Related papers: HANN: Homotopy auxiliary neural network for solvin…
The Harrow-Hassidim-Lloyd algorithm is intended for solving the system of linear equations on quantum devices. The exponential advantage of the algorithm comes with four caveats. We present a numerical study of the performance of the…
In this paper, we introduce Logic Tensor Network-Enhanced Generative Adversarial Network (LTN-GAN), a novel framework that enhances Generative Adversarial Networks (GANs) by incorporating Logic Tensor Networks (LTNs) to enforce…
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…
Neural architecture search (NAS) automatically finds the best task-specific neural network topology, outperforming many manual architecture designs. However, it can be prohibitively expensive as the search requires training thousands of…
Physics-informed holomorphic neural networks (PIHNNs) have recently emerged as efficient surrogate models for solving differential problems. By embedding the underlying problem structure into the network, PIHNNs require training only to…
Since the advent of generative adversarial networks (GANs), various loss functions have been developed and combined to constitute the overall training objective function, in order to improve model performance or for specific learning tasks.…
Homological algebra techniques can be found in almost all modern areas of mathematics. Many interesting problems in mathematics can be formulated, computed, or can find their equivalence in terms of Ext-groups. For instance, important…
Analog crossbar arrays comprising programmable nonvolatile resistors are under intense investigation for acceleration of deep neural network training. However, the ubiquitous asymmetric conductance modulation of practical resistive devices…
We present the first hard-constraint neural network for predicting activity coefficients (HANNA), a thermodynamic mixture property that is the basis for many applications in science and engineering. Unlike traditional neural networks, which…
There has been a growing interest in the use of Deep Neural Networks (DNNs) to solve Partial Differential Equations (PDEs). Despite the promise that such approaches hold, there are various aspects where they could be improved. Two such…
This paper presents a novel framework for high-dimensional nonlinear quantum computation that exploits tensor products of amplified vector and matrix encodings to efficiently evaluate multivariate polynomials. The approach enables the…
The homotopy continuation method has been widely used in solving parametric systems of nonlinear equations. But it can be very expensive and inefficient due to singularities during the tracking even though both start and end points are…
Permanent gravity waves propagating in deep water, spanning amplitudes from infinitesimal to their theoretical limiting values, remain a classical yet challenging problem due to its inherent nonlinear complexities. Traditional analytical…
Homotopy perturbation method is used for solving the multi-point boundary value problems. The approximate solution is found in the form of a rapidly convergent series. Several numerical examples have been considered to illustrate the…
Conventional application of convolutional neural networks (CNNs) for image classification and recognition is based on the assumption that all target classes are equal(i.e., no hierarchy) and exclusive of one another (i.e., no overlap).…
Physics-Informed Neural Networks (PINNs) have recently emerged as a promising alternative for solving partial differential equations, offering a mesh-free framework that incorporates physical laws directly into the learning process. In this…
Pseudo-Hamiltonian neural networks (PHNN) were recently introduced for learning dynamical systems that can be modelled by ordinary differential equations. In this paper, we extend the method to partial differential equations. The resulting…
Hybrid optical neural networks (HONNs) offload some electronic computation to optical preprocessors to achieve low-power and fast training and inference phases in machine learning tasks. Our contribution to the development of HONNs is a…
Based on neural network and adaptive subspace approximation method, we propose a new machine learning method for solving partial differential equations. The neural network is adopted to build the basis of the finite dimensional subspace.…
Interpretability has become a necessary feature for machine learning models deployed in critical scenarios, e.g. legal system, healthcare. In these situations, algorithmic decisions may have (potentially negative) long-lasting effects on…