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Physics-informed neural networks (PINNs) is an emerging category of neural networks which can be trained to solve supervised learning tasks while taking into consideration given laws of physics described by general nonlinear partial…

Deep neural networks have been one of the dominant machine learning approaches in recent years. Several new network structures are proposed and have better performance than the traditional feedforward neural network structure.…

Physics-informed neural networks (PINNs) have attracted attention as an alternative approach to solve partial differential equations using a deep neural network (DNN). Their simplicity and capability allow them to solve inverse problems for…

Quantum Fisher Information (QFI) sets the ultimate precision limit for parameter estimation and is therefore a central quantity in quantum metrology. In time-dependent many-body systems, however, maximizing QFI is a highly non-trivial task…

We introduce NeuroPINNs, a neuroscience-inspired extension of Physics-Informed Neural Networks (PINNs) that incorporates biologically motivated spiking neuron models to achieve energy-efficient PDE solving. Unlike conventional PINNs, which…

Recent years have witnessed the success of deep neural networks in many research areas. The fundamental idea behind the design of most neural networks is to learn similarity patterns from data for prediction and inference, which lacks the…

This paper presents a framework for physics-informed learning in complex cyber-physical systems governed by differential equations with both unknown dynamics and algebraic invariants. First, we formalize the Hybrid Recurrent…

Physics-informed deep learning has drawn tremendous interest in recent years to solve computational physics problems, whose basic concept is to embed physical laws to constrain/inform neural networks, with the need of less data for training…

In this paper, we introduce a novel approach to neural learning: the Feature-Imitating-Network (FIN). A FIN is a neural network with weights that are initialized to reliably approximate one or more closed-form statistical features, such as…

We introduce a machine-learning framework named statistics-informed neural network (SINN) for learning stochastic dynamics from data. This new architecture was theoretically inspired by a universal approximation theorem for stochastic…

We revisit the original approach of using deep learning and neural networks to solve differential equations by incorporating the knowledge of the equation. This is done by adding a dedicated term to the loss function during the optimization…

The proliferation of high-dimensional datasets in fields such as genomics, healthcare, and finance has created an urgent need for machine learning models that are both highly accurate and inherently interpretable. While traditional deep…

Deep neural networks (DNNs) are powerful black-box function approximators which have been shown to yield improved performance compared to traditional neural network (NN) architectures. However, black-box algorithms do not incorporate known…

We propose a new method to probe the learning mechanism of Deep Neural Networks (DNN) by perturbing the system using Noise Injection Nodes (NINs). These nodes inject uncorrelated noise via additional optimizable weights to existing…

Physics-informed neural networks (PINNs) solve time-dependent partial differential equations (PDEs) by learning a mesh-free, differentiable solution that can be evaluated anywhere in space and time. However, standard space--time PINNs take…

Classical deep neural networks can learn rich multi-particle correlations in collider data, but their inductive biases are rarely anchored in physics structure. We propose quantum-informed neural networks (QINNs), a general framework that…

The human brain processes information showing learning and prediction abilities but the underlying neuronal mechanisms still remain unknown. Recently, many studies prove that neuronal networks are able of both generalizations and…

Big-data-based artificial intelligence (AI) supports profound evolution in almost all of science and technology. However, modeling and forecasting multi-physical systems remain a challenge due to unavoidable data scarcity and noise.…

Deep learning has become a pivotal technology in fields such as computer vision, scientific computing, and dynamical systems, significantly advancing these disciplines. However, neural Networks persistently face challenges related to…

The concepts and techniques of physics-informed neural networks (PINNs) is studied and limitations are identified to make it efficient to approximate dynamical equations. Potential working research domains are explored for increasing the…