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Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path…
This paper addresses the problem of learning binary hash codes for large scale image search by proposing a novel hashing method based on deep neural network. The advantage of our deep model over previous deep model used in hashing is that…
Recent works have shown that deep neural networks can be employed to solve partial differential equations, giving rise to the framework of physics informed neural networks. We introduce a generalization for these methods that manifests as a…
Physics-informed neural networks (PINNs) have recently emerged as a prominent paradigm for solving partial differential equations (PDEs), yet their training strategies remain underexplored. While hard prioritization methods inspired by…
In this work we set out to find a method to classify protein structures using a Deep Learning methodology. Our Artificial Intelligence has been trained to recognize complex biomolecule structures extrapolated from the Protein Data Bank…
Physics-informed neural networks solve partial differential equations by training neural networks. Since this method approximates infinite-dimensional PDE solutions with finite collocation points, minimizing discretization errors by…
This paper focuses on the PINNs algorithm by proposing the ALM-PINNs computational framework to solve various nonlinear partial differential equations and corresponding parameters identification problems. The numerical solutions obtained by…
We propose the first learning scheme for functional differential equations (FDEs). FDEs play a fundamental role in physics, mathematics, and optimal control. However, the numerical analysis of FDEs has faced challenges due to its…
This paper provides an entry point to the problem of interpreting a deep neural network model and explaining its predictions. It is based on a tutorial given at ICASSP 2017. It introduces some recently proposed techniques of interpretation,…
This work proposes deep network models and learning algorithms for unsupervised and supervised binary hashing. Our novel network design constrains one hidden layer to directly output the binary codes. This addresses a challenging issue in…
We introduce NewPINNs, a physics-informing learning framework that couples neural networks with conventional numerical solvers for solving differential equations. Rather than enforcing governing equations and boundary conditions through…
One of the most common and universal problems in science is to investigate a function. The prediction can be made by an Artificial Neural Network (ANN) or a mathematical model. Both approaches have their advantages and disadvantages.…
Deep learning, a branch of artificial intelligence, is a data-driven method that uses multiple layers of interconnected units or neurons to learn intricate patterns and representations directly from raw input data. Empowered by this…
Recent work has shown logical background knowledge can be used in learning systems to compensate for a lack of labeled training data. Many methods work by creating a loss function that encodes this knowledge. However, often the logic is…
In this work, we introduce a machine/deep learning methodology to solve parametric integrals. Besides classical machine learning approaches, we consider a differential learning framework that incorporates derivative information during…
Despite the power of deep neural networks for a wide range of tasks, an overconfident prediction issue has limited their practical use in many safety-critical applications. Many recent works have been proposed to mitigate this issue, but…
Automated mathematical reasoning is a challenging problem that requires an agent to learn algebraic patterns that contain long-range dependencies. Two particular tasks that test this type of reasoning are (1) mathematical equation…
We propose a neural network-based algorithm for solving forward and inverse problems for partial differential equations in unsupervised fashion. The solution is approximated by a deep neural network which is the minimizer of a cost…
The neural network-based approach to solving partial differential equations has attracted considerable attention due to its simplicity and flexibility in representing the solution of the partial differential equation. In training a neural…
This paper presents a novel algorithm to obtain the closed-form anti-derivative of a function using Deep Neural Network architecture. In the past, mathematicians have developed several numerical techniques to approximate the values of…