Related papers: Compiling Elementary Mathematical Functions into F…
Dealing with NP-hard problems, kernelization is a fundamental notion for polynomial-time data reduction with performance guarantees: in polynomial time, a problem instance is reduced to an equivalent instance with size upper-bounded by a…
In convolutional neural networks (CNNs), pooling operations play important roles such as dimensionality reduction and deformation compensation. In general, max pooling, which is the most widely used operation for local pooling, is performed…
Deep neural networks (DNNs) have achieved great success in a wide range of computer vision areas, but the applications to mobile devices is limited due to their high storage and computational cost. Much efforts have been devoted to compress…
The main aim of this study is to introduce a 2-layered Artificial Neural Network (ANN) for solving the Black-Scholes partial differential equation (PDE) of either fractional or ordinary orders. Firstly, a discretization method is employed…
[New and updated results were published in Nature Chemistry, doi:10.1038/s41557-020-0544-y.] The electronic Schr\"odinger equation describes fundamental properties of molecules and materials, but can only be solved analytically for the…
The software for chemical interaction networks (SCINE) project aims at pushing the frontier of quantum chemical calculations on molecular structures to a new level. While calculations on individual structures as well as on simple relations…
Randomization has been applied to Hamiltonian simulation in a number of ways to improve the accuracy or efficiency of product formulas. Deterministic product formulas are often constructed in a symmetric way to provide accuracy of even…
In this paper, we propose a novel formulation to extend CNNs to two-dimensional (2D) manifolds using orthogonal basis functions, called Zernike polynomials. In many areas, geometric features play a key role in understanding scientific…
Modeling atmospheric chemistry is complex and computationally intense. Given the recent success of Deep neural networks in digital signal processing, we propose a Neural Network Emulator for fast chemical concentration modeling. We consider…
We develop fast and scalable methods for computing reduced-order nonlinear solutions (RONS). RONS was recently proposed as a framework for reduced-order modeling of time-dependent partial differential equations (PDEs), where the modes…
Non-equilibrium chemistry is a key process in the study of the InterStellar Medium (ISM), in particular the formation of molecular clouds and thus stars. However, computationally it is among the most difficult tasks to include in…
Reversibility, weak reversibility and deficiency, detailed and complex balancing are generally not "encoded" in the kinetic differential equations but they are realization properties that may imply local or even global asymptotic stability…
This paper is concerned with the utilization of deterministically modeled chemical reaction networks for the implementation of (feed-forward) neural networks. We develop a general mathematical framework and prove that the ordinary…
As a method of universal approximation deep neural networks (DNNs) are capable of finding approximate solutions to problems posed with little more constraints than a suitably-posed mathematical system and an objective function.…
We show that quantum search can be used to compute the hardness to round an elementary function, that is, to determine the minimum working precision required to compute the values of an elementary function correctly rounded to a target…
In most control applications, theoretical analysis of the systems is crucial in ensuring stability or convergence, so as to ensure safe and reliable operations and also to gain a better understanding of the systems for further developments.…
We investigate the dynamics of chemical reaction networks (CRNs) with the goal of deriving an upper bound on their reaction rates. This task is challenging due to the nonlinear nature and discrete structure inherent in CRNs. To address…
Chemputation reframes synthesis as the programmable execution of reaction code on a universally re-configurable hardware graph. Here we prove that a chemputer equipped with a finite, but extensible, set of reagents, catalysts and process…
Despite recent advances in improving the sample-efficiency of reinforcement learning (RL) algorithms, designing an RL algorithm that can be practically deployed in real-world environments remains a challenge. In this paper, we present…
Spectral methods are an important part of scientific computing's arsenal for solving partial differential equations (PDEs). However, their applicability and effectiveness depend crucially on the choice of basis functions used to expand the…