear many-body problem for realistic nuclear forces is expected to possess a high degree of predictive power. In this contribution we treat the main obstacle, namely the…
Recently there has been an explosion of books and articles complaining about the weirdness of Quantum Mechanics and crying out for a solution. Three problems in particular have been singled out: the double-slit experiment, the measurement…
Some recent artificial neural networks (ANNs) claim to model aspects of primate neural and human performance data. Their success in object recognition is, however, dependent on exploiting low-level features for solving visual tasks in a way…
Conventional predictive Artificial Neural Networks (ANNs) commonly employ deterministic weight matrices; therefore, their prediction is a point estimate. Such a deterministic nature in ANNs causes the limitations of using ANNs for medical…
In real world systems, the predictions of deployed Machine Learned models affect the training data available to build subsequent models. This introduces a bias in the training data that needs to be addressed. Existing solutions to this…
The challenge of quantum many-body problems comes from the difficulty to represent large-scale quantum states, which in general requires an exponentially large number of parameters. Recently, a connection has been made between quantum…
Artificial neural networks (ANNs) are used in various applications for data-driven black-box modeling and subsequent optimization. Herein, we present an efficient method for deterministic global optimization of ANN embedded optimization…